Transcript Year 3 Objectives - Nutgrove Primary

Focus on Mathematics
Clive Davies
Helen Rowland
© Clive Davies & Helen Rowland 2014
All rights reserved
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First Published in the UK in 2014 by Focus Education (UK) Ltd
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© Focus Education (UK) Ltd 2014
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ABOUT THE AUTHORS
CLIVE DAVIES OBE
Clive Davies has a vast experience in primary education. He has inspected more than 200
schools. Whilst a headteacher Clive’s school gained a National Curriculum award and his
school was featured in the Times Educational Supplement as one of 3 recognised for its quality
practice. The development of pupil autonomy was at the heart of the culture of his successful
headships. Clive is well known nationally and internationally having worked in schools
throughout England and Wales as well as Dubai, Kuwait, Greece, Turkey, Holland, Cyprus,
Germany and Spain. He was awarded an OBE for his services to education in 2007.
HELEN ROWLAND
Helen is the Academy Improvement Officer for the Focus-Trust and an Associate Consultant for
Focus Education. She joined the Focus-Trust from the headship of a school judged outstanding
in all aspects. Helen worked in Oldham LA since 1990 and has experience of the full diversity of
schools that Oldham offers: English as an additional language, challenging social contexts,
village and faith schools.
A former headteacher with over 12 years’ experience, Helen now works in partnership with
academy leaders, governors and academy teams on developing & improving teaching and
leadership for positive impact on children. Helen has led schools in moving from ‘good’ to
‘outstanding’ teaching and learning and implementing the Learning Challenge Curriculum
and the new National Curriculum.
© Focus Education (UK) Ltd 2014
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Contents
5
Introduction
8
Year 1
61
Year 2
131
Year 3
195
Year 4
273
Year 5
353
Year 6
© Focus Education (UK) Ltd 2014
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Introduction
•
•
•
•
•
•
Focus on Mathematics is a resource aimed to support schools, academies, staff and pupils to meet the year
group expectations set out in the National Curriculum 2014. It is intended for ‘thinking’ teachers and support staff
who want to organise the learning for their pupils in a way that will maximise the progress they make. It breaks
down the teaching sequences for teachers but gives schools and academies complete autonomy to provide
their own methods.
In simple terms, Focus on Mathematics takes the year expectations and breaks them down into teaching
objectives and provides a framework so that each objective has its own teaching sequence. Most of the
teaching objectives are further supported by a series of pre-learning tasks which help teachers decide where to
start with different groups of pupils based on their prior knowledge and understanding. In this way pupils should be
challenged more rapidly and stretched to reach their full potential. No more than 4 starting positions are
suggested in order to make it manageable for staff.
In addition Focus on Mathematics provides a target setting continuum which is aimed to help pupils and staff
assess progress through each objective. These are referred to as ‘Stepping up to the Challenge’ because they are
set in such a way as to suggest pupils are moving onwards and upwards as they progress through each objective.
Focus on Mathematics also provides a suggested Assessment procedure which is not based on the old levelling
system. It takes, instead, a 3 or a 9-point approach which can then be used to check on key stage, key phase or
within year progress. It spells out what has to be done for pupils to meet the year expectations and also explains
what it means if they have exceeded these expectations. In short, it provides a valid, but innovative, way of
tracking progress and provides a framework for reporting progress to parents.
There is strong emphasis placed on the Non-Negotiables¹ and a suggested planning tool is provided to help
teachers plan for pupils to meet these expectations. Finally, there is also a Parents’ Guide which aims to help
parents understand what learning their children will be experiencing during that year.
¹The Non-Negotiables is a framework written by Simon Camby for Focus Education aimed at helping teachers to
ensure pupils are able to meet basic skills in reading, writing and mathematics.
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
What the section for each group offers:
Year Group
Expectations
•This section takes the Year Group expectations as outlined in the
National Curriculum and where appropriate breaks down the
teaching sequence for each. The Objectives related to number
then suggest starting points (no more than 4) so that pupils are not
covering learning that they are already confident with and are
therefore challenged more rapidly. There are 2 groups of
expectations, one for number and the other for measurement,
geometry and where applicable statistics.
Pre- Learning
Tasks
•These are a series of tasks for many of the ‘number’ year group objectives
which aim to help teachers assess the best starting position for each pupil.
In this way time is not wasted covering learning already known and
understood. The tasks are linked to the teaching sequences by * numbers
so that it makes it easier for teachers to decide starting points. What will be
interesting is that the groups in classrooms should look different for many
objectives because the groupings will be determined by the outcome of
the task. It was felt that these would be helpful for the number content but
somewhat extravagant for other aspects of mathematics.
Step-up to the
Challenge
•This section provides both teachers and pupils with a resource that
helps focus on the progress being made by pupils. It can be used as a
self-assessment tool or as check for the teacher. It is designed to break
down the progression towards the number, measurement, geometry
and statistics objectives. Not all objectives have this resource but the
vast majority do. Where they do not exist it was felt that this particular
tool was not necessary. This section of the resource can be obtained as
individual books for Key Stage 1; Lower Key Stage 2 or Upper Key Stage
2.
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
What the section for each group offers (2):
NonNegotiables
• This section takes the previously published non-negotiables
for mathematics and provides a clear framework for
planning their use across the year. The expectation is that
there will be a focus on the non-negotiables on a daily
basis and the framework suggests where the focus ought
to be each half term. In addition, there is a parents’ guide
provided to help support home school partnership.
Assessment
•This is potentially the exciting part of this resource. What has
been created is a comprehensive overview of how teachers can
judge pupils according to how they have met the year group
expectations. Schools are then provided with either a 3 or 9-point
system aimed at helping assess and track progress. The main
focus on assessment will be measuring pupils’ journey towards,
and beyond, the Year group expectations. It also has the
potential to be used as a tracker going through school.
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year Group Objectives
Year 1
Focus on Mathematics
Year 1 Group Objectives
Number
Year 1 Objectives: Number 1
NUMBER AND PLACE VALUE
Objective 1:Counting: 0 to 100, forwards and
backwards, from any given number
Count on from 0 to 20
*1
Counting: 0 to 100, forwards and backwards,
from any given number (continued)
Count back from 100 to 0
Count on from 0 to 50
Count back from any number smaller than 10 to
0
Count on from 0 to 100
Count on from any number to 20
NUMBER AND PLACE VALUE
*2
Count back from any number smaller than 20 to
0
Count on from any number to 50
Count back from any number smaller than 50 to
0
Count on from any number to 100
Count back from any number smaller than 100
to 0
Count back from 10 to 0
Count back from 20 to 0
Count back from 50 to 0
*3
*4
Count on beyond 100
Count back starting with a number greater than
100
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Number 2
NUMBER AND PLACE VALUE
Objective 2: Count, read and write to 100; in
different multiples including 1s, 2s, 5s and
10s
Count in 10s to 50
*1
Count in 10s to 100
NUMBER AND PLACE VALUE
Objective 3: Identify one more and one less
than a given number
Know one more than a given number to 20
Count in 2s to 20
*2
Count in 2s to 50
*1
Know one more than a given number to 50
Know one more than a given number to 100
Count in 2s to 100
Count in 5s to 50
*3
Count in 5s to 100
Know one less than a given number to 20
*2
Know one less than a given number to 50
*3
Know one less than a given number to 100
Write and read all numbers accurately to 10
*4
Write and read all numbers accurately to 20
Write a number that is one more than any given
number to 20
*4
Write a number that is one less than any given
number to 20
Write and read all numbers accurately to 50
Write and read all numbers accurately to 100
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Number 3
NUMBER AND PLACE VALUE
Objective 4: Recognise odd and even
numbers
Know all even numbers to 10
*1
NUMBER AND PLACE VALUE
Objective 6: Distinguish between and use:
ordinal and cardinal numbers
Know all odd numbers to 10
Know all even numbers to 20, then to 50, then to
100
*2
Know all odd numbers to 20, then to 50, then to
100
*3
Know that an even number can be shared
between 2
Find missing numbers in a sequence up to 10
*1
Find missing numbers in a sequence up to 20
*2
Order objects using the terms 1st, 2nd, 3rd, etc.
*3
Know the 5ness of 5
Know that an odd number cannot be shared
equally between 2
Know that a set of 5 objects contains more
objects than, say 3, etc. (up to 10)
Objective 5: Read and write: 1 to 20 in
numerals and words
Read all numbers as numerals and words to 10
*1
Write all numbers as numerals and words to 10
*2
Read all numbers as numerals and words to 20
*3
Write all numbers as numerals and words to 20
*4
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Number 4
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 7: Add and subtract 1-digit and 2digit numbers to 20, including 0
Objective 9: Know and use all number
bonds to 20 and related subtraction facts
Add two, 1-digit numbers to 10
Know all number bonds to 10, using addition
*1
Know all number bonds to 10, using subtraction
*2
Know all number bonds to 20, using addition
*3
Know all number bonds to 20, using subtraction
*4
*1
Add two, 1-digit numbers to 20 (18)
Add a 1-digit number to a 2-digit number to 20
*2
Check understanding of 0 (zero)
Subtract two, 1-digit numbers
*3
Subtract a 1-digit number from a 2-digit number
(up to 20)
*4
Objective 8: Add three 1-digit numbers
Add three, 1-digit numbers (up to 10)
*1
Add three, 1-digit numbers to total no more
than 20
*2
Objective 10: Solve simple one-step
problems that involve addition and
subtraction using concrete objects, pictorial
representations and missing number
problems
Solve simple problems involving addition to 10
*1
Solve simple problems involving subtraction to
10
*2
Solve simple problems involving addition to 20
*3
Solve simple problems involving subtraction to
20
*4
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Number 5
MULTIPLICATION AND DIVISION
FRACTIONS
Objective 11: Recognise and write
multiplication (x) and division symbols (÷)
Know the symbol (x) stands for multiplication
Objective 14: Recognise, find and name a
half as one of two equal parts of an object,
shape or quantity
Know the symbol (÷) stands for division
Can estimate what half of a given object might
be
Can estimate what half of a given regular
shape might be
Objective 12: With support solve onestep problems involving multiplication
and division, by calculating the
answer using concrete objects,
pictorial representations and arrays
With support use practical examples of
multiplication and division
Using practical materials can show half of a
given number of objects
*1
*2
*2
Objective 15: Recognise, find and name a
quarter as one of four equal parts of an
object, shape or quantity
Can estimate what a quarter of a given object
might be
Objective 13: With support solve simple
multiplication and division problems
With support solve practical examples of
multiplication and division up to 20
*1
*1
Can estimate what a quarter of a given regular
shape might be
Using practical materials can show a quarter of
a given number of objects
© Focus Education (UK) Ltd 2014
*2
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Focus on Mathematics
Year 1 Pre-Learning Tasks
Number
Focus on Mathematics: Year 1
Name
Date
Number
Objective 1 Counting: 0 to 100, forwards and backwards, from any given
number
Can you finish off these sequences?
3, 4, 5,
*1
15, 16, 17,
8, 7, 6,
*4
16, 15, 14,
33, 34, 35,
*2
37, 36, 35,
72, 73, 74,
*3
82, 81, 80,
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Date
Number
Objective 2 Count, read and write to 100; in different multiples including 1s, 2s,
5s & 10s
Can you finish off these sequences?
10, 20, 30,
*1
40, 50, 60,
2, 4, 6, 8,
24, 26, 28,
5, 10, 15,
*3
75, 80, 85,
*2
Can you read the number
twelve and write in the box?
*4
Can you read the number
fifty- nine and write in the box?
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Date
Objective 3
Number
Identify 1 more than or one less than a given number
What is 1 more than…..?
7
What is 1 less than …..?
*1
8
13
17
34
46
98
78
Write down a number that is one more than thirteen
*2
*3
*4
Write down a number that is one less than twelve
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Date
Objective 4
Number
Recognise odd and even numbers
Can you put these numbers in the correct place?
1
2
3
4
5
6
7
8
9
10
36
25
13
41
14
29
32
46
33
15
*1
Even
Odd
*3
Even
Starting Position:
Odd
9
12
13
14
15
16
17
18
19
20
Even
Odd
34
67
58
17
91
63
28
69
98
77
Even
Odd
*2
19
Focus on Mathematics: Year 1
Name
Objective 5
Date
Number
Read and write: 1 to 20 in numerals and words
Can you read these numbers and put their
numerical value in the box?
seven
*1
six
thirteen
fourteen
Can you read these numerals and write the
word (their value) in the box?
8
*2
4
*3
16
*4
12
Write down a number that is one more than fifteen.
Write down a number that is one less than eighteen.
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 6
Date
Number
Distinguish between ordinal and cardinal numbers
Can you find the missing numbers?
1, 3, 5, ….
*1
0, 3, 6, ….
9, 11, 13, 15…
7, 10, 13, 16,…
Can you work these out?
John won 5 marbles;
Claire won 6 marbles and
Adin won 4 marbles. Who
came first?
*3
In a race Abdul was
fastest; then India and
finally Joe. Who was
second?
*2
Hussain built a tower with
10 blocks; Jayne’s tower
was 7 bocks and Josh’s
tower was 3 blocks. Who
came first?
In a race Sophia filled 3
bottles with water; Amin
filled 6 bottles and
Charlotte filled 5 bottles.
Who was first?
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 7
Date
Number
Add and subtract 1-digit and 2-digit numbers to 20 including 0
Can you add these numbers together?
4 +5
*1
3 +6
7+6
7-5
*3
8-3
*2
12 + 6
Can you add these together:
Can you subtract these numbers?
16 - 4
*4
12 - 6
13 + 0 =
Can you subtract 0 from 12
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 8
Date
Number
Add three one-digit numbers
Can you add these numbers together?
1 +2+1
*1
7+2+3
2+2+1
8+2+9
1+1+2
6+6+5
0+1+2
7+5+6
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 9
Date
Number
Know and use all number bonds to 20 and related subtraction
facts
Can you work these out within 2 seconds?
7+3
*1
3+4
9-4
7-5
12 + 5
*3
11 + 8
*2
17 - 6
*4
18 - 5
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 10
Date
Number
Solve simple one-step problems that involve addition and subtraction
using concrete objects, pictorial representations and missing number
problems
Can you work these out within 2 seconds?
If I have 3 sweets and
someone gives me another 5,
how many have I altogether?
*1
If I score 2 goals in one match
and I score 3 in another, how
many goals have I scored in the
2 matches?
If I have 9 cards and I give 4
away, how many cards have
I left?
How many coins have I left if
I have 7 and I give 3 away?
If I have 15 stickers and I buy
another 4, how many will I
have altogether?
*3
If I listen to 12 songs and
then another 3, how many
will I have listened to
altogether?
*2
If I have 18 books and give 3
away, how many will I have
left?
*4
What is 19 take away 5?
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Objective 12
and 13
Date
Number
With support and real objects solve multiplication and division
calculations using concrete objects, pictorial representations and arrays
Can you work out the answers (using apparatus)?
What are 3 lots of 2?
*1
Can you share 8 objects
between 2 people?
What are 2 lots of 5?
Can you share 9 objects
between 3 people?
What are 4 lots of 2?
Can you share 12 objects
*2
between 3 people?
What are 3 lots of 3?
Can you divide 15 objects
between 5 people?
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Date
Number
Objective 14 Recognise, find and name a half as one of two equal parts of an
object, shape or quantity
Can you work out the answers (using apparatus)?
*1
Can you
shade
in half of
these 2
shapes?
*2
What is half
of these 2
numbers?
How much of the
whole shape is red?
How much of 12 is 6?
14
16
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 1
Name
Date
Number
Objective 15 Recognise, find and name a quarter as one of four equal parts of
an object, shape or quantity
Can you work out the answers (using apparatus)?
Can you
shade
in a quarter
of these 2
shapes?
What is a
quarter
of these 2
numbers?
*1
12
*2
How much of the
circle is missing?
How much of 16 is 4?
8
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 1 Group Objectives
Measurement and Geometry
Year 1 Objectives : Measurement 1
MEASUREMENT
Objective 1m - Compare, describe and solve
MEASUREMENT
practical problems for:
Length and height (long/ short, longer/ shorter;
tall/short; double/half)
Mass/ weight (heavy/ light, heavier than, lighter
than)
capacity and volume (full/ empty, more than, less
than, half, half full, quarter)
time (quicker, slower, earlier and later)
Objective 2m - Measure and begin to record the
Can compare 2 objects and say which is the
longer and shorter
Can measure the length of an object in m
Can compare up to 5 objects and say which is
the longest and shortest
Can measure the height of an object in cm
Can compare 2 objects and say which is the
heavier and lighter
Can compare up to 5 objects and say which is
the heaviest and lightest
Can compare 2 containers and say which is full,
empty, half full
Can describe events which happened earlier
and later
following:
Length and height
Mass/ weight
Capacity and volume
Time (hours, minutes, seconds)
Can measure the length of an object in cm
Can measure the height of an object in m
Can measure the weight of an object in
Kg/g
Can measure how much liquid is in a
container in l/ml
Can measure how long it takes to do an
activity in hours/minutes/seconds
Can compare the movement of 2 objects and
describe which is slower, quicker
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Measurement 2
MEASUREMENT
MEASUREMENT
Objective 3m - Recognise and know the
value of different denominations of coins
and notes
Objective 5m - Recognise and use
language of dates: days of the week,
weeks, months and years
Recognise 1p, 2p, 5p coins
Know days of the week in order
Know months of the year in order
Recognise 10p, 20p and 50p coins
Know that seven days make up one week
Recognise a £1 coin
Know that there are twelve months in a year
Recognise £5 and £10 notes
Objective 6m - Tell time: to hour and half
past
Compare the value of the different
denominations of coins and notes
Objective 4m - Sequence events in
Tell the time to o’clock from one o’clock
through to twelve o’clock
chronological order using language (e.g. before,
after, next, first, today, yesterday, tomorrow,
morning, afternoon and evening)
Tell the time to half past the hour from half past
one through to half past twelve
Can order: morning, afternoon and evening
Draw hands on the clock to show time to
‘o’clock’
Use terms: before, next and after accurately
Draw hands on the clock to show time to ‘half
past’ the hour
Use terms: today, tomorrow, yesterday
accurately
Know that key events such as lunchtime
happen at 12 o’clock/home time half past 3
© Focus Education (UK) Ltd 2014
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Year 1 Objectives : Geometry
Geometry – Properties of shape
Geometry – Position and direction
Objective 1g - Recognise and name 2-D
shapes: to include: rectangle (including
squares), circle and triangle
Objective 3g - Describe position, directions
and movements including whole, half,
quarter and three-quarter turns
Know vocabulary: left, right, top, middle,
bottom, on top of, in front of, above, between,
around, near, close and far, up, down, forwards,
backwards, inside and outside
Know and name squares
Know and name rectangles
Know and name circles
Can demonstrate a full turn (by moving own
body)
Know and name triangles
Can demonstrate half a turn
Objective 2g - Recognise and name 3-D
shapes: to include cuboids (including
cubes), pyramid and sphere
Can demonstrate quarter of a turn
Know and name cubes
Can hold up right or left hand as required
Know and name pyramids
Can point to the left or right as required
Know and name spheres
Can describe position, directions and
movements using above vocabulary
Can demonstrate three-quarters of a turn
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Step up to the Challenge
Year 1
Number
Year 1: Can you challenge yourself to meet the Objective?
Objective 1: Can you count forwards and backwards 0 to 100 from
any given number?
Me
My
Teacher
Can you count back from any number smaller than 100 to 0?
Can you count back from any number smaller than 50 to 0?
Can you count back from any number smaller than 20 to 0?
Can you count back from 100 to 0?
Can you count back from 50 to 0?
Can you count back from 20 to 0?
Can you count on from any number to 100?
Can you count on from any number to 50?
Can you count on from any number to 20?
Can you count on from 0 to 100?
Can you count on from 0 to 50?
Can you count on from 0 to 20?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 2: Can you count, read and write to 100, in different
multiples of 1, 2s, 5s and 10?
Me
My
Teacher
Can you read and write all numbers to 100?
Can you read and write all ‘tens’ numbers from 0 to 100?
Can you read and write all numbers to 20?
Can you read and write all numbers to 10?
Can you count in 5s to 100?
Can you count in 2s to 100?
Can you count in 2s to 50?
Can you count in 2s to 20?
Can you count in 10s to 100?
Can you count in 10s to 50?
Can you count from 1 to 100?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 3: Can you tell what is ‘one more than’ and ‘one less than’
a number up to 100?
Me
My
Teacher
Can you write a number that is ‘one less than’ any number to 100?
Can you write a number that is ‘one more than’ any number to
100?
Can you say a number that is ‘one less than’ any number to 100?
Can you say a number that is ‘one less than’ any number to
50?
Can you say a number that is ‘one less than’ any number to
20?
Can you say a number that is ‘one more than’ any number
up to 100?
Can you say a number that is ‘one more than’ any number
up to 50?
Can you say a number that is ‘one more than’ any
number up to 20?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 4: Can you recognise odd and even numbers to 100?
Me
My
Teacher
Can you explain why an odd number cannot be shared
equally by 2?
Can you explain why all even numbers can be shared by 2?
Can you say all the odd numbers to 100?
Can you say all the even numbers to 100?
Can you say all the odd numbers to 50?
Can you say all the even numbers to 20?
Can you say all the odd numbers between 0 and 10?
Can you say all the even numbers between 0 and 10?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 7: Can you add and subtract 1-digit and 2-digit numbers
to 20, including 0?
Me
My
Teacher
Me
My
Teacher
Can you subtract a 1-digit number from a 2-digit number?
Can you subtract two, 1-digit numbers?
Can you add a 1-digit number to a 2-digit number to 20?
Can you add two, 1-digit numbers to 20?
Can you add two, 1-digit numbers to 10?
Objective 8: Can you add three, 1-digit numbers?
Can you add three, 1-digit numbers to 20?
Can you add three, 1-digit numbers to 10?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 9: Can you work out all number bonds to 20?
Me
My
Teacher
Me
My
Teacher
Can you work out all subtraction number bonds to 20?
Can you work out all addition number bonds to 20?
Can you work out all subtraction number bonds to 10?
Can you work out all addition number bonds to 10?
Objective 10: Can you solve simple word problems involving
addition and subtraction to 20?
Can you solve simple word problems involving subtraction to 20?
Can you solve simple word problems involving addition to 20?
Can you solve simple word problems involving subtraction to
10?
Can you solve simple word problems involving addition to
10?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 11 to 13: Can you do simple multiplications (x) and
divisions (÷)?
Me
My
Teacher
Can you see that adding in 2s, 5s and 10s is just like
multiplication?
Without using real objects, can you use division involving
numbers to 20?
Without using real objects, can you use multiplication
involving numbers to 20?
Using real objects, can you use division involving numbers
to 20?
Using real objects, can you use multiplication involving
numbers to 20?
Do you know that the symbol (÷) stands for division?
Do you know that the symbol (x) stands for
multiplication?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Step up to the Challenge
Year 1
Measurement and Geometry
Year 1: Can you challenge yourself to meet the Objective?
Objective 1m and 2m: Can you describe measures and start to use
standard measures?
Me
My
Teacher
Can you order the time you would do things during a school day?
Do you know that time is measured in hours and minutes?
Do you know the term litre and can you show some objects that hold
more or less than a litre?
Do you know the term kilogram and can you show some objects
that weigh more or less than a kilogram?
Do you know the term metre and can you show objects that are
longer or shorter than a metre?
Can you order the time it takes to do many things starting with the
quickest?
Can you work out which object is the heaviest and lightest of a
number of objects?
Can you work out which object is the longest and shortest of a
number of objects?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 3m: Can you tell me about money?
Me
My
Teacher
Can you work out how many 10p coins is the same as £1?
Can you work out how many 50p coins is the same as £1?
Can you work out how many £1 coins is the same as a £10
note?
Can you point to a £5 note and a £10 note?
Can you point to a 10p and a 20p coin?
Can you point to a 50p coin?
Can you point to a £1 coin?
Can you point to a 1p, 2p and 5p coin?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 4m to 6m: Can you begin to tell the time?
Me
My
Teacher
Can you name the months of the year in order?
Can you name the days of the week in order?
Can you use the terms before, after and next accurately?
Can you use the terms yesterday, today and tomorrow
accurately?
Can you think of things that normally happen in the
morning, afternoon and night time?
Can you tell the time to half past the hour from half
past one through to half past twelve?
Can you tell the time to o’clock from one o’clock
through to twelve o’clock?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 1g and 2g: Can you recognise 2D and 3D shapes?
Me
My
Teacher
Do you know this shape and can you name it?
Do you know this shape and can you name it?
Do you know this shape and can you name it?
Do you know this shape and can you name it?
Do you know this shape and can you name it?
Do you know this shape and can you name it?
Do you know this shape and can you name it?
© Focus Education (UK) Ltd 2014
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Year 1: Can you challenge yourself to meet the Objective?
Objective 3g: Can you describe position by using your body?
Me
My
Teacher
Can you turn to the left?
Can you turn to the right?
Can you hold out your left hand?
Can you hold out your right hand?
Can you turn your body through three-quarters of a turn?
Can you turn your body through a quarter of a turn?
Can you turn your body through half a turn?
Can you turn your body through one full turn?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Helping pupils meet the (new)
National Curriculum Year Objectives
Non-Negotiables
Year 1 Possible Planning Outline
Year 1 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
© Focus Education (UK) Ltd 2014
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Year 1 Mathematics Non-Negotiables
• Here are the Year 1 mathematics non-negotiables:
•
•
•
•
•
•
•
Count to and across 100, forwards and backwards from any number.
Read and write numbers to 20 in digits and words.
Read and write numbers to 100 in digits.
Say ‘1 more’ and ‘1 less’ to 100.
Count in multiples of 1, 2, 5 and 10.
Know bonds to 10 by heart.
Use bonds and subtraction facts to 20.
• Add and subtract:
o 1 digit and 2 digit numbers to 20, including zero.
o Add any three 1-digit numbers with a total up to 20.
o Solve simple addition and division with apparatus and arrays.
•
•
•
•
Recognise half and quarter of object, shape or quantity.
Sequence events in order.
Use language of day, week, month and year.
Tell time to hour and half past.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
The following 3 pages suggest a planning outline for delivering the non-negotiables
in classrooms. There should be some element of teaching of these each day.
Autumn Term
Ist Half Term
•
•
•
•
•
•
•
2nd Half Term
Count to and across to at least 20 –
forwards and backwards beginning with 1
Read and write numbers to 20 in numerals
and write numbers in words to 10
Count in 2s to 20
Identify one more and one less than a
given number to 20
Order objects using the terms 1st , 2nd, 3rd,
4th, 5th
Find the missing number in a sequence up
to 10
Add/subtract 2, 1-digit numbers to 10
•
•
•
•
•
•
•
•
•
Count to and across to at least 50 –
forwards and backwards beginning with 0
and 1, or from any other given number
Read and write numbers to 20 and beyond
in numerals and write numbers in words to
10
Count in 2s to 20 and beyond
Count in 5s to beyond 20
Count in 10s to 50
Identify one more and less than a given
number to 20 and beyond
Order objects using the terms 1st , 2nd, 3rd,
4th, 5th and beyond
Find the missing number in a sequence up
to 10 and beyond
Add/subtract 2 1-digit numbers to 10,
including 0
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Spring Term
Ist Half Term
•
•
•
•
•
•
•
•
2nd Half Term
Count to and across to at least 50 –
forwards and backwards beginning with 0
and 1 or from any other given number
Read and write numbers to 50 in numerals
and begin to write numbers in words to 20
Count in 2s and 5s to 50
Count in 10s to 50 and beyond
Identify one more and one less than a
given number to 50
Order objects using the terms 1st, 2nd, 3rd to
10th
Find the missing number in a sequence up
to 20
Add/subtract 2-digit and 1-digit numbers
to 10 and beyond
•
•
•
•
•
•
•
•
Count to and across to at least 50 –
forwards and backwards beginning with 0
and 1 or from any other given number
Read and write numbers to 50 and
beyond in numerals and continue to write
numbers in words to 20
Count in 2s and 5s to 50 and beyond
Count in 10s to 100
Identify one more and one less than a
given number to 50 and beyond
Order objects using the terms 1st , 2nd, 3rd
to 10th
Find the missing number in a sequence up
to 20 and beyond
Add/subtract 2-digit and 1-digit numbers
to 10 and beyond
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Summer Term
Ist Half Term
•
•
•
•
•
•
•
•
2nd Half Term
Count to and across to at least 100 and
beyond forwards and backwards from
any given number
Read and write numbers to 100 in
numerals and write numbers in words to
20
Count in 2s, 5s and 10s to 100
Identify one more and one less than a
given number to 100
Find the missing number in a sequence up
to 50
Add/subtract 2-digit and 1-digit numbers
to 20
Double numbers up to 5
Halve even numbers up to 10
•
•
•
•
•
•
•
Count to and across to at least 100 and
beyond forwards and backwards
beginning with 0 and 1 or from any given
number
Count in 2s, 5s and 10s to 100 and beyond
Identify and write down the number
which is one more and less than a given
number to 100
Find the missing number in a sequence up
to 100
Add/subtract 2-digit and 1-digit numbers
to 20
Double numbers up to 10
Halve even numbers up to 20
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 1 Assessment
Assessment: Meeting Year 1 Expectations
Year 1 Expectations: Number
•
•
•
•
•
The main focus on assessment will be
measuring a pupil’s journey towards and
beyond the Year 1 expectations. The Year 1
expectations for number are set out on the
right hand side of this page.
To meet the Year 1 expectations a pupil
must be able to meet all of the statements
outlined in the table, plus the ones for
measurement and geometry, shown later.
If they have not met all the statements then
they will be deemed to be emerging. If a
pupil is meeting the expectations then an
assessment needs to made as to whether a
pupil is exceeding the expectations.
The next page sets out how to assess
whether a pupil is exceeding this
expectation or whether a pupil is at the
emerging stage.
The next page also provides you with a 9point scale for deeper analysis, if required.
• Count reliably to 100
• Count on and back in 1s, 2s, 5s, and 10s from any
given number to 100
• Write all numbers in words to 20
• Say the number that is one more or one less than
a number to 100
• Recall all pairs of addition and subtraction
number bonds to 20
• Add and subtract 1-digit and 2-digit numbers to
20, including zero
• Know the signs (+); (-) and (=)
• Solve a missing number problem, such as 5 = 8 - x
•
Solve a one-step problem involving an addition and
subtraction, using concrete objects, pictorial
representations and arrays
•
Solve a one-step problem involving a multiplication and
division, using concrete objects, pictorial representations
and arrays
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 1 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 1 Expectations
A pupil will be deemed to be
meeting the expectations only if
they can satisfy their teacher
that they meet all the
expectations for their age
A pupil will be deemed to be
emerging towards the
expectations if they do not meet
all of the statements outlined for
that year group
•Meeting the expectations (Stage
C) – Point 4
•It is accepted that a pupil might
make the occasional error if they
are at this stage. However,
despite that, the teacher needs
to be satisfied that they
understand the concept fully.
•Meeting the expectations (Stage
B) - Point 5
•At this stage a pupil will rarely
make mistakes and is very
confident at meeting the
statements.
•Meeting the expectation (Stage
A)- Point 6
•At this stage, not only is the pupil
confident at meeting the
statements but works at a rapid
rate. However, they are not yet
meeting all the statements for
exceeding.
•If they meet more than 75% of
the statements but not all then
they will be described as:
•Emerging towards the
expectations (Stage C) – Point 3
•If they meet between 50% and
75% of the statements then they
will be described as:
•Emerging towards the
expectations (Stage B) – Point 2
•However if they are not meeting
50% of the expectations they will
be described as:
•Emerging towards the
expectations (Stage A) – Point 1
•There is, therefore, no
requirement to write a set of
emerging statements
© Focus Education (UK) Ltd 2014
A pupil will be deemed to be
exceeding the expectations when, in
addition to the statements set out for
meeting the expectation (Stage
A)they meet one or more of three sets
of further expectations
•Pupils will be deemed to be exceeding
expectations if, in addition to what is
outlined as Point 6, they show evidence
of:
•Accessing some of the following year
group’s objectives
•Being able to use the year group’s
expectation within context
•Being able to consistently apply the year
group objectives in a range of situations.
•A set of exceeding statements are set out
for you to feel secure about your
judgements.
•If a pupil is meeting the exceeding
statements, they will be deemed to be at
Point 7 (Stage C)
•If they are very confident and rarely
make a mistake in relation to the
‘exceeding’ statements then they will be
judged at Point 8 (Stage B)
•A few pupils will be judged at Point 9
(Stage A). These will be pupils who are
exceptionally confident in handling the
exceeding statements and show
exceptional mathematical ability for their
age
56
Assessment: Meeting Year 1 Expectations
Year 1 Expectations: Measurement
and Geometry
Year 1 Expectations: Number
• Count reliably to 100
• Count on and back in 1s, 2s, 5s, and 10s from any
given number to 100
• Write all numbers in words to 20
• Say the number that is one more or one less than
a number to 100
• Recall all pairs of addition and subtraction
number bonds to 20
• Add and subtract 1-digit and 2-digit numbers to
20, including zero
• Recognise all coins: £1; 50p; 20p; 10p; 5p and 1p
• Recognise and name the 2D shapes: circle;
triangle; square and oblong
• Recognise and name the 3D shapes: cube;
sphere; cuboid
• Name the days of the week and months of the
year
• Tell the time to ‘o’clock’ and half past the hour
• Know the signs (+); (-) and (=)
• Solve a missing number problem, such as:
5=8• Solve a one-step problem involving an addition and
subtraction, using concrete objects, pictorial
representations and arrays
• Solve a one-step problem involving a multiplication
and division, using concrete objects, pictorial
representations and arrays
© Focus Education (UK) Ltd 2014
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Assessment: Exceeding Year 1 Expectations
Year 1 Exceeding Expectations:
• Count reliably well beyond 100
• Count on and back in 3s from any given number to beyond
100
• Say the number that is 10 more or 10 less than a number to 100
• Know the signs (+); (-); (=); (<); (>)
• Apply knowledge of number to solve a one-step problem
involving an addition, subtraction and simple multiplication
and division
• Add and subtract 1-digit and 2-digit numbers to 50, including
zero
• Recognise all coins and notes and know their value
• Use coins to pay for items bought up to £1
• Use knowledge of time to know when key periods of the day
happen, eg, lunchtime, home time, etc.
• Recognise different 2D and 3D shapes in the environment
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 1 Parents’ Guide
Parents’ Guide
‘Must do’ by the end of Year 1
Number
•
•
•
•
•
•
•
Shape and Measures
Be able to count on in 2s, 5s and
10s to 100
Know one more and one less than
any numbers to 100
Know all odd and even numbers to
100
Find missing numbers in sequence
up to 20
Add 2, one-digit numbers to 20
Add 3, one-digit numbers to 20
Know all number bonds for
numbers to 20, e.g. 2+4, 5+6,17+3,
etc.
•
Name the following shapes:
•
Tell time to the hour and half past
the hour
Recognise the £1, 50p, 20p, 10p,
5p, 2p and 1p coins
Name the days of the week
Name the months of the year
•
•
•
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year Group Objectives
Year 2
Focus on Mathematics
Year 2 Group Objectives
Number
Year 2 Objectives: Number 1
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 1: Count on in steps of 2, 3, 5 and 10
from any number
Objective 3: Give 10 more or less than any
number to 100
Count in 10s to 100
*1
Know 10 more than any number to 50 and then
to 100
*1
Count in 2s to 50 then 100
*2
*2
Count in 5s to 50 then 100
*3
Know 10 less than any number from 50 and then
from 100
Count in 3s to 30, 60 and then to 99
*4
Objective 2: Recognise the place value of
each digit in a two-digit number (tens and
ones)
Know which is the tens and ones part of a 2-digit
number
*1
Partition a 2-digit number showing the true value of
each digit
*2
Objective 4: Use ˂ , ˃ and = signs to
compare and order numbers to 100
Know what the = sign stands for
*1
Know what the ˃ sign stands for
*2
Know what the ˂ sign stands for
*3
Use the = sign accurately in simple calculations
Use the ˂ sign between 2 numbers accurately
Use the ˃ sign between 2 numbers accurately
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 2
NUMBER AND PLACE VALUE
ADDITION AND SUBTRACTION
Objective 5: Read and write numbers to 100
in numerals and words
Objective 8: Recall and use addition and
subtraction facts to 20 fluently
Read and write all numbers to 20 in numerals
and words
*1
Know all addition number bonds to 10 instantly
*1
Know all addition number bonds to 20 instantly
Read and write all numbers to 50 in numerals
and words
Know all subtraction number bonds to 10 instantly
Read and write all numbers to 100 in numerals
and words
*2
Objective 6: Order, read and write numbers
in increasing and decreasing value
Order a set of numbers (at least 3) in increasing
value using numbers up to 50
*1
Order a set of numbers (at least 3) in
decreasing value using numbers up to 50
Order a set of numbers (at least 3) in increasing
value using numbers up to 100
*2
Order a set of numbers (at least 3) in
decreasing value using numbers up to 100
*2
Know all subtraction number bonds to 20 instantly
Relating these number facts to work out larger
numbers, if 3 + 5 = 8, then 30 + 50 = 80
*3
Objective 9: Add and subtract mentally up
to two-digit numbers using concrete objects
and pictorial representations.
Complete horizontal addition of a two-digit and a
one-digit number with answers up to 50 and then
up to 100
*1
Complete horizontal subtraction, taking a onedigit number from a two-digit number with answers
of no more than 50 and then with answers of no
more than 100
*2
Objective 7: Use number facts and place
value to solve number facts
Solve problems such as 50 + □ = 54; and □ + 9 =
39
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 3
NUMBER AND PLACE VALUE
ADDITION AND SUBTRACTION
Objective 10: Recognise odd and even numbers
Recall all even numbers to 10
*1
Recall all odd numbers to 10
Recall rapidly all even numbers to 20, then to 50, then to 100
*2
Recall rapidly all odd numbers to 20, then to 50, then to 100
*3
Know that an even number can be shared between 2 and
that an odd number cannot
Objective 11: Distinguish between and use: ordinal and
cardinal numbers
Objective 12: Add and subtract up
to two-digit numbers using written
methods including columnar
addition (without carrying or
borrowing).
Add a two-digit number and tens with
answers of no more than 50 and then
with answers of no more than 100
*1
Subtract tens from a two-digit number
with answers of no more than 50 and
then with answers of no more than 100
*2
Add three one-digit numbers
*3
Find missing numbers in a sequence up to 10
Find missing numbers in a sequence up to 20
Order objects using the terms 1st, 2nd, 3rd, etc.
Know the 5ness of 5
Know that a set of 5 objects contains more objects than, say
3, etc. (up to 10)
Subtract a 2-digit number from another 2-digit number with
numbers which do not involve borrowing from the tens
column
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 4
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 13: Add and subtract mentally:
a two-digit number and ones, a two-digit
number and tens, 2 two-digit numbers; and 3
one-digit numbers
Objective 14: Use subtraction in ‘take away’
and ‘find the difference’ problems
Rapid recall of a two-digit number added to a
one-digit number
*1
Rapid recall of a one-digit number taken away
from a two-digit number
Rapid recall of 10 added to a two-digit number
*1
Complete number problems which require
working out the difference between two numbers,
e.g. John has read 16 books and Nadir has read
13 books. How many more books has John read?
*2
Objective 15: Recognise that addition can
be done in any order but subtraction cannot
Rapid recall of any 10s number added to a twodigit number (answer no more than 100)
Rapid recall of 10 subtracted from a two-digit
number
Complete number problems which require a
number to be taken away from another, e.g. If I
have 23 sweets and I eat 5, how many are there
left?
*2
Rapid recall of any 10s number subtracted from
a two-digit number
Know that when adding numbers together they
can be set out in any order, e.g. 5 + 7 will be same
as 7 + 5; or 3 + 5 + 4 will be the same as 5 + 4 + 3
Know that when subtracting the order is very
important, e.g. 7 – 5 cannot be set out as 5 - 7
Rapid recall of the addition of any 2 two-digit
numbers that do not total above 100
Rapid recall of the addition of any 3 one-digit
numbers that do not total above 100
*3
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 5
ADDITION AND SUBTRACTION
MULTIPLICATION AND DIVISION
Objective 16: Recognise that subtraction is
the inverse of addition and use for checking
calculations and solve missing numbers
Objective 18: Recall multiplication and division
facts for the 2, 5 and 10 times tables
Know that 5 + 7 = 12 involves the same process as
12 - 7 = 5, or 12 – 5 = 7
Recite the 2x table rapidly, up to x12, without error
Answer rapidly any calculation involving the 2x
table out of order
Complete calculations such as: If 6 + 8 = 14; what
is 14 – 8?
Know that 2 x 4 is the same as 4 x 2
Complete calculations such as: If 9 + 6 = 15; what
is the missing number in 15 - □ = 9?
Recite the 10x table rapidly, up to x12, without error
Objective 17: Solve addition and subtraction
word problems with up to 2-digits
Recognise x2 is doubling
Solve simple word problems involving addition
to 50
*1
Recognise ÷2 is halving
Solve simple word problems involving
subtraction to 50
*2
Answer rapidly any calculation involving the 10x
table out of order
Know that 3 x 10 is the same as 10 x 3
Solve simple word problems involving addition
to 100
Solve simple word problems involving
subtraction to 100
*1
*3
Recite the 5x table rapidly, up to x12, without error
*2
Answer rapidly any calculation involving the 5x
table out of order
*3
Know that 6 x 5 is the same as 5 x 6
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 6
MUTIPLICATION AND DIVISION
MULTIPLICATION AND DIVISION
Objective 19: Use x, ÷ and = signs to read
and write mathematical statements
Objective 22: Recognise that multiplication
can be done in any order but division cannot
Know that the ‘x’ sign stands for multiplication
*1
Know that 8 x 2 = 16 can be set out as 2 x 8 = 16
Know that the ÷ sign stands for division
*2
Know that 20 ÷ 5 = 4 cannot be set out as 5 ÷20=
Know that the = sign stands for equals
Uses the x, ÷, and = signs in simple calculations
for numbers up to 100
Objective 20: Calculate and write
multiplication and division statements
Calculate and write out simple multiplication
statements, such as 6 x 2 = 12
Solve simple word problems involving multiplication
to 50
*1
Solve simple word problems involving division to 50
Calculate and write simple division statements,
such as 16 ÷ 2 = 8
Objective 21: Recognise that division is the
inverse of multiplication and use to check
calculations
Know that examples such as 8 x 2 = 16
correspond to 16 ÷2 = 8
Objective 23: Solve word problems involving
multiplication and division, using materials,
arrays, repeated addition, mental methods,
and multiplication and division facts, including
problems in contexts
Solve simple word problems involving multiplication
to 100
Solve simple word problems involving division to
100
*2
Know that if 40 ÷ 2 = 20 then 20 is a half of 40
Know that examples such as 20 ÷ 5 = 4
correspond to 4 x 5 = 20
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Number 7
FRACTIONS
FRACTIONS
Objective 24: Recognise, find, name and
write fractions ⅓, ¼, 2/4 and ¾ of a length,
shape, set of objects or quantity
Objective 25: Recognise, find, name and write
fractions ⅓, ¼, 2/4 and ¾ of a length, shape,
set of objects or quantity (continued)
Know that the symbol ½ stands for half the
value of…
Calculate 2/4 of a given number up to 100
*1
Calculate ¾ of a given number up to 100
Know that the symbol ¼ stands for a third of the
value of…
Write simple fractions such as ½ of 6 = 3
Know that the symbol ¾ stands for a quarter of
the value of…
Recognise the equivalence of 2/4 and ½
Know that the symbol ⅓ stands for a third of the
value of…
Find ⅓ of a shape
*2
Objective 26: Count in halves and quarters to
10
Find ¼ of a shape
Count in sequence up to 10: ½; 1; 1½, 2, 2½,
……………
Find 2/4 of a shape
Count in sequence up to 10: ¼, ½, ¾, 1, 1¼,
1½,………….
Find ¾ of a shape
Use the ½ and 2/4 equivalence on a number line,
e.g. 1¼ , 12/4 (or 1 ½) , 1¾ , 2
Calculate ⅓ of a given number up to 100
*1
*2
Calculate ¼ of a given number up to 100
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 2 Pre-Learning Tasks
Number
Focus on Mathematics: Year 2
Name
Objective 1
Date
Number
Count on in steps of 2, 3, 5 and 10 from any number
Can you complete these sequences?
20, 30, 40
*1
15, 20, 25
12, 14, 16
*2
17, 22, 27
75, 80, 85
*3
6, 9, 12
35, 38, 41
*4
35, 38, 41
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 2
Number
Recognise the place value of each digit in a two-digit number (tens and
ones)
Can you place the tens and the units in the correct place?
17
Tens
Units
45
Tens
Units
23
Tens
Units
67
Tens
Units
40
Tens
Units
87
Tens
Units
61
Tens
Units
92
Tens
Units
*1
*2
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Objective 3
Date
Number
Give 10 more or less than any number to 100
Can you add 10 to these numbers?
27
Can you take away 10 from these
numbers?
*1
78
56
45
89
67
67
49
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 4
Number
Objective 4: Use ˂ , ˃ and = signs to compare and order numbers to 100
Which sign should be used?
8
4+4
*1
9
7
*2
17
18
*3
34
67
Can you complete these?
16
˃
23
˂
˂
19
˃
56
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Objective 5
Date
Number
Read and write numbers to 100 in numerals and words
Can you write these numbers in
numerals?
thirteen
*1
Can you write these numbers in
words?
27
twentyfour
48
forty-two
75
eightyfive
*2
92
© Focus Education (UK) Ltd 2014
*1
*2
75
Focus on Mathematics: Year 2
Name
Objective 6
Date
Number
Order, read and write numbers in increasing and decreasing value
Can you order these numbers
(smallest first)?
23, 1, 46
*1
Can you order these numbers
(largest first)?
78, 4, 81
32, 5, 15
77, 6, 89
6, 17, 50
90, 95, 91
41, 8, 23
78, 76, 79
© Focus Education (UK) Ltd 2014
*2
76
Focus on Mathematics: Year 2
Name
Date
Objective 8
Number
Recall and use addition and subtraction facts to 20 fluently
Can you work out these answers quickly? (2 minutes)
14 + 5
*1
2 + 15
15 - 3
19 - 12
*2
If 3 + 5 = 8
what is 30 +50?
*3
If 7 + 2 = 9
what is 70 +20?
If 5 + 2 = 7
what is 50 + 20?
If 6 + 4 = 10
what is 60 + 40?
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 9
Number
Add and subtract mentally up to two-digit numbers using concrete objects
and pictorial representations.
Can you add these numbers?
23 + 5
Can you subtract one number from the
other?
*1
25 – 7
17 + 9
19 - 6
48 + 9
67 - 6
67 + 6
72 - 7
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 10
Number
Recognise odd and even numbers to 100
Can you put these numbers in the correct place?
1
2
3
4
5
6
7
8
9
10
36
23
23
43
24
21
22
44
23
18
*1
Even
Odd
*3
Even
Starting Position:
Odd
9
12
13
14
15
16
17
18
19
20
Even
Odd
34
69
58
27
91
68
28
19
88
67
Even
Odd
© Focus Education (UK) Ltd 2014
*2
79
Focus on Mathematics: Year 2
Name
Date
Objective 12
Number
Add and subtract up to two-digit numbers using written methods
including columnar addition (without carrying or borrowing).
What are the answers?
17 + 10
*1
45 - 10
26 + 10
89 - 10
89 + 10
6+7+6
28 - 10
*2
*3
8+9+3
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 13
Number
Add and subtract mentally: a two-digit number and ones, a two-digit
number and tens, 2 two-digit numbers; and 3 one-digit numbers
Can you work these out?
17 + 10
*1
25 + 16
26 - 10
89 - 16
69 + 20
4+7+6
48 - 20
*2
23 + 14
Starting Position:
*3
7+9+3
9–3-2
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Objective 14
Date
Number
Use subtraction in ‘take away’ and ‘find the difference’ problems
Can you solve these problems?
If I have 10 sweets and I
give 4 away, how many
have I left?
*1
What is the difference
between 10 and 3?
There were 15 biscuits on
a plate and 5 people ate
one each. How many
were left?
There are 12 balls in one
basket and 5 in another
basket. What is the
difference?
During lunch there were
12 cup cakes on a plate
and 8 children had one
each. How many are left?
Hamza had 15 stickers this
week and Helen had 9.
What is the difference?
John lined up all his play
people. There were 23
altogether. Then he took
away 5. How many were
left?
Manchester United scored
14 goals in March and
Liverpool scored 10 goals.
What is the difference?
© Focus Education (UK) Ltd 2014
*2
82
Focus on Mathematics: Year 2
Name
Objective 17
Date
Number
Solve addition and subtraction word problems with up to 2-digits
Can you work out the answers?
If I have 10 sweets and my
mum gives me 13 more.
How many have I got?
*1
There were 15 biscuits in
one packet and 13 in
another. How many
biscuits altogether?
There were 12 cup cakes
on one shelf and 8 on
another. How many more
were on the first shelf?
Harry had 12 cars and
Abdul had 11. How many
did they have altogether?
What is the difference
between 60 and 13?
*3
There are 22 balls in one
basket and 50 in another
basket. How many are there
altogether?
*2
Saffiya had 25 stickers this
week and Chloe had 19.
How many did they have
between them?
Oldham scored 30 goals this
year and Bolton scored 50
goals. Who scored more?
How many more?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 18
Number
Recall multiplication and division facts for the 2, 5 and 10 times tables
Can you work these out?
10 x 2
*1
8x2
5x5
7 x 10
*2
11 x 2
How many 2s in
16?
How many 5s in
30?
How many 10s in
70?
*3
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Date
Objective 19
Number
Use x, ÷ and = signs to read and write mathematical statements
Can you work these out?
12 X 2
*1
15 ÷ 5
7X2
25 ÷ 5
10 x 3
24 ÷ 2
8x5
60 ÷ 10
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Objective 23
Date
Number
Solve word problems involving multiplication and division
Can you work out the answers?
A mum gave each of her
children 2 coins. She had
4 children. How many
coins did she give out?
*1
Dad had 16 toy cars. He
shared them equally with
me and my brother. How
many did I get?
In the PE hall there are
different coloured balls: red;
yellow; green and blue. There
are 5 of each colour. How
many are there altogether?
In the PE lesson there are 20
bean bags to be shared
between 5 children. How many
bean bags did each child get?
For dinner, everyone had
2 sausages. There were 8
children on the table.
How many sausages were
there altogether?
Five boys shared 25 marbles
between them. How many
marbles did each boy get?
In pre-school 7 mums sat
together. They each had 2
children. How many children
were there altogether?
In the tray there were 15
coloured pencils. 3 boys
shared these out. How many
pencils did each boy get?
© Focus Education (UK) Ltd 2014
*2
86
Focus on Mathematics: Year 2
Name
Objective 24
Date
Number
Recognise, find, name and write fractions ⅓, ¼, 2/4 and ¾ of a length,
shape, set of objects or quantity
Can you work these out?
What is half of 8?
*1
Can you colour in a half
of this shape?
What is a quarter (¼)
of 12?
Can you colour in a
quarter of this shape?
What is three quarters (3/4)
of 12?
Can you colour in three
quarters of this shape?
What is a third (1/3) of 9?
Can you colour in a
third of this shape?
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 2
Name
Objective 26
Date
Number
Count in halves and quarters to 10
Can you continue these sequences?
½, 1, 1 ½ , 2, 2 ½ ,….
*1
¼ , ½, ¾ , 1, 1 ¼, 1 ½, ….
4 ½ , 5, 5 ½ , 6, 6 ½ ,….
5 ¼, 5 ½, 5 ¾, 6, 6 ¼ ,….
7, 7 ½ , 8, 8 ½, 9,…….
8, 7 ¾, 7 ½, 7 ¼, 7, 6 ¾,…
5, 4 ½, 4, 3 ½, 3, 2 ½, …
5, 4 ¾, 4 ½, 4 ¼, 4, 3 ¾ ,…
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 2 Group Objectives
Measurement, Geometry and
Statistics
Year 2 Objectives : Measurement 1
MEASUREMENT
MEASUREMENT
Objective 1m: Choose and use appropriate standard units
to estimate and measure using rulers, scales,
thermometers and measuring vessels,
Length/height (m, cm) in any direction
Mass (kg, g)
Temperature (°C)
Capacity (l, ml) to the nearest appropriate unit
Objective 2m: Compare and order lengths,
mass, volume/capacity and record results
using ˂,˃ and =
Know 1 m and make reasonable estimates of length/height
up to 10m
Know 1cm and make reasonable estimates of length/height
up to 100cm
Know 1kg and make reasonable estimates of weight up to
5kg
Order different lengths using metres and
centimetres
Order different weights using kilograms and
grams
Use the symbols ˃, ˂, and = to compare two
amounts of lengths and weight
Record information using ˃, ˂, and =
Name objects that weigh more or less than 1kg, 10kg
Record amounts of liquid using litres and
millilitres
Know how much they weigh in kg
Use ˃, ˂, and = to compare amounts of liquid
Know that kg is a written format for kilogram
Objective 3m: Read scales to the nearest
numbered unit
Know how much 1 litre is
Know that many liquids are sold in 1 litre amounts
Know amounts that are more or less than 1 litre
Know that 0°C is freezing
Know that 100°C is boiling
Estimate the temperature outside to a reasonable
approximation
Read weighing scales to the nearest 10 gram
units
Read lengths to the nearest centimetre
Read liquid amounts to the nearest 10 ml
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Measurement 2
MEASUREMENT
MEASUREMENT
Objective 4m: Recognise and use symbols for
pounds (£) and pence (p); combine amounts
to make a particular value
Objective 7m: Estimate and measure using appropriate
standard units, using appropriate measuring vessels, rulers
and scales:
Height/length (m, cm)
Mass (kg, g)
Temperature (°C)
Volume and capacity (l, ml)
Know that 1p + 2p = 3p, 10p + 5p = 15p and 50p + 20p
= 70p
Know that £1 = 50p + 50p
Estimate a distance of up to 5 metres
Objective 5m: Find different combinations of
coins that equal the same amount of money
Find all the different ways of using coins to make 20p
Name objects that are more or less than a metre long
or high
Know how long a centimetre is
Find all the different ways of using coins to make 50p
Know that 100 centimetres make up 1 metre
Find all the different ways of using coins to make £1
Objective 6m: Solve simple problems in a
practical context involving addition and
subtraction of money of the same unit,
including giving change
Calculate how much Imran spends if he buys an apple
for 20p and a banana for 10p.
Calculate how much change he would get from 50p
Calculate how much change he would get from £1.
Use a ruler to measure 5cm, 10cm, 20cm and 30cm
accurately
Name objects that are approximately 10 cm long
Write m and cm to represent metre and centimetres
respectively
Recognise mm as a very small measurement
Know that 10 mm is 1 centimetre
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Measurement 3
MEASUREMENT
Objective 8m: Tell and write the time to 5 minutes (including
quarter to and past)
MEASUREMENT
Read the clock to o’clock and half past
Objective 11m: Add and subtract money of
the same unit
Read the clock to quarter past and quarter to
Read the clock in five minute intervals past the hour
Add 2 different amounts of money using
combinations of £ and 50p
Read the clock to five minute intervals to the hour
Draw times on clock faces to the intervals of o’clock,
half past, quarter past and quarter to the hour
Objective 9m: Recognise coins and notes of different values
Add 2 different amounts of money using
combinations of £ and 10p
Add 2 different amounts of money using a
combination of notes and coins to the value of
£10
Recognise all coins from 1p to £2
Recognise all notes from £5 to £50
Objective 10m: Combine amounts to make values and
match combinations of coins to amounts of money
Combine coins between the value of 10p and 50p
and say how much altogether up to the value of £1
Combine coins between the value of 10p and 50p
and say how much altogether up to the value of £5
Combine notes and coins to make up amounts to the
value of £10
Combine notes and coins to make up amounts to the
value of £50
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Geometry 1
PROPERTIES OF SHAPES
PROPERTIES OF SHAPES
Objective 1g: Recognise and name
common 2D and 3D shapes
Objective 4g: Identify and describe properties of
3D shapes, including the number of edges, vertices
and faces
Know and name squares, rectangles, triangles
and circles
Identify simple 3D shapes according to edges, vertices
and faces
Know and name cubes, cuboids, spheres,
pyramids
Use terms vertices and faces when describing 3D shapes
Objective 2g: Identify and describe
properties of 2D shapes, including the
number of sides and line symmetry in a
vertical line
Identify a line of symmetry in simple shapes
Objective 5g: Identify 2D shapes on the surface of
3D shapes
Describe 3D shapes according to their 2D make up, e.g.
number of squares, triangles, etc.
Identify a circle on a cylinder/a triangle on a pyramid,
etc.
Make up own symmetrical shapes
Begin to explore nets of 3D shapes according to 2D
shapes contained within them, e.g. a cube has 6 squares
Identify 2-D shapes according to sides and
number of edges, etc.
Describe 2-D shapes including the number of
sides and line symmetry
Objective 6g: Compare and sort common 2D and
3D shapes
Objective 3g: Identify and describe
properties of polygons and non-polygons
Put together sets of triangles, recognising their similarities
and differences
Draw lines and shapes using a straight edge
Put together sets of rectangles recognising their similarities
and differences
Put together sets of circles and spheres recognising the
differences in their size
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Geometry 2
POSITION, DIRECTION AND MOTION
Objective 7g: Order and arrange
combinations of mathematical objects in
patterns and sequences
Objective 8g: Use mathematical vocabulary
to describe position, direction and
movement, including movement in a
straight line and distinguishing between
rotation as a turn and in terms of right angles
for quarter, half and three-quarter turns
(clockwise and anti-clockwise)
Use the term clockwise, anticlockwise, right
angle, quarter turn, half turn, three quarter turn,
accurately to describe movement
© Focus Education (UK) Ltd 2014
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Year 2 Objectives : Statistics
STATISTICS
Objective 1s: Interpret and construct simple pictograms, tally charts, block diagrams
and simple tables
Read information contained within a simple pictogram
Read information contained within a simple tally chart
Read information contained within a block diagram
Read information contained within a simple table
Construct a pictogram to show information collected (amounts of less than 20)
Construct a tally chart to show information collected (amounts of less than 20)
Construct a block diagram to show information collected (amounts of less than 20)
Construct a simple table to show information collected (amounts of less than 20)
Objective 2s: Ask and answer simple questions by counting the number of
objects in each category and sorting the categories by quantity
Objective 3s: Ask and answer questions about totalling and comparing
categorical data
© Focus Education (UK) Ltd 2014
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Making Mathematics Work
Step up to the Challenge
Year 2
Number
Year 2: Can you challenge yourself to meet the Objective?
Objective 1: Can you count on in 2s, 3s, 5s, and 10s from any number
up to 100?
Me
My
Teacher
Can you count on in 3s from any number up to 100?
Can you count on in 2s from any number up to 100?
Can you count on in 5s from any number up to 100?
Can you count on in 10s from any number up to 100?
Objective 2: Do you recognise the place value of each digit in a 2digit number (tens and ones)?
Can you partition a 2-digit number to show the value of each digit?
Can you recognise the ‘tens’ number in a 2-digit number?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 3: Can you add or subtract 10 from any number up
to 100?
Me
My
Teacher
Me
My
Teacher
Can you subtract 10 from any number up to 100?
Can you subtract 10 from any number up to 50?
Can you add 10 on to any number up to 100?
Can you add 10 on to any number up to 50?
Objective 4: Can you use ˂ , ˃ and = signs to compare and order
numbers to 100?
Can you use the ˃ symbol between 2 numbers accurately?
Can you use the ˂ symbol between 2 numbers accurately?
Can you use the = sign accurately in simple calculations?
Do you know what the ˃ symbol stands for?
Do you know what the ˂ symbol stands for?
Do you know what the = symbol stands for?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 5: Can you read and write all numbers to 100 in numerals
and words?
Me
My
Teacher
Can you read and write all numbers to 100 in numerals and
words?
Can you read and write all numbers to 50 in numerals and
words?
Can you read and write all numbers to 20 in numerals and
words?
Objective 6: Can you order, read and write numbers in increasing and
decreasing value
Me
My
Teacher
Can you order a set of numbers (at least 3) in decreasing value using numbers
up to 100?
Can you order a set of numbers (at least 3) in increasing value using
numbers up to 100?
Can you order a set of numbers (at least 3) in decreasing value using
numbers up to 50?
Can you order a set of numbers (at least 3) in increasing value using
numbers up to 50?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 8: Can you rapidly recall and use addition and subtraction
facts to 20?
Me
My
Teacher
Can you relate number facts (within bonds of 20) to working out larger numbers,
e.g. If 3 + 5 = 8, then 30 + 50 = 80?
Do you know all subtraction number bonds to 20 instantly?
Do you know all subtraction number bonds to 10 instantly?
Do you know all addition number bonds to 20 instantly?
Do you know all addition number bonds to 10 instantly?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 10: Do you recognise all odd and even numbers to 100?
Me
My
Teacher
Do you know that an even number can be shared between 2?
Do you know all odd numbers to 20, then to 50, then to 100?
Do you know all even numbers to 20, then to 50, then to 100?
Do you know all odd numbers to 11?
Do you know all even numbers to 10?
Objective 12: Can you add and subtract up to 2-digit numbers using
written methods including columnar addition (without carrying or
borrowing)?
Can you subtract a 2-digit number from another 2-digit number with numbers
which do not involve borrowing from the tens column?
Can you add two 2-digit numbers together using columnar addition (where
the two units do not add up to 10)?
Can you complete horizontal subtraction, taking a 1-digit number from
a 2-digit number with answers of no more than 50?
Can you complete horizontal addition of a 1-digit and a 2-digit
number with answers up to 50; and then up to 100?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 13: Can you add and subtract mentally: a 2-digit number
and ones, a 2-digit number and tens, two 2-digit numbers?
Me
My
Teacher
Can you add any two, 2-digit numbers that do not total above 100 and give
the answer rapidly?
Can you take away any 10s number from a 2-digit number and give the
answer rapidly?
Can you take away 10 from a 2-digit number and give the answer rapidly?
Can you add any 10s number to a 2-digit number (answer no more than
100) and give the answer rapidly?
Can you add 10 to a 2-digit number and give the answer rapidly?
Can you take away a 1-digit number from a 2-digit number and give
the answer rapidly?
Can you add a 2-digit number to a 1-digit number and give the
answer rapidly?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 14: Do you recognise subtraction as ‘taking away’ and
‘finding’ the difference’?
Me
My
Teacher
Can you complete a subtraction problem requiring you to find the
difference in value between two numbers?
Can you complete a subtraction problem requiring you to ‘take away’
one number from another?
Objective 15: Do you know that addition can be done in any order,
but subtraction cannot?
Do you know that when subtracting you must always take the smaller
number from the larger one?
Do you know that when adding you can start with any number?
Objective 16: Do you know that subtraction is the inverse of addition
and can be used for checking calculations
Do you know that in the calculation ‘a + b = c’; that c – a = b and
c- b = a?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 17: Can you solve addition and subtraction word problems
with up to 2-digits?
Me
My
Teacher
Can you solve simple word problems involving subtraction to
100?
Can you solve simple word problems involving addition to
100?
Can you solve simple word problems involving
subtraction to 50?
Can you solve simple word problems involving
addition to 50?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 18: Can you recall multiplication and division facts for the 2,
5 and 10 times tables?
Me
My
Teacher
Can you answer rapidly any calculation involving the 5x table out of order?
Can you recite the 5x table rapidly, up to x12, without error?
Can you answer rapidly any calculation involving the 10x table out of
order?
Do you recognise that ÷2 is halving?
Do you recognise that x2 is doubling?
Can you recite the 10x table rapidly, up to x12, without error?
Do you know the inverse rule; i.e. that 2 x 4 is the same as 4 x
2?
Can you answer rapidly any calculation involving the 2x
table out of order?
Can you recite the 2x table rapidly, up to x12, without
error?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 19: Can you use x, ÷ and = signs to read and write
mathematical statements?
Me
My
Teacher
Can you use the x, ÷, and = signs in simple calculations for numbers up to
100?
Do you know that the = sign stands for equals?
Do you know that the ÷ sign stands for division?
Do you know that the ‘x’ sign stands for multiplication?
Objective 20: Can you calculate and write multiplication and division
statements?
Can you calculate and write simple division statements, such as 15 ÷ 3 = 5?
Can you calculate and write out simple multiplication statements, such as
8 x 2 = 16?
Objective 21: Do you recognise that division is the inverse of
multiplication and use to check calculations?
Do you know the inverse rule; i.e. that examples such as 35 ÷ 5 = 7 correspond to 7 x
5 = 35?
Do you know the inverse rule; i.e. that examples such as 9 x 2 = 18
correspond to 18 ÷ 2 = 9?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 24: Can you recognise, name and write fractions ¼, ⅓, ½, ⅔
and ¾ of a whole?
Me
My
Teacher
Can you calculate ⅔ of a given number up to 100?
Can you calculate ¾ of a given number up to 100?
Can you calculate ¼ of a given number up to 100?
Can you calculate ⅓ of a given number up to 100?
Can you calculate ½ of a given number up to 100?
Do you know that the symbol ⅔ stands for two-thirds of the value of
a number or object?
Do you know that the symbol ¾ stands for three-quarters of the
value of a number or object?
Do you know that the symbol ¼ stands for a quarter of the
value of a number or object?
Do you know that the symbol ⅓ stands for a third of the
value of a number or object?
Do you know that the symbol ½ stands for half the
value of a number or object?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 26: Can you count in halves, quarters and thirds to 10?
Me
My
Teacher
Can you count in thirds sequence up to 10: ⅓, ⅔, 1, 1⅓,
1⅔,………….?
Can you count in quarters sequence up to 10: ¼, ½, ¾,
1, 1¼, 1½,………….?
Can you count in half sequence up to 10: ½; 1; 1½, 2,
2½, ……………?
© Focus Education (UK) Ltd 2014
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Making Mathematics Work
Step up to the Challenge
Year 2
Measurement, Geometry and Statistics
Year 2: Can you challenge yourself to meet the Objective?
Objective 1m: Can you estimate and measure using appropriate
standard units, using appropriate measuring vessels, rulers and
scales?
Me
My
Teacher
Do you know that 10 mm is 1 centimetre?
Do you recognise mm as a very small amount?
Can you write m and cm to represent metre and centimetres respectively?
Can you name objects that are approximately 10 cm long?
Can you use a ruler to measure 5cm, 10cm, 20cm and 30cm
accurately?
Do you know that 100 centimetres make up 1 metre?
Do you know how long a centimetre is?
Can you name objects that are more or less than a metre long
or high?
Can you estimate a distance of up to 5 metres?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 2m: Can you compare and order lengths, mass,
volume/capacity and record results (using ˂,˃ and =)?
Me
My
Teacher
Can you use ˃, ˂, and = to compare amount of liquid?
Can you record amounts of liquid using litres and millilitres?
Can you record information using ˃, ˂, and =?
Can you use the symbols ˃, ˂, and = to compare two amounts of
lengths and weight?
Can you order different weights using kilograms and grams?
Can you order different lengths using metres and centimetres?
Objective 3m: Can you read scales to the nearest numbered unit?
Can you read weighing scales to the nearest 10 gram units?
Can you read lengths to the nearest centimetre?
Can you read liquid amounts to the nearest 10ml?
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Year 2: Can you challenge yourself to meet the Objective?
Objective 7m: Can you estimate and measure using appropriate
standard units, using appropriate measuring vessels, rulers and
scales? (continued)
Me
My
Teacher
Can you estimate the temperature outside to a reasonable approximation?
Do you know that 0°C is freezing and that 100°C is boiling?
Do you know amounts that are more or less than 1 litre?
Do you know that many liquids are sold in 1 litre amounts?
Do you know how much 1 litre is?
Do you know that kg is a written format for kilogram?
Do you know how much you weigh in kg?
Can you name objects that weigh more or less than 1kg,
10kg?
Do you know 1kg and make reasonable estimates of
weight up to 5kg?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 8m: Can you tell and write the time to 5 minutes (including
quarter to and past)?
Me
My
Teacher
Can you draw times on clock faces to the intervals of o’clock, half past,
quarter past and quarter to the hour?
Can you read the clock in five minute intervals to the hour?
Can you read the clock in five minute intervals past the hour?
Can you read the clock to quarter past and quarter to?
Can you read the clock to o’clock and half past?
Objective 9m: Do you recognise coins and notes of different values?
Can you recognise all notes from £5 to £50?
Can you recognise all coins from 1p to £2?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 10m: Can you combine amounts to make values and
match combinations of coins to amounts of money?
Me
My
Teacher
Can you combine notes and coins to make up amounts to the value of
£50?
Can you combine notes and coins to make up amounts to the value of
£10?
Can you combine coins between the value of 10p and 50p and say
how much altogether up to the value of £5?
Can you combine coins between the value of 10p and 50p and say
how much altogether up to the value of £1?
Objective 11m: Can you add and subtract money of the same unit?
Can you add 2 different amounts of money using combinations of notes
and coins to the value of £10
Can you add 2 different amounts of money using combinations of £
and 10p?
Can you add 2 different amount of money using combinations of
£ and 50p?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 2g: Can you identify and describe properties of 2D and 3D
shapes (sides, lines of symmetry)?
Me
My
Teacher
Can you identify simple 3-D shapes according to sides, edges, faces, etc.?
Can you identify 2-D shapes according to sides and number of edges,
etc.?
Can you make up your own symmetrical shapes?
Can you identify a line of symmetry in simple shapes?
Objective 3g: Can you identify and describe properties of 3D shapes
(edges, vertices and faces)?
Do you use the terms ‘vertices’ and ‘faces’ when describing 3D shapes?
Can you identify simple 3D shapes according to sides, edges, faces,
etc.?
© Focus Education (UK) Ltd 2014
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Year 2: Can you challenge yourself to meet the Objective?
Objective 1s: Can you interpret and construct simple pictograms, tally
charts, block diagrams and tables?
Me
My
Teacher
Can you read information contained within a pictogram?
Can you read information contained within a simple tally chart?
Can you read information contained within a block diagram?
Can you read information contained within a simple table?
Can you construct a pictogram to show information collected
(amounts of less than 20)?
Can you construct a tally chart to show information collected
(amounts of less than 20)?
Can you construct a tally chart to show information
collected (amounts of less than 20)?
Can you construct a block diagram to show information
collected (amounts of less than 20)?
Can you construct a simple table to show information
collected (amounts of less than 20)?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Non-Negotiables
Year 2 Possible Planning Outline
Year 2 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell, we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
© Focus Education (UK) Ltd 2014
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Year 2 Mathematics Non-Negotiables
• Compare and order numbers up to 100.
• Read and write all numbers to 100 in digits
and words.
• Say 10 more/less than any number to 100.
• Count in multiples of 2, 3, 5 and 10 from
any number up to 100.
• Recall and use multiplication and division
facts for 2, 5 and 10 tables.
• Recall and use addition and subtraction
facts to 20.
• Derive and use related facts to 100.
• Recognise place value of any 2-digit
number.
• Use the < > and = signs correctly
• Add and subtract:
o 2-digit numbers and ones
o 2-digit numbers and tens
o Two 2-digit numbers
o Three 1-digit numbers
• Recognise and use inverse for addition
and subtraction
• Calculate and write multiplication and
division calculations using multiplication
tables.
• Recognise and use inverse for
multiplication and division
• Recognise, find, name and write 1/3; 1/4;
2/4; 3/4.
• Recognise equivalence of simple fractions.
• Tell time to five minutes, including quarter
past and to the hour.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
The following 3 pages suggest a planning outline for delivering the nonnegotiables in classrooms. There should be some element of teaching of these
each day.
Autumn Term
Ist Half Term
2nd Half Term
• Count on/back in steps of 2s and 5s to 100 from 0;
and in 10s to 100 and beyond from 0 and any
given number
• Read and write all numbers to 100 in numerals and
write all numbers in words to 30
• Order a set of numbers (at least 3) to 50 in
increasing value
• Recall fluently all addition number bonds to 10
and know all the subtraction number bonds to 10
• Add/subtract 2-digit and 1-digit numbers to 20
• Find 1/10 more/less than a given number up to 30
• Recall the 2 times tables up to 12x12
• Double any number up to 20
• Halve any even 2-digit number up to 40
• Count on/back in steps of 2s and 5s to 100, 3s to 30
from 0; and in 10s to 100 and beyond from 0 and any
given number
• Identify even and odd numbers to 20
• Read and write all numbers to 100 and beyond
accurately in numerals and write all numbers in words
to 30 and beyond
• Order a set of numbers (at least 3) to 50 in decreasing
value
• Recall fluently all addition number bonds to 10 and
beyond and know all the subtraction number bonds to
10
• Add/subtract 2-digit and 1-digit numbers to 20 and
beyond
• Find 1/10 more/less than a given number up to 30
• Recite the 2 times tables and answer any calculation
involving the 2 times table in any order
• Recite the 10 times tables
• Double any number up to 30
• Halve any even 2-digit number up to 60
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Spring Term
Ist Half Term
2nd Half Term
• Count on/back in steps of 2s and 5s to 100; 3s to 30 and
beyond from 0; and in 10s to 100 and beyond from 0
and any given number
• Identify even and odd numbers to 20 and beyond
• Read and write all numbers to 100 and beyond in
numerals and write all numbers in words to 50
• Order a set of numbers (at least 3) to 100 in increasing
value
• Compare numbers up to 20 using =, <, > symbols
• Recall fluently all addition number bonds to 15 and
beyond and know all the subtraction number bonds to
15
• Find 1/10 more/less than 50
• Round numbers to the nearest 10 up to 50
• Add/subtract : 2-digit and 1-digit numbers, a 2-digit
number and ten and add 3 one digit numbers
• Recite the 2 and 10 times tables and answer any
calculation involving the 2 and 10 times table in any
order
• Double any number up to 40
• Halve any even 2-digit number up to 80
• Count on/back in steps of 2s and 5s to 100, 3s to 60
from 0; and in 10s to 100 and beyond from 0 and any
given number
• Count in ½s to 5
• Identify even and odd numbers to 50
• Read and write all numbers to 100 and beyond in
numerals and write all numbers in words to 50 and
beyond
• Order a set of numbers (at least 3) to 50 and beyond in
decreasing value
• Compare numbers up to 50 using =, <, > symbols
• Round numbers to the nearest 10 up to at least 50
• Recall fluently all addition number bonds to 20 and
know all the subtraction number bonds to 20
• Find 1/10 more/less than a given number up to 50 and
beyond
• Add/subtract 2-digit and 1-digit numbers to 20; a 2-digit
number and tens
• Add/subtract: 2-digit and 1-digit numbers, a 2-digit
number and tens and add 3 one digit numbers
• Recite the 2 and 10 times tables and answer any
calculation involving the 2 and 10 times table in any
order
• Recite the 5 times tables
• Double any number up to at least 40
• Halve any even 2-digit number up to 80
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Planning to meet the requirement of the nonnegotiables
Summer Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 2s and 5s to 100 and beyond, 3s to 60
from 0; and in 10s to 100 and beyond from 0 and any given
number
Count in ½s to 10
Count in 1p, 2p, 5p, 10p and £1
Identify even and odd numbers to 50 and beyond
Read and write all numbers to 100 and beyond in numerals and
write all numbers in words to 100
Order a set of numbers (at least 3) to 100 in increasing and
decreasing value
Round numbers to the nearest 10 up to 100
Compare numbers up to 100 using =, <, > symbols
Recognise the place value of a 2 digit number (tens and ones)
Find 1/10 more/less than a given number up to 100
Recall fluently all addition number bonds to 20 and know all the
subtraction number bonds to 20 to begin to become fluent in
deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to
calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30)
Add/subtract: 2-digit and 1-digit numbers, a 2-digit number and
tens, two 2- digit numbers which do not involve
bridging/exchanging across the 10s boundary and add 3 one
digit numbers
Recite the 2, 10 and 5 times tables and answer any calculation
involving the 2, 10 and 5 times table in any order
Double any number up to 50
Halve any even 2-digit number up to 100
• Count on/back in steps of 2s and 5s to 100 and beyond, 3s to
99 from 0; and in 10s to 100 and beyond from 0 and any
given number
• Count in 1p, 2p, 5p, 10p and £1
• Count in ½s to 10; in ¼s to 5
• Read and write all numbers to 100 and beyond in numerals
and write all numbers in words to 100 and over
• Order a set of numbers (4 and/or) to 100 in increasing and
decreasing value
• Round numbers to the nearest 10 up to at least 100
• Compare numbers up to 100 using =, <, > symbols
• Begin to recognise the place value of a 3 digit number
(hundreds, tens and ones)
• Find 1/10 more/less than a given number up to 100 and
beyond
• Recall fluently all addition number bonds to 20 and know all
the subtraction number bonds to 20 to begin to become
fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3
to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30)
• Add/subtract: 2-digit and 1-digit numbers, a 2-digit number
and tens, two 2- digit numbers and add 3 one digit numbers
• Recite the 2, 10 and 5 times tables and answer any
calculation involving the 2, 10 and 5 times table in any order
• Identify even and odd numbers to 100
• Double any number up to at least 50
• Halve any even 2-digit number up to 100
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 2 Assessment
Assessment: Meeting Year 2 Expectations
Year 2 Expectations: Number
•
•
•
•
•
•
The main focus on assessment will be
measuring a pupil’s journey towards and
beyond the Year 2 expectations. The Year 2
expectations for number are set out on the
right hand side of this page.
To meet the Year 2 expectations a pupil
must be able to meet all of the statements
outlined in the table, plus the ones for
measurement and geometry, shown later.
If they have not met all the statements then
they will be deemed to be emerging.
If a pupil is meeting the expectations then
an assessment needs to made as to
whether a pupil is exceeding the
expectations.
The next page sets out how to assess
whether a pupil is exceeding this
expectation or whether a pupil is at the
emerging stage.
The next page also provides you with a 9point scale for deeper analysis, if required.
• Read and write numbers to at least 100 in
numerals and words
• Recognise odd and even numbers to 100
• Count in steps of 2, 3 and 5 from 0
• Recognise place value of each digit in 2-digit
numbers
• Compare and order numbers from 0 to 100 using
the >; <; and = signs
• Name the fractions 1/3 ; ¼ ; ½ and ¾ and find
fractional values of shapes; lengths and numbers
• Recall and use multiplication and division facts for
the 2, 5 and 10x multiplication tables
• Add and subtract: two 1-digit; 2-digit and a 1
digit; 2-digit and 10s; two 2-digit and three 1-digit
numbers
• Solve problems with addition and subtraction
• Understand commutativity in relation to addition,
subtraction, multiplication and division
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 2 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
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Assessment: Meeting Year 2 Expectations
A pupil will be deemed to be
meeting the expectations only if
they can satisfy their teacher
that they meet all the
expectations for their age
A pupil will be deemed to be
emerging towards the
expectations if they do not meet
all of the statements outlined for
that year group
•Meeting the expectations (Stage
C) – Point 4
•It is accepted that a pupil might
make the occasional error if they
are at this stage. However,
despite that, the teacher needs
to be satisfied that they
understand the concept fully.
•Meeting the expectations (Stage
B) - Point 5
•At this stage a pupil will rarely
make mistakes and is very
confident at meeting the
statements.
•Meeting the expectation (Stage
A)- Point 6
•At this stage, not only is the pupil
confident at meeting the
statements but works at a rapid
rate. However, they are not yet
meeting all the statements for
exceeding.
•If they meet more than 75% of
the statements but not all then
they will be described as:
•Emerging towards the
expectations (Stage C) – Point 3
•If they meet between 50% and
75% of the statements then they
will be described as:
•Emerging towards the
expectations (Stage B) – Point 2
•However if they are not meeting
50% of the expectations they will
be described as:
•Emerging towards the
expectations (Stage A) – Point 1
•There is, therefore, no
requirement to write a set of
emerging statements
© Focus Education (UK) Ltd 2014
A pupil will be deemed to be
exceeding the expectations when, in
addition to the statements set out for
meeting the expectation (Stage
A)they meet one or more of three sets
of further expectations
•Pupils will be deemed to be exceeding
expectations if, in addition to what is
outlined as Point 6, they show evidence
of:
•Accessing some of the following year
group’s objectives
•Being able to use the year group’s
expectation within context
•Being able to consistently apply the year
group objectives in a range of situations.
•A set of exceeding statements are set out
for you to feel secure about your
judgements.
•If a pupil is meeting the exceeding
statements, they will be deemed to be at
Point 7 (Stage C)
•If they are very confident and rarely
make a mistake in relation to the
‘exceeding’ statements then they will be
judged at Point 8 (Stage B)
•A few pupils will be judged at Point 9
(Stage A). These will be pupils who are
exceptionally confident in handling the
exceeding statements and show
exceptional mathematical ability for their
age
126
Assessment: Meeting Year 2 Expectations
Year 2 Expectations: Number
• Read and write numbers to at least 100 in
numerals and words
• Recognise odd and even numbers to 100
Year 2 Expectations: Measurement,
Geometry and Statistics
• Choose and use appropriate standard units to
estimate length/ height/ temperature and
capacity
• Count in steps of 2, 3 and 5 from 0
• Tell and write the time to 5 minute intervals
• Recognise place value of each digit in 2-digit
numbers
• Recognise and use the symbols £ and p when
solving problems involving addition and
subtraction of money
• Compare and order numbers from 0 to 100 using
the >; <; and = signs
• Name the fractions 1/3 ; ¼ ; ½ and ¾ and find
fractional values of shapes; lengths and numbers
• Recall and use multiplication and division facts for
the 2, 5 and 10x multiplication tables
• Describe the properties of 2D and 3D shapes to
include: edges, vertices and faces
• Interpret and construct pictograms, tally charts,
block diagrams and simple tables
• Add and subtract: two 1-digit; 2-digit and a 1
digit; 2-digit and 10s; two 2-digit and three 1-digit
numbers
• Solve problems with addition and subtraction
• Understand commutativity in relation to addition,
subtraction, multiplication and division
© Focus Education (UK) Ltd 2014
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Assessment: Exceeding Year 2 Expectations
Year 2 Exceeding Expectations:
• Count reliably up to 1000 in 2s, 5s and 10s
• Count on and back in multiples of 4, 8, 25, 50 and 100 from
any given number to beyond 1000
• Add and subtract fractions with a common denominator
• Apply knowledge of number up to 100 to solve a one-step
problem involving a addition, subtraction and simple
multiplication and division
• Apply knowledge of addition and subtraction to pay for items,
up to £10, within a problem solving context
• Add and subtract two 2-digit and numbers to 100
• Use an appropriate strategy to add and subtract numbers that
move between and through 100, eg, 97 + 7; 103 - 8
• Know about right angles and where they can be seen in the
environment
• Tell time to 5 minute intervals in both analogue and digital and
relate one to the other
• Measure, compare, add and subtract using common metric
measures
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 2 Parents’ Guide
Parents’ Guide
‘Must do’ by the end of Year 2
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on in 2s, 3s, 5s and 10s to 100
Find 10 more than a given number to 100
Find 10 less than a given number to 100
Use the < > and = signs correctly
Order a set of 3 numbers in increasing and
decreasing value
Know all addition bonds to 20
Know all subtraction bonds to 20
Add a 1-digit number to a 2-digit number
to 100
Add 2, 2-digit numbers using column
addition
Subtract a 1-digit number from a 2-digit
number using columns with no carry over
Rapid recall of 2-digit number add a 1-digit
number
Rapid recall of a 2-digit number add 10
Rapid recall of 2-digit add 2-digit number
Rapid recall of 2-digit number take away 1digit number
Rapid recall of a 2-digit number take away
10
•
•
•
•
•
•
•
•
Know all odd and even numbers to 100
Write any written number as digits
Problem solving involving take away or
difference
Know the 2x, 5x and 10x tables
Know the fractions: ½; ¼; ¾; ⅓; ⅔
Tell time to 5 minute intervals
Recognise all coins from 1p to £2
Add and subtract money values
involving 10p, 50p, and £notes
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year Group Objectives
Year 3
Year 3 Objectives: Number
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 1: Read and write numbers up to
1000 in numerals and words
Objective 3: Compare and order numbers up
to 1000
Read and write all numbers to 100
*1
Read and write all numbers in 100s from 100 to
1000
Read and write all numbers in 50s from 50 to
1000
Know which of two 3-digit numbers is the greater and
smaller
*1
*2
Order a set of 3-digit numbers from smallest to largest
*2
*3
Order a set of 3-digit numbers from largest to smallest
Read and write all numbers in 10s from 10 to
1000
Read and write all numbers to the value of 1000
Objective 4: Count in multiples of 4, 8, 50 and
100 from 0
*4
Objective 2: Recognise place value of each
digit in a 3-digit number (hundreds, tens,
ones)
Count on and back in 10s from 0 to 1000
*1
Count on and back in 100s from 0 to 1000
*2
Count on and back in 50s from 0 to 1000
Know and use terms: units, tens and hundreds
correctly
*1
Count on and back in 4s from 0 to 1000
*3
Partition any number up to 999 showing the
value of each digit
*2
Count on and back in 8s from 0 to 1000
*4
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Year 3 Objectives : Number 2
ADDITION AND SUBTRACTION
NUMBER AND PLACE VALUE
Objective 5: Find 10 or 100 more or less than
a given number
Objective 6: Mental addition and subtraction: pairs of
one and 2-digit numbers; a 3-digit number and ones; a
3-digit number and tens; a 3-digit number and
hundreds
Add rapidly any 2 single-digit numbers
Find 10 more than a given number between 0
and 1000
*1
Subtract rapidly any 2 single-digit number
Find10 less than a given number between 0 and
1000
*2
Add together mentally any single-digit and any 2digit number
Find100 more than a given number between 0
and 1000
Subtract any single-digit number from a 2-digit
number
Find100 less than a given number between 0
and 1000
Add together mentally any 3-digit number and any
single-digit number
*1
*2
*3
Subtract any single-digit number from a 3-digit
number
Add together mentally any 3-digit number and any
10s number
Subtract any 10s number from a 3-digit number
*4
Add together mentally any 3-digit number and any
100s number
Subtract any 100s number from a 3-digit number
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Year 3 Objectives : Number 3
NUMBER AND PLACE VALUE
Objective 7: Identify, represent and estimate
numbers using different representations,
including those related to measure
Know that 7 tens and 3 ones is 73
*1
Know that 6 hundreds, 5 tens and 2 ones is 652
Know that an object of 4.8m is longer than one
of 356cm
*2
Know that 257cm is 2.57m
*3
Objective 8: Solve number problems and
practical problems involving numbers up to
1000
Solve problems such as which is greater:
3 hundreds, 6 tens and 4 ones or 578?
Use everyday situations to solve problems
involving addition with answers no greater than
1000
Use everyday situations to solve problems
involving subtraction using numbers that are no
greater than 1000
© Focus Education (UK) Ltd 2014
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Year 3 Objectives : Number 4
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 9: Add and subtract numbers with
up to 3 digits, using formal written methods
of columnar addition and subtraction
Objective 10: Solve word problems,
including missing numbers, using number
facts, place value, and more complex
addition and subtraction
Add 2 numbers with 2-digits together using
columnar addition without exchange between
units and tens
*1
Solve simple word problems involving missing
numbers
Subtract a 2-digit number from another using
columnar subtraction which requires no
exchange between the units, tens or hundreds
Solve simple word problems involving place
value
Solve simple word problems involving complex
addition to 1000
Add 2 numbers with 3-digits together using
columnar addition without exchange between
units and tens
Add 2 numbers with 3-digits together using
columnar addition, where the units and tens
when added make more than 10.
*2
Solve simple word problems involving complex
subtraction to 1000
Add 3 numbers with 3-digits using columnar
addition where the units or tens make more
than 10
Subtract a 3-digit number from another using
columnar subtraction which requires no
exchange between the units, tens or hundreds
*3
Subtract a 3-digit number from another using
columner subtraction which requires exchange
between the units, tens or hundreds
*4
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Year 3 Objectives : Number 5
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 11: Estimate the answer to a
calculation and use inverse operations to
check answers
Objective 12: Solve problems, including
missing number problems, using number
facts, place value, and more complex
addition and subtraction
*1
Estimate the answer to 65 add 32
Estimate the answer to 76 subtract 44
Solve simple word problems involving missing
numbers
Estimate the answer to 673 add 25
Solve simple word problems involving place
value
Estimate the answer to 864 subtract 523
*2
Know that 500 + 300 = 800 involves the same
process as 800 - 300 = 500, or 800 – 500 = 300
Subtract any single-digit number from a 3-digit
number
Solve simple word problems involving complex
addition to 1000
Solve simple word problems involving complex
subtraction to 1000
© Focus Education (UK) Ltd 2014
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Year 3 Objectives : Number 6
MULTIPLICATION AND DIVISION
MULTIPLICATION AND DIVISION
Objective 13: Know all table calculations for
2, 3, 4, 5, 8 and 10
Objective 15: Write and calculate mathematical statements
for multiplication and division using the multiplication
tables that they know, including for 2-digit times one-digit
numbers, using mental and progressing to formal written
methods
Recite all multiplication facts for the x2 table
*1
Recite all multiplication facts for the x5 table
Multiply a 10s number by a single-digit number
mentally, using 2, 3, 4, 5, 8 and 10x
*1
Multiply a 2-digit number by a single-digit number using
2, 3, 4, 5, 8 and 10x
*2
*3
Recite all multiplication facts for the x4 table
Divide 2, 3, 4, 5, 8 and 10 into any 10s number (no
remainder)
Recite all multiplication facts for the x8 table
Divide 2, 3, 4, 5, 8 and 10 into any 2-digit number (no
remainder)
*4
Recall all number facts for the 2, 3, 4, 5, 8 and
10x table out of sequence
Objective 16: Solve word problems involving 4 operations,
including missing number problems
Recite all multiplication facts for the x10 table
Recite all multiplication facts for the x3 table
Know the inverse of all table facts involving 2, 3,
4, 5, 8 and 10x table, eg. how many 4s in 24?
*2
Solve word problems involving addition with numbers
up to 1000
Know the inverse of all table facts involving 2, 3,
4, 5, 8 and 10x table, eg. What is 48÷8?
Solve word problems involving subtraction with
numbers up to 1000
Objective 14: Solve problems, including missing number
problems, involving multiplication and division, including
positive integer scaling problems and correspondence
problems in which n objects are connected to m objects
Solve word problems involving multiplication with
numbers up to 100
Solve word problems involving division with numbers up
to 100
© Focus Education (UK) Ltd 2014
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Year 3 Objectives : Number 7
FRACTIONS
FRACTIONS
Objective 17: Count up and down in tenths
Objective 20: Recognise and show, using
diagrams, equivalent fractions with small
denominators
Count up in tenths
*1
Count down in tenths
*2
Know that ½ is the same as 2/4, etc.
Know that tenths arise from dividing an object
into 10 equal parts
*3
Be able to show 1/3 of a square and 2/6 of a
square
Objective 18: Recognise, find and write
fractions of a discrete set of objects: unit
fractions and non-unit fractions with small
denominators
Objective 19: Recognise and use fractions
as numbers: unit fractions and non-unit
fractions with small denominators
Know what fractional values are: eg. ¼ is one
part of four, etc.
Name all fractions from ½ to 1/12
Find ½,¼,⅕ of a given 2-digit number
Objective 21: Add and subtract fractions
with same denominator within one whole
Add 2 fractions with the same denominator that
add up to no more than 1 whole, eg. 5/7 + 1/7 =
6/7
*1
Subtract one fraction from another of the same
denominator, eg. ⅘ – 2/5 = 2/5
*2
Objective 22: Compare and order unit
fractions, and fractions with the same
denominators
Order any fraction between ½ to 1/12
Order any fraction where the denominator is the
same (between ½ to 1/12th)
Objective 23: Solve problems that
© Focus Education involve
(UK) Ltd 2014all of the above
138
Focus on Mathematics
Year 3 Pre-Learning Tasks
Number
Focus on Mathematics: Year 3
Name
Objective 1
Date
Number
Read and write numbers to 1000 in numerals and words
Can you write these numbers in
numerals?
sixty-four
*1
89
*3
247
one hundred
three
hundred and
eighty- three
Can you write these numbers in words?
*2
392
Six hundred
and five
709
eight
hundred and
eighteen
968
© Focus Education (UK) Ltd 2014
*4
140
Focus on Mathematics: Year 3
Name
Date
Objective 2
Number
Recognise place value of each digit in a 3-digit number (hundreds, tens,
ones)
Can you place the hundreds, tens and the units in the correct place?
317
Hundreds
Tens
Units
*1
Partition the following
numbers
415
670
300
Hundreds
Tens
Units
426
Hundreds
Tens
Units
87
615
Hundreds
Tens
Units
902
© Focus Education (UK) Ltd 2014
*2
(400 + 10 + 5)
141
Focus on Mathematics: Year 3
Name
Date
Objective 3
Number
Compare and order numbers up to 1000
Can you say which is the greater and
the smaller number?
Greater
Smaller
*1
Can you order these numbers (smallest
first)?
26, 134, 98
132 or 235
202, 506, 113
132 or 569
67, 980, 127
657 or 234
803, 296, 105
113 or 233
230, 788, 982
109 or 201
115, 78, 902
100 or 98
67, 98, 230
207 or 702
119, 657, 458
666 or 444
201, 506, 561
17 or 767
205, 290, 256
© Focus Education (UK) Ltd 2014
*2
142
Focus on Mathematics: Year 3
Name
Objective 4
Date
Number
Count on in steps of 4, 8, 50 and 100 from 0
Can you count on or back as required?
0, 100, 200
*1
0, 50,100
400,300,200
200,150,100
0, 4, 8
*3
16, 12, 8
*2
0, 8, 16
*4
32,24,16
Starting Position:
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Focus on Mathematics: Year 3
Name
Objective 5
Date
Number
Find 10 or any 100 more or less than a given number
Can you find the number 10 more than?
56
*1
Can you find the number 10 less than?
78
98
17
786
876
395
905
291
503
© Focus Education (UK) Ltd 2014
*2
144
Focus on Mathematics: Year 3
Name
Date
Objective 6
Number
Mental addition and subtraction: pairs of one and 2-digit numbers; a 3-digit
number and ones; a 3-digit number and tens; a 3-digit number and
hundreds
Can you complete these very quickly? (2 minutes)
7+6
*1
9-3
23 + 6
345 + 40
492 + 30
*2
569 - 50
56 + 9
348 - 90
67 - 5
363 + 200
45 - 9
875 + 300
129 + 6
*3
*4
560 - 200
345 + 9
789 - 300
124 - 8
678 -200
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Focus on Mathematics: Year 3
Name
Objective 7
Date
Number
Identify, represent and estimate numbers using different representations,
including those related to measure
Can you put each number in the correct
column?
H
T
U
*1
51
579
911p
760
167p or £1.23
45cm or 1m 16cm
3m 78cm or 567cm
6m or 567cm
*3
823cm
106
145p or £3.21
493p
178cm
63
Which is the greater?
Can you write these as £ and p or as
m and cm?
*2
378cm
208p
134p
78cm
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Focus on Mathematics: Year 3
Name
Date
Objective 9
Number
Add and subtract numbers with up to 3 digits, using formal written methods
of columnar addition and subtraction
Can you calculate these accurately?
*1
321
137
223+
345
124
228+
156
216
422+
138
212
114+
23
14+
35
14+
62
25+
72
23+
37
14-
48
25-
27
16-
18
12-
345
112-
789
356-
389
272-
479
345-
*3
345
242+
236
342+
123
356+
321
321+
535
246-
621
373-
735
567-
843
467-
*4
345
136+
236
437+
123
458+
321
559+
*2
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Focus on Mathematics: Year 3
Name
Objective 11
Date
Number
Estimate the answer to a calculation and use inverse operations to
check answers
Can you quickly estimate the answers
to these calculations?
77 + 65
39 - 13
*1
What do you notice about these
calculations?
100 + 200
*2
300 - 100
123 + 65
256 + 99
250 + 130
367 - 50
380 - 130
345 - 90
429 + 60
560 - 200
345 + 90
760 - 560
424 - 8
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Focus on Mathematics: Year 3
Name
Objective 13
Date
Number
Know all table calculations for 2, 3, 4, 5, 8 and 10
Can you complete these very quickly?
(2 minutes maximum)
5x5
*1
Can you complete these very quickly?
(2 minutes maximum)
How many 5s in 35?
9x3
How many 4s in 24?
10 x 8
How many 2s in 16?
6 x 10
How many 8s in 64?
7x8
How many 3s in 27?
7x4
How many 5s in 35?
4x3
How many 3s in 21?
10 x 4
How many 8s in 32?
10 x 10
How many 10s in 90?
© Focus Education (UK) Ltd 2014
*2
149
Focus on Mathematics: Year 3
Name
Objective 15
Date
Number
Write and calculate mathematical statements for multiplication and
division using the multiplication tables that they know, including for 2-digit
times one-digit numbers, using mental and progressing to formal written
methods
Can you complete these calculations?
20 x 3
*1
Can you complete these calculations?
50 ÷ 2
30 x 5
150 ÷ 3
40 x 8
240 ÷ 8
70 x 10
250 ÷ 5
24 x 8
*2
27 ÷ 3
41 x10
88 ÷ 8
35 x 5
72 ÷ 4
17 x 4
55 ÷ 5
© Focus Education (UK) Ltd 2014
*3
*4
150
Focus on Mathematics: Year 3
Name
Objective 17
Date
Number
Count up and down in tenths
Can you complete the sequences?
1/10; 2/10; 3/10
*1
7/10; 6/10; 5/10
1 3/10; 1 4/10; 1 5/10
2 3/10 ; 2 2/10
1 8/10; 1 9/10; 2;
How many tenths
in 2 and a half?
7 9/10; 8; 8 1/10
How many tenths
in 4 and 3 tenths?
*2
*3
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 3
Name
Objective 21
Date
Number
Add and subtract fractions with same denominator within one whole
Can you add these fractions?
3/5 + 1/5 =
*1
Can you subtract these fractions?
6/10 - 5/10 =
5/8 + 1/8 =
8/9 - 1/9 =
2/7 + 4/7 =
5/6 – 2/6 =
2/9 + 5/9 =
6/7 – 2/7 =
*2
Starting Position:
© Focus Education (UK) Ltd 2014
152
Focus on Mathematics
Year 3 Group Objectives
Measurement, Geometry and
Statistics
Year 3 Objectives : Measurement
MEASUREMENT
MEASUREMENT
Objective 1m: Measure, compare, add and subtract:
lengths (m/cm/mm); mass (kg, g); volume and
capacity (l/ ml)
Objective 2m: Measure the perimeter of simple
2D shapes
Practise using appropriate tools to measure distances
and weight
Know the term ‘perimeter’
Recognise 1m as having 100cm
Know that the perimeter is the distance around the
four sides of a rectangle
Know that 50cm is ½ a metre
Know that the perimeter is the distance around the
outside of any shape
Measure to the nearest metre a distance of up to 10m
Measure accurately each side of a 2D shape and
add up all the sides to find the perimeter
Measure accurately a distance of up to 30cm using a
ruler
Measure a distance of up to 5m using a tape
measure giving the answer in m and cm
Objective 3m: Add and subtract
amounts of money to give change,
using both £ and p in practical contexts
Recognise 1Kg as having 1000g
Add any two amounts of money using notes and coins
Know that 500g is ½ a Kg
Sort out an amount of money by organising it into sets of the
same coins and then making up sets of pounds, etc.
Measure to the nearest Kg a weight of up to 10Kg on
a weighing machine
From a given amount give change from £1, £5, £10
Measure accurately a weight of up to 500g on a
weighing scale
Measure a weight of up to 5Kg using a weighing
machine giving the answer in Kg and g
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Year 3 Objectives : Measurement 2
MEASUREMENT
Objective 4m: Tell and write the time from an
analogue clock, using Roman numerals 1 to
X11, and 12 hour & 24 hour clocks
MEASUREMENT
Objective 6m: Record and compare time in terms of
seconds, minutes, hours
Recognise all Roman numerals from 1 to 12 and
their associated place on a clock
Know that 60 seconds is one minute and that 60
minutes is one hour
Can tell the time on an analogue clock and
write down its equivalent, e.g. ten past two can
be written as 2:10
Know that quarter past is 15 minutes past; and that half
past is 30 minutes past
Know that 90 seconds is a minute and a half
Understand the 24 hour system, e.g. 2pm is 1400
hours
Know that 75 minutes is one hour and a quarter
Objective 5m: Estimate and read time with
increasing accuracy to the nearest minute
Revise reading the time in five minute intervals
Read the time to one minute intervals
Objective 7m: Use vocabulary such as: o’clock, am, pm,
morning, afternoon, noon and midnight
Know that am represents time from midnight to noon
Know that pm represents time from noon to midnight
Estimate the time to the nearest five minutes,
eg, it is almost ten past three
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Year 3 Objectives : Measurement 4
MEASUREMENT
Objective 8m: Know the number of seconds in a
minute; minutes in an hour; and the number of days
in each month, year and leap year
Know that 60 minutes make 1 hour; and that 60
seconds make 1 minute
Know that the number of days per month varies
between 28 to 31
Know that the number of days in a year varies
between 365 and 366 and know the term leap
year
Know the rhyme associated with days of the
month
Objective 9m: Compare durations of events, e.g.
calculate time taken by particular events or tasks
Measure in minutes and seconds any duration
using a stop watch or hand held clock
Know that certain events last a given time: e.g.
lunch hour = 60 minutes, playtime = quarter of
an hour, football match = 90 minutes
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Year 3 Objectives : Geometry
PROPERTIES OF SHAPES
PROPERTIES OF SHAPES
Objective 1g: Draw 2D shapes and make
3D shapes using modelling materials
Objective 4g: Identify right angles; know that 2
and 4 right angles make half and a full turn
respectively
Draw 2D shapes and name them
Know a right angle as having 90 degrees which is
written as 90˚
Make a range of 3D shapes using playdough,
clay
Objective 2g: Recognise 3D shapes in
different orientations and describe them
Describe a range of 3D shapes set out in different
ways
Objective 3g: Recognise angles as a
property of shape or a description of a turn
Know that the opening between two lines
joined at a point is known as an angle and can
be measured in degrees
Know that the measurement in degrees is
greater when the opening is wider
Know that two right angles effectively make a
straight line and is equivalent to 180˚
Know that 2 right angles make a half-turn
Know that three right angles make three quarters
of a turn
Know that 4 right angles is a complete turn
Objective 5g: Identify whether angles are
greater or less than a right angle
Identify angles that are smaller than a right angle
Identify angles that are larger than a right angle
Know that an angle smaller than a right angle is
known as an acute angle
Know that an angle larger than a right angle is
known as an obtuse angle
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Year 3 Objectives : Geometry 2/ Statistics
PROPERTIES OF SHAPES
STATISTICS
Objective 6g: Identify horizontal and vertical
lines and pairs of perpendicular and parallel
lines
Objective 1s: Interpret and present data using
bar charts, pictograms and tables
Know the terms: horizontal and vertical
Read information set out in a bar chart, pictogram
or table
Read information from a bar chart that has a scale
on the vertical axes
Recognise horizontal and vertical in everyday
situations, e.g. telephone pole being vertical,
the sea being horizontal
Present information in a pictogram, bar chart or
table
Know the relationship between horizontal and
horizon
Present information on a bar chart where there is a
scale on the vertical axes
Know the terms perpendicular and parallel
Draw lines that are perpendicular and parallel
to a given line
Objective 2s: Solve one-step and two-step
questions using information presented in
scaled bar charts, pictograms and tables
Objective 7g: Recognise and use
abbreviations of metric units of measure
Solve problems involving pictograms, bar charts
and tables
Know that metres, centimetres and millimetres
are written as : m, cm, mm. respectively
Work out the answer to: ‘How many more children like
carrots than potatoes?’
Know that grams and Kilograms are written a: g.
and Kg respectively
Work out the answer to: ‘How many fewer children
travel to school by car than walk?’
Know that litres and millilitres and written as: l,
ml, respectively
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Step up to the Challenge
Year 3
Number
Year 3: Can you challenge yourself to meet the Objective?
Objective 1: Can you read and write numbers : to at least a 1000 in
numerals and words?
Me
My
Teacher
Can you read and write all numbers to the value of 1000?
Can you read and write all numbers in 10s from 10 to 1000?
Can you read and write all numbers in 50s from 50 to 1000?
Can you read and write all numbers in 100s from 100 to 1000?
Can you read and write all numbers to 100?
Objective 2: Can you recognise place value of each digit in a 3-digit
number?
Can you partition any number up to 999 showing the value of
each digit?
Do you know and use terms: units; tens and hundreds
correctly?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 3: Can you compare and order numbers up to 1000?
Me
My
Teacher
Can you order a set of 3-digit numbers from largest to smallest?
Can you order a set of 3-digit numbers from smallest to largest?
Do you know which of two 3-digit numbers is the greater and smaller?
Objective 4: Can you count in multiples of: 2, 3, 4, 5, 8, 10, 50 and 100
from 0?
Can you count on and back in 8s from 0 to 96?
Can you count on and back in 5s from 0 to 100?
Can you count on and back in 4s from 0 to 100?
Can you count on and back in 3s from 0 to 99?
Can you count on and back in 50s from 0 to 1000?
Can you count on and back in 10s from any given number between
0 and 1000?
Can you count on and back in 10s from 0 to 100?
Can you count on and back in 100s from 0 to 1000?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 5: Do you know 10 or 100 more or less than a given
number?
Me
My
Teacher
Do you know 100 less than a given number between 0 and 1000?
Do you know 100 more than a given number between 0 and 1000?
Do you know 10 less than a given number between 0 and 1000?
Do you know 10 more than a given number between 0 and 1000?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 6: Can you work out these mental addition and
subtraction: pairs of one and 2-digit numbers; 3-digit numbers and
ones; 3-digit numbers and tens; 3-digit numbers and hundreds?
Me
My
Teacher
Can you subtract any 100s number from a 3-digit number?
Can you add together mentally any 100s number and any 3-digit number?
Can you subtract any 10s number from a 3-digit number?
Can you add together mentally any 10s number and any 3-digit
number?
Can you subtract any single-digit number from a 3-digit number?
Can you add together mentally any single-digit and any 3-digit
number?
Can you subtract any single-digit number from a 2-digit number?
Can you add together mentally any single-digit and any 2-digit
number?
Can you subtract rapidly any 2 single-digit numbers?
Can you add rapidly any 2 single-digit numbers?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 8: Can you solve word problems, including missing
numbers, using number facts, place value, and more complex
addition and subtraction?
Me
My
Teacher
Can you solve simple word problems involving complex subtraction to 1000?
Can you solve simple word problems involving complex addition to 1000?
Can you solve simple word problems involving place value?
Can you solve simple word problems involving missing numbers?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 9: Add and subtract numbers with up to 3 digits, using
formal written methods of columnar addition and subtraction
Me
My
Teacher
Can you subtract a 3-digit number from another using column subtraction
which requires exchange between the units, tens or hundreds ?
Can you subtract a 3-digit number from another using columnar subtraction
which requires no exchange between the units, tens or hundreds?
Can you add 3 numbers with 3-digits using columnar addition where
the units or tens make more than 10?
Can you add 2 numbers with 3-digits together using columnar addition,
where the units and tens when added make more than 10?
Can you add 2 numbers with 3-digits together using columnar
addition without exchange between units and tens?
Can you subtract a 2-digit number from another using columnar subtraction
which requires no exchange between the units, tens or hundreds?
Can you add 2 numbers with 2-digits together using columnar
addition without exchange between units and tens?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 10: Can you solve word problems involving 4 operations,
including missing number problems?
Can you solve word problems involving division with numbers up to 100?
Can you solve word problems involving multiplication with numbers
up to 100?
Can you solve word problems involving subtraction with numbers
up to 1000?
Can you solve word problems involving addition with
numbers up to 1000?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 11: Estimate the answer to a calculation and use inverse
operations to check answers
Me
My
Teacher
Can you subtract any single-digit number from a 3-digit number?
Do you know that 500 + 300 = 800 involves the same process as 800 - 300 = 500, or 800
– 500 = 300?
Can you estimate the answer when subtracting one 3-digit number from another 3digit number?
Can you estimate the answer when adding a 3-digit number to a 2-digit numbers?
Can you estimate the answer when subtracting one 2-digit number from
another 2-digit number?
Can you estimate the answer when adding 2, 2-digit numbers?
Objective 12: Solve problems, including missing number problems,
using number facts, place value, and more complex addition and
subtraction
Can you solve simple word problems involving complex subtraction to
1000?
Can you solve simple word problems involving complex addition to
1000?
Can you solve simple word problems involving place value?
Can you solve simple word problems involving missing
numbers?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 13: Can you recall and use multiplication and division facts
for: 2, 3, 4, 5, 8 and 10?
Me
My
Teacher
Do you know the inverse of all table facts involving 2, 3, 4, 5, 8 and 10x
table, e.g. how many 4s in 24?
Can you recall all number facts for the 2, 3, 4, 5, 8 and 10x table out
of sequence?
Can you recite all multiplication facts for the x8 table?
Can you recite all multiplication facts for the x4 table?
Can you recite all multiplication facts for the x3 table?
Can you recite all multiplication facts for the x10
table?
Can you recite all multiplication facts for the x5
table?
Can you recite all multiplication facts for the x2
table?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 15: Can you write and calculate using multiplication and
division within multiplication tables; 2-digit x one-digit; using mental
and written methods?
Me
My
Teacher
Me
My
Teacher
Can you divide 2, 3, 4, 5, 8 and 10 into any 2-digit number (no remainder)?
Can you divide 2, 3, 4, 5, 8 and 10 into any 10s number (no remainder)?
Can you multiply a 2-digit number by a single-digit number using 2, 3, 4, 5, 8
and 10x ?
Can you multiply a 10s number by a single-digit number mentally, using 2, 3,
4, 5, 8 and 10x?
Objective 16: Solve word problems involving 4 operations, including
missing number problems
Can you solve word problems involving division with numbers up to 100?
Can you solve word problems involving multiplication with numbers up to 100?
Can you solve word problems involving subtraction with numbers up to
1000?
Can you solve word problems involving addition with numbers up to 1000?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 17: Count up and down in tenths
Me
My
Teacher
Do you know that tenths arise from dividing an object into 10 equal parts?
Can you count down in tenths?
Do you know what fractional values are: eg ¼ is one part of four, etc.?
Objective 19: Recognise and use fractions as numbers: unit fractions
and non-unit fractions with small denominators
Can you find ½,¼,⅕ of a given 2-digit number
Can you name and order any fraction between ½ to 1/12?
Do you know what fractional values are: eg. ¼ is one part of four, etc.?
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Making Mathematics Work
Step up to the Challenge
Year 3
Measurement, Geometry and Statistics
Year 3: Can you challenge yourself to meet the Objective?
Objective 1m: Can you measure, compare, add and subtract:
lengths (m/cm/mm); masses (kg, g); volume and capacity (l/ ml);
and time (hr/mins/sec)?
Me
My
Teacher
Do you know that 60 minutes make 1 hour; and that 60 seconds make 1 minute?
Can you measure a weight of up to 5Kg using a weighing machine giving the
answer in Kg and g?
Can you measure accurately a weight of up to 500g on a weighing scale?
Can you measure to the nearest Kg a weight of up to 10Kg on a weighing
machine?
Do you know that 500g is ½ a Kg?
Do you recognise 1Kg as having 1000g?
Can you measure a distance of up to 5m using a tape measure giving the
answer in m and cm?
Can you measure accurately a distance of up to 30cm using a ruler?
Can you measure to the nearest metre a distance of up to 10m?
Do you know that 50cm is ½ a metre?
Do you recognise 1m as having 100cm?
Can you practise using appropriate tools to measure distances
© Focus Education (UK) Ltd 2014
and weight?
172
Year 3: Can you challenge yourself to meet the Objective?
Objective 2m: Can you measure perimeter of simple 2D shapes?
Me
My
Teacher
Can you measure accurately each side of a 2D shape and add up all the sides to
find the perimeter?
Do you know that the perimeter is the distance around the outside of any
shape?
Do you know that the perimeter is the distance around the four sides of a
rectangle?
Do you know the term perimeter?
Objective 3m: Can you add and subtract amounts of money to give
change, using £ and p?
From a given amount can you give change from £1, £5, £10 ?
Can you sort out an amount of money by organising it into sets of the
same coins and then making up sets of pounds, etc.?
Can you add any two amounts of money using notes and coins?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 4m: Can you tell and write the time from an analogue clock,
using Roman numerals 1 to X11, and 12 hour & 24 hour digital clocks?
Can you tell the time in digital format and write it down?
Do you understand the 24 hour system, e.g. 2pm is 1400 hours?
Can you tell the time on an analogue clock and write down its
equivalent, e.g. ten past two can be written as 2:10?
Do you recognise all Roman numerals from 1 to 12 and their
associated place on a clock?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 5m: Can you estimate and read time to the nearest minute?
Me
My
Teacher
Can you estimate the time to the nearest five minutes, eg, it is almost ten past
three?
Can you read the time to one minute intervals?
Can you revise reading the time in five minute intervals?
Objective 6m: Can you compare time in terms of seconds, minutes,
hours and o’clock?
Do you know that 90 seconds is a minute and a half?
Do you know that quarter past is 15 minutes past; and that half past is 30
minutes past?
Do you know that 60 seconds is one minute and that 60 minutes is one
hour?
Objective 7m: Do you use terms such as: am, pm, morning, afternoon,
noon and midnight?
Do you know that pm represents time from noon to midnight?
Do you know that am represents time from midnight to noon?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 8m: Know the number of seconds in a minute; minutes in an
hour; and the number of days in each month, year and leap year
Do you know the rhyme associated with days of the month?
Do you know that the number of days in a year varies between 365 and 366
and know the term leap year?
Do you know that the number of days per month varies between 28
to 31?
Do you know that 60 minutes make 1 hour; and that 60 seconds
make 1 minute?
Objective 9m: Can you compare duration of events, e.g. calculate
time taken up by particular events or tasks?
Me
My
Teacher
Do you know that certain events last a given time: e.g. lunch hour; football match =
90 minutes?
Can you measure in minutes and seconds any duration using a stop watch or hand
held clock?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 3g: Do you recognise angles as a property of shape and
as an amount of turning?
Me
My
Teacher
Do you know that the measurement in degrees is greater when the opening
is wider?
Do you know that the opening between two lines joined at a point is known
as an angle and can be measured in degrees?
Objective 4g: Can you identify right angles; know that 2 and 4 right
angles make half and a full turn respectively?
Do you know that 4 right angles is a full turn?
Do you know that 2 right angles is half a turn?
Do you know that two right angles make a straight line and is
equivalent to 180˚?
Do you know a right angle has 90 degrees which is written as
90˚?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 5g: Can you identify whether angles are greater or less than
a right angle?
Me
My
Teacher
Do you know that an angle larger than a right angle is known as an obtuse angle?
Do you know that an angle smaller than a right angle is known as an acute
angle?
Can you identify angles that are larger than a right angle?
Can you identify angles that are smaller than a right angle?
Objective 6g: Can you identify horizontal, vertical, perpendicular,
parallel, and curved lines?
Can you draw lines that are perpendicular and parallel to a given line?
Do you know the terms perpendicular and parallel?
Do you know the relationship between horizontal and horizon?
Can you recognise horizontal and vertical in everyday situations,
eg, telephone pole being vertical, the sea being horizontal?
Do you know the terms: horizontal and vertical?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 7g: Recognise and use abbreviations of metric units of
measure
Me
My
Teacher
Do you know that litres and millilitres and written as: l and ml, respectively?
Do you know that grams and Kilograms are written a: g and Kg respectively?
Do you know that metres, centimetres and millimetres are written as : m,
cm and mm respectively?
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Year 3: Can you challenge yourself to meet the Objective?
Objective 1s: Can you read, interpret and present data using
pictograms and bar charts with scales?
Me
My
Teacher
Can you present information on a bar chart where there is a scale on the vertical
axes?
Can you present information in a pictogram or bar chart?
Can you read information from a bar chart that has a scale on the vertical
axes?
Can you read information set out in a bar chart or pictogram?
Objective 2s: Solve one-step and two-step questions using information
presented in scaled bar charts, pictograms and tables
Work out the answer to: ‘How many fewer children travel to school
by car than walk?’
Work out the answer to: ‘How many more children like carrots
than potatoes?’
Solve problems involving pictograms, bar charts and tables
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Focus on Mathematics
Non-Negotiables
Year 3 Possible Planning Outline
Year 3 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
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Year 3 Mathematics Non-Negotiables
• Compare and order numbers up to 1000.
• Read and write all numbers to 1000 in
digits and words.
• Find 10 or 100 more/less than a given
number.
• Count from 0 in multiples of 4, 8, 50 & 100.
• Recall and use multiplication & division
facts for 3, 4, 8 tables.
• Recognise place value of any 3-digit
number.
• Add and subtract:
o 3-digit numbers and ones
o 3-digit numbers and tens
o 3-digit numbers and hundreds
• Add and subtract:
o Numbers with up to 3-digits using
efficient written method (column).
• Use inverse to check.
• Multiply:
o 2-digit by 1-digit
• Count up/down in tenths.
• Compare and order fractions with same
denominator.
• Addition and subtraction of fractions with
same denominator with whole.
• Know pairs of fractions that total 1.
• Tell time using 12 and 24 hour clocks; and
using Roman numerals.
• Tell time to nearest minute.
• Know number of days in each month.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
The following 3 pages suggest a planning outline for delivering the non-negotiables in
classrooms. There should some element of teaching of these each day.
Autumn Term
Ist Half Term
2nd Half Term
• Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond,
from 0 and any given number
• Count on/back in 4s from 0 to 100
• Count on/back in 50s and 100s from 0 to 1000
• Find 10/100 more or less than a given number up to 500
• Read and write all numbers to 1000 in numerals and write
all numbers in words to 200 and over
• Order a set of numbers (4 and/or 5 ) to at least 1000 in
increasing and decreasing value
• Compare numbers up to 200 using =, <, > symbols
• Round numbers to the nearest 10 to at least 200
• Partition 3 digit numbers (hundreds, tens and ones)
• Recall fluently all addition number bonds to 20 and know all
the subtraction number bonds to 20 to begin to become
fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10
-3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30
and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 –
300)
• Add/subtract: 2-digit and 1-digit numbers, a 2-digit number
and tens, two 2- digit numbers and add 3 one digit
numbers
• Recall the 2, 5 and 10 times tables and the derived division
facts and begin to learn the 4 and 3 times tables
• Double any number up to 50 and halve any even 2-digit
number up to 100
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond,
from 0 and any given number
Count on/back in multiples of 4 and 8 from 0
Count on/back in 50s, 100s from 0 to 1000
Find 10/100 more or less than a given number up to 500
Count on/back in tenths
Read and write all numbers to 1000 in numerals and write all
numbers in words to 400 and over
Order a set of numbers (4 and/or 5 ) to at least 1000 in
increasing and decreasing value
Compare numbers up to 200 and beyond using =, <, > symbols
Round numbers to the nearest 10 to at least 500 and to the
nearest 100 to 500
Partition 3 digit numbers (hundreds, tens and ones)
Recall fluently all addition number bonds to 20 and know all
the subtraction number bonds to 20 to begin to become
fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3
to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and
300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300)
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number
and tens and a 3-digit number and hundreds
Count on/back in ½s , ¼s and 1/3s including on a number line
Recall the 2, 3, 4, 5 and 10 times tables and the derived
division facts
Double any number up to 50 and halve any even 2-digit
number up to 100
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Spring Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 2s,5s, 10s, 3s to 100 and beyond, from
0 and any given number
Count on/back in multiples of 4 and 8 from 0
Count on/back in 50s, 100s from 0 to 1000
Find 10/100 more or less than a given number up to 500 and
more
Read and write all numbers to 1000 in numerals and write all
numbers in words to 500
Order a set of numbers (4 and/or 5 ) to at least 1000 in
increasing and decreasing value
Compare numbers up to 500 using =, <, > symbols
Round numbers to the nearest 10 to at least 1000 and to the
nearest 100 to 1000
Recognise the place value of each digit (hundreds, tens and
ones)
Recall fluently all addition number bonds to 20 and know all the
subtraction number bonds to 20 to begin to become fluent in
deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to
calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300
+ 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300)
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds
Recall the 2, 3, 4, 5 and 10 times tables and the derived division
facts
Double any number up to 100; double any multiple of 50 up to
500 and halve any number up to 100
Find complements to 100 and recall addition and subtraction
facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 –
63 = 37)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond, from 0
and any given number
Count on/back in multiples of 4 and 8 from 0
Count on/back in 50s, 100s from 0 to 1000
Find 10/100 more or less than a given number up to 500 and more
Read and write all numbers to 1000 in numerals and write all
numbers in words to 500 and over
Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing
and decreasing value
Compare numbers up to 500 and beyond using =, <, > symbols
Round numbers to the nearest 10 to at least 1000 and to the
nearest 100 to 1000
Partition 3 digit numbers (hundreds, tens and ones) and partition
numbers in different ways
Recall fluently all addition number bonds to 20 and know all the
subtraction number bonds to 20 to begin to become fluent in
deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate
30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000;
1000 – 700 = 300 and 700 = 1000 – 300)
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds
Count on/back in ½s , ¼s and 1/3s including on a number line
Recall the 2, 3, 4, 5, and 10 times tables and the derived division
facts
Double any number up to 100; double any multiple of 50 up to 500
and halve any number up to 100
Find complements to 100 and recall addition and subtraction facts
for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37)
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Planning to meet the requirement of the nonnegotiables
Summer Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 1s, 10s, or 100 from any 2/3 digit
numbers
Count on/back in 50s, 100s from 0 to 1000
Find 10/100 more or less than a given number up to 1000
Read and write all numbers to 1000 in numerals and write all
numbers in words to at least 1000
Order a set of numbers (4 and/or 5 ) to at least 1000 in
increasing and decreasing value
Compare numbers up to 1000 using =, <, > symbols
Round numbers to the nearest 10 to 1000 and beyond and to
the nearest 100 to 1000 and beyond
Partition 3 digit numbers (hundreds, tens and ones) and partition
numbers in different ways
Count in tenths, read and write numbers with 1 decimal place
and compare numbers with one decimal place
Recall fluently all addition number bonds to 20 and know all the
subtraction number bonds to 20 to begin to become fluent in
deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to
calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300
+ 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300)
Find complements to 100 and recall addition and subtraction
facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 –
63 = 37)
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds
Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived
division facts
Double any number up to 100; double any multiple of 50 up to
500 and halve any number up to 200
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back in steps of 2s,5s, 10s, 3s to 100 and beyond, from
0 and any given number
Count on/back in multiples of 4 and 8 from 0
Count on/back in 50s, 100s from 0 to 1000
Find 10/100 more or less than a given number up to 1000 and
more
Read and write all numbers to 1000 in numerals and write all
numbers in words to at least 1000
Order a set of numbers (4 and/or 5 ) to 1000 and beyond in
increasing and decreasing value
Compare numbers up to 1000 and beyond using =, <, > symbols
Round numbers to the nearest 10 to 1000 and beyond and to
the nearest 100 to 1000 and beyond
Begin to partition 4 digit numbers (thousands, hundreds, tens
and ones)
Count in tenths, read and write numbers with 1 decimal place
and compare numbers with one decimal place
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds
Count on/back in ½s , ¼s , 1/3s and 1/10s including on a number
line
Find complements to 100 and recall addition and subtraction
facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 –
63 = 37)
Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived
division facts
Double any number up to 100; double any multiple of 50 up to
500 and halve any number up to 200
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 3 Assessment
Assessment: Meeting Year 3 Expectations
Year 3 Expectations: Number
•
•
•
•
•
•
The main focus on assessment will be
measuring a pupil’s journey towards and
beyond the Year 3 expectations. The Year 3
expectations for number are set out on the
right hand side of this page.
To meet the Year 3 expectations a pupil
must be able to meet all of the statements
outlined in the table, plus the ones for
measurement and geometry, shown later.
If they have not met all the statements then
they will be deemed to be emerging.
If a pupil is meeting the expectations then
an assessment needs to made as to
whether a pupil is exceeding the
expectations.
The next page sets out how to assess
whether a pupil is exceeding this
expectation or whether a pupil is at the
emerging stage.
The next page also provides you with a 9point scale for deeper analysis, if required.
• Compare and order numbers to 1000 and read
and write numbers to 1000 in numerals and words
• Count from 0 in multiples of 4, 8, 50 and 100
• Recognise the value of each digit in a 3-digit
number
• Understand and count in tenths, and find the
fractional value of a given set
• Add and subtract fractions with a common
denominator
• Derive and recall multiplication facts for 3, 4 and
8x multiplication tables
• Add and subtract mentally combinations of 1digit and 2-digit numbers
• Add and subtract numbers with up to 3-digits
using formal written methods
• Write and calculate mathematical statements for
multiplication and division; including 2-digit number
with a 1-digit number (from multiplication tables they
know, ie, 2, 3, 4, 5, 8 and 10)
• Solve number problems using one and two step
operations
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 3 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
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Assessment: Meeting Year 3 Expectations
A pupil will be deemed to be
meeting the expectations only if
they can satisfy their teacher
that they meet all the
expectations for their age
A pupil will be deemed to be
emerging towards the
expectations if they do not meet
all of the statements outlined for
that year group
•Meeting the expectations (Stage
C) – Point 4
•It is accepted that a pupil might
make the occasional error if they
are at this stage. However,
despite that, the teacher needs
to be satisfied that they
understand the concept fully.
•Meeting the expectations (Stage
B) - Point 5
•At this stage a pupil will rarely
make mistakes and is very
confident at meeting the
statements.
•Meeting the expectation (Stage
A)- Point 6
•At this stage, not only is the pupil
confident at meeting the
statements but works at a rapid
rate. However, they are not yet
meeting all the statements for
exceeding.
•If they meet more than 75% of
the statements but not all then
they will be described as:
•Emerging towards the
expectations (Stage C) – Point 3
•If they meet between 50% and
75% of the statements then they
will be described as:
•Emerging towards the
expectations (Stage B) – Point 2
•However if they are not meeting
50% of the expectations they will
be described as:
•Emerging towards the
expectations (Stage A) – Point 1
•There is, therefore, no
requirement to write a set of
emerging statements
© Focus Education (UK) Ltd 2014
A pupil will be deemed to be
exceeding the expectations when, in
addition to the statements set out for
meeting the expectation (Stage
A)they meet one or more of three sets
of further expectations
•Pupils will be deemed to be exceeding
expectations if, in addition to what is
outlined as Point 6, they show evidence
of:
•Accessing some of the following year
group’s objectives
•Being able to use the year group’s
expectation within context
•Being able to consistently apply the year
group objectives in a range of situations.
•A set of exceeding statements are set out
for you to feel secure about your
judgements.
•If a pupil is meeting the exceeding
statements, they will be deemed to be at
Point 7 (Stage C)
•If they are very confident and rarely
make a mistake in relation to the
‘exceeding’ statements then they will be
judged at Point 8 (Stage B)
•A few pupils will be judged at Point 9
(Stage A). These will be pupils who are
exceptionally confident in handling the
exceeding statements and show
exceptional mathematical ability for their
age
190
Assessment: Meeting Year 3 Expectations
Year 3 Expectations: Number
• Compare and order numbers to 1000 and read
and write numbers to 1000 in numerals and words
• Count from 0 in multiples of 4, 8, 50 and 100
• Recognise the value of each digit in a 3-digit
number
• Understand and count in tenths, and find the
fractional value of a given set
• Add and subtract fractions with a common
denominator
• Derive and recall multiplication facts for 3, 4 and
8x multiplication tables
Year 3 Expectations: Measurement,
Geometry and Statistics
• Identify right angles; compare other angles to
being greater or smaller than a right angle
• Identify horizontal and vertical lines and pairs of
perpendicular and parallel lines
• Tell time to nearest minute and use specific
vocabulary: seconds, am and pm
• Measure, compare, add and subtract using
common metric measures
• Solve one-step and two step problems using
information presented in scaled bar charts,
pictograms and tables
• Add and subtract mentally combinations of 1digit and 2-digit numbers
• Add and subtract numbers with up to 3-digits
using formal written methods
• Write and calculate mathematical statements for
multiplication and division; including 2-digit number
with a 1-digit number (from multiplication tables they
know, ie, 2, 3, 4, 5, 8 and 10)
• Solve number problems using one and two step
operations
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Assessment: Exceeding Year 3 Expectations
Year 3 Exceeding Expectations
• Recognise the value of each digit in a 4-digit number and the
value of a tenth
• Know all multiplication facts up to 10 x 10 and be able to
instantaneously answer questions such as, how many 7s in 42?
• Add and subtract numbers with any number of digits using
formal written methods
• Begin to have an understanding about negative numbers
recognising they are smaller than zero
• Multiply and divide any 2-digit number by a single digit
number and have an understanding of ‘remainder’
• Can find fractional values (from ½ to 1/10 )of amounts up to
1000
• Use knowledge of number to solve problems related to
money, time and measures
• Know that the total internal angles of a triangle measure 180°
and can measure each
• Can relate knowledge of time to problems related to
timetables
• Measure, compare, add and subtract more complex problems
using common metric measures set out in Kg, g; Kl, l; Km and m,
etc.
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Focus on Mathematics
Year 3 Parents’ Guide
‘Must Dos’ by the end of Year 3
•
•
•
•
•
•
•
•
•
Write down all numbers said to them
up to 1000
Know place value of each digit in a
3-digit number
Order a set of 3-digit numbers:
greatest first, smallest first
Count on and back from any number
in 2s, 3s, 4s, 5s, 8s, 10s, 50s, and 100s
up to 1000
Know 100 more than a given number
to 1000
Know 100 less than a given number to
1000
Add 2 or 3 numbers with 3-digits, using
column addition
Subtract 2 numbers with 3-digits using
column subtraction
Rapid recall: Add rapidly a 3-digit
number to a 1-digit number; to a 10s
number; and to a 100s number
•
•
•
•
•
•
•
•
•
•
Subtract rapidly a 1-digit number
from a 3-digit number; a 10s number
and a 100s number
Rapid Recall: 2x, 3x, 4x, 5x, 8x, 10s
tables and their inverses
Multiply a 2-digit number by a 1-digit
number
Divide 2, 3, 4, 5, 8 and 10 into a 2-digit
number (no remainder)
Fractions: Find ½,¼, 1/5 of a 2-digit
number
Order fractions from ½ to 1/12
Know pairs of fractions that make up
1 whole
Know equivalent fractions of ½,¼,⅕
and 1/10
Add 2 fractions with same
denominator
Subtract 1 fraction from another with
same denominator
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year Group Objectives
Year 4
Year 4 Objectives: Number 1
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 1: Count in multiples of 6, 7, 8, 9,
10, 25, 50, 100 and 1000 from any given
number.
Objective 2: Read and write numbers to at
least 10,000
Count on and back in 1000s from 0 to 10,000
*1
Count on and back in 10s from any given
number between 0 and 10,000
Count on and back in 100s from 0 to 10,000
Count on and back in 50s from 0 to 1000 starting
at any given number
*2
Read and write numbers to 5000
*2
Read and write numbers to 10,000
*3
Objective 3: Find a 1000 more or less than a
given number
*1
Find 100 more or less than any 4-digit number
*3
Find 1000 more or less than any 4-digit number
Count on in 8s from 0 to 1000 starting at any
given number
Count on in 7s from 0 to 1000 starting at any
given number
*1
Find 100 more or less than any 3-digit number
Count on and back in 25s from 0 to 1000 starting
at any given number
Count on and back in 9s from 0 to 1000 starting
at any given number
Revise reading and writing numbers to: 100 and
then to 1000;
*2
Find 1000 more than any 2 or 3-digit number
*4
Count on in 6s from 0 to 1000 starting at any
given number
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Year 4 Objectives: Number 2
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 4: Recognise the place value of
each digit in a 4-digit number (thousands,
hundreds, tens and ones)
Objective 6: Identify, represent and estimate
numbers using different representations
Know and use terms: units, ones, tens, hundreds
and thousands correctly
*1
Know that 6 thousands, 3 hundreds, 2 tens and 5
ones is 6325
Partition any number up to 9,999 showing the
value of each digit
*2
Know that an object of 74.8m is longer than one of
476cm
*2
Know that 8562cm is 85.62m
*3
Objective 5: Order and compare numbers
beyond 1000
Know which of two 4-digit numbers is the
greater and smaller
*1
Order a set of 4-digit numbers from smallest to
largest
*2
Order a set of 4-digit numbers from largest to
smallest
Know that 5 hundred, 6 tens and 3 ones is 563
*1
Know that 9042ml is 9.042l
Objective 7: Round any number to the nearest
10, 100 or 1000
Round any number up to 100 to the nearest 10
*1
Round any number up to 1000 to the nearest 10
Round any number up to 1000 to the nearest 100
*2
Round any number up to 10,000 to the nearest 1000
*3
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Year 4 Objectives : Number 3
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 8: Count backwards through zero to
include negative numbers
Objective 10: Read Roman numerals to 100
(1 to C) and know that, over time, the
numeral system changed to include the
concept of zero and place value
Know that the value of any negative number is less than
0
*1
Know which of 2 negative numbers is the greater, eg. -2
is greater than -5
Know the Roman numerals from 1 to 10
*1
Know which of 2 negative numbers is the smaller, eg. -7
is smaller than -4
Know the Roman numerals for 50
*2
Count accurately forwards from any negative number
to any positive number, moving across the 0
*2
Know the Roman numerals for 100
Count accurately backwards from any positive number
to any negative number, moving across the 0
Order a set of negative and positive numbers showing
largest or smallest first
Objective 9: Solve word problems involving
all of the above and increasingly large
positive numbers
Solve problems which require movement between
negative and positive numbers
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 4
ADDITION AND SUBTRACTION
Objective 11: Add and subtract numbers
with up to 4-digits using the formal written
methods of columnar addition and
subtraction where appropriate
Objective 12: Add and subtract numbers
mentally including two 2-digit numbers (with
increasingly larger numbers)
(Non- statutory)
Add 2 numbers with 4-digits together using
columnar addition without exchange between
units and tens
*1
Add together mentally any single-digit and any
2-digit number
Add 2 numbers with 4-digits together using
columnar addition, where the units, tens or
hundreds when added make more than 10.
*2
Subtract any single-digit number from a 2-digit
number
Add together mentally any single-digit and any
3-digit number
Add 3 numbers with 4-digits using columnar
addition where the units, tens or hundreds make
more than 10
Subtract any single-digit number from a 3-digit
number
Subtract a 4-digit number from another using
columnar subtraction which requires no
exchange between the units, tens, hundreds or
thousands
*3
Subtract a 4-digit number from another using
columnar subtraction which requires exchange
between the units, tens, hundreds or thousands
(or any two of these)
*4
Add together mentally any two 2-digit numbers
Subtract mentally any two 2-digit numbers
Add together mentally any 1000s number and
any 4-digit number
Subtract any 1000s number from a 4-digit
number
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 5
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 13: Estimate and use inverse
operations to check answers to a
calculation
Objective 14: Solve addition and subtraction
two-step problems in contexts, deciding
which operations to use and why
Estimate the answer to any given addition
involving two 2-digit numbers to the nearest 10
*1
Solve two-step word problems involving addition
with numbers up to 1000
Estimate the answer to any given addition
involving two 3-digit numbers to the nearest 100
*2
Solve two-step word problems involving
subtraction with numbers up to 1000
Estimate the answer to any given addition
involving two 3-digit numbers to the nearest 10
Solve two-step word problems involving
addition and subtraction with numbers up to
1000
Estimate the answer to any given subtraction
involving two 2-digit numbers to the nearest 10
Estimate the answer to any given subtraction
involving two 3-digit numbers to the nearest 100
Estimate the answer to any given subtraction
involving two 3-digit numbers to the nearest 10
Know the meaning of the term ‘inverse’
*3
Check the answer to any given addition
involving 2 numbers by using the inverse method
Check the answer to any given subtraction by
using the inverse method
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 6
Objective 15: Recall multiplication and division
facts for tables up to 12 x 12
MULTIPLICATION AND DIVISION
Recite all multiplication facts for the x9 table
Objective 17: Multiply and divide 2-digit and 3digit numbers by 1-digit number using formal
written layout
Multiply a 100s number by a single-digit number
mentally, using 2, 3, 4, 5, 6, 7, 8, and 9x
*1
Recite all multiplication facts for the x11 table
Recite all multiplication facts for the x7 table
Multiply a 2-digit number by a
single-digit number using 2, 3, 4, 5, 6, 7, 8, and 9x
*2
Recite all multiplication facts for the x12 table
Multiply a 3-digit number by a single-digit number
using 2, 3, 4, 5, 6, 7, 8, and 9x
Recall all number facts for the 6, 7, 9, 11 and 12x
table out of sequence
Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 10s number
(no remainder)
*3
Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 2-digit
number (no remainder)
*4
Recite all multiplication facts for the x6 table
*1
Know the inverse of all table facts involving 6, 7, 9,
11 and 12x table, eg. how many 7s in 63?
*2
Objective 16: Use place value, known and derived
facts to multiply and divide mentally, including
multiplying by 0 and 1; dividing by 1; multiplying
together three numbers
Use all table facts up to 12x in calculations
involving multiplication and division
Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 3-digit
number (no remainder)
Objective 18: Recognise and use factor pairs
and commutativity in mental calculations
Know the term ‘prime factor’ and what it means
Know what happens when multiplying by 0 or 1
Know all the factors within all numbers to 10
Know what happens when dividing by 1
Work out all the factors within any number up to 144
Know what happens when 3 numbers are
multiplied together
Know the term ‘square number’ and know all the
square numbers associated with numbers 1 to 144
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 7
MULTIPLICATION AND DIVISION
Objective 19: Solve problems involving multiplying
and dividing including using the distributive law to
multiply two digits by one digit, integer scaling
problems and harder correspondence problems
such as n objects are connected to m objects
Solve word problems involving multiplication with
numbers up to 1000
Solve word problems involving division with numbers up
to 1000
Use the distributive law to solve problems, eg. 39 x 7 = 30
x7+9x7
Use the associative law to solve problems, eg. (2x3) x 4 =
2 x (3x4)
Solve mental and written calculations, eg. 2 x 6 x 5 = 10
x 6 = 60
Solve a range of two-step problems, choosing the
appropriate operation
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 8
FRACTIONS
FRACTIONS
Objective 20: Recognise and show, using
diagrams, families of common equivalent
fractions with denominators up to and
including 12
Objective 22: Move up and down in
hundredths; recognise that hundredths arise
when dividing an object by one hundred
and dividing tenths by ten
Know all the equivalent fractions of ½ up to
and including the denominator 12
*1
Count from 1/100 to 99/100
Know all the equivalent fractions of ¾ up to
and including the denominator 12
*2
Know all the equivalent fractions of ⅓ up to
and including the denominator 12
*3
Objective 23: Solve problems involving
increasingly harder fractions to calculate
quantities, and fractions to divide quantities,
including non-unit fractions where the
answer is a whole number
Know all the equivalent fractions of ⅔ up to
and including the denominator 12
*4
Know all the equivalent fractions of ¼ up to
and including the denominator 12
Objective 21: Write equivalent fraction of a
fraction given the denominator or numerator
Objective 24: Recognise fractions in their
simplest form
Reduce any fraction with a denominator of up
to 12 to its simplest form
Write the equivalent fraction when given the
denominator
Objective 25: Add and subtract 2 fractions
with the same denominator
Write the equivalent fraction when given the
numerator
Add two fractions with a denominator of 4, 5, 6,
10 where the answer is less than 1 whole
*1
Subtract any two fractions with a denominator
of 4, 5, 6, 10
*2
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Number 9
DECIMALS
Objective 26: Recognise and write decimal
equivalents of any number of tenths and
hundredths
Know that 1/10 is 0.1
*1
Know that 6/10 is 0.6
Know that 0.01 is 1/100
*2
Know that 3/100 is 0.03
Objective 27: Recognise and write decimal
equivalents to ¼, ½, ¾
Know that ½ is 0.5
Know that ¼ is 0.25
Know that ¾ is 0.75
Objective 28: Find the effect of dividing a 1 or 2-digit
number by 10 and 100; identify the value of the digits
in the answer as ones, tenths and hundredths
Divide any 2-digit number by 10 and express
answer in terms of tenths
*1
Divide any 2-digit number by 100 and express
answer in terms of tenths and hundredths
*2
DECIMALS
Objective 29: Estimate, compare and
calculate different measures, including
money in pounds and pence
Carry out simple problems involving money,
length, weight, and time
Objective 30: Compare numbers with the
same number of decimal places up to 2
decimal places
Given 3 numbers with one decimal place, eg.
34.2; 45.7; 12.8; work out the smallest and largest
number and put them in order
*1
Given 3 numbers with two decimal places, eg.
15.67; 19.56; 12.78; work out the smallest and
largest number and put them in order
*2
Given a set of numbers with either 1 or 2
decimal places put them in order of either
largest first or smallest first
*3
204
© Focus Education (UK) Ltd 2014
Focus on Mathematics
Year 4 Pre-Learning Tasks
Number
Focus on Mathematics: Year 4
Name
Objective 1 (i)
Date
Number
Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given
number.
Can you count on or back as required?
3000, 4000
*1
200, 300
2315, 3315
173, 273
8000, 7000
500, 400
4136, 3136
883, 783
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 1(ii)
Date
Number
Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given
number.
Can you count on or back as required?
150, 200
*3
75, 100
231, 281
67, 92
850, 800
500, 475
413, 363
883, 858
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 1(iii)
Date
Number
Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given
number.
Can you count on or back as required?
36, 45, 54
*4
64, 72, 80
41, 50, 59
165,173
72, 63, 54
880, 872
177,168,159
673, 665
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 1(iv)
Date
Number
Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given
number.
Can you count on or back as required?
49, 56, 63
*4
66, 72, 78
89, 96,103
168,174
84, 77, 70
881, 875
176,169,162
693, 687
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 2
Date
Number
Read and write numbers to 10,000 in numerals and words
Can you write these numbers in
numerals?
Can you write these numbers in words?
Two hundred and
fourteen
*1
461
One thousand,
three hundred
and sixty-four
*2
79
Nine thousand,
one hundred and
two
1,247
Four thousand,
three hundred
and eighty- three
8,392
Sixteen thousand,
four hundred and
five
*3
9,709
© Focus Education (UK) Ltd 2014
*2
*3
210
Focus on Mathematics: Year 4
Name
Objective 3
Date
Number
Find a 1000 more or less than a given number
Can you find the number 100 more or
less than?
*1
100 more than
356
Can you find the number 1000 less
than?
100 less than
498
1000 less than
3417
100 more than
1786
1000 more than
876
100 less than
3395
1000 more than
85
100 more and
then 100 less
than
2291
more
less
*2
1000 more than
2478
1000 more and
then 1000 less
than 2503
© Focus Education (UK) Ltd 2014
more
less
211
Focus on Mathematics: Year 4
Name
Date
Objective 4
Number
Recognise place value of each digit in a 4-digit number (thousands,
hundreds, tens, ones)
Can you place the thousands, hundreds, tens and the units in the correct
place?
2317
Thousands
Hundreds
Tens
Units
Partition these numbers
*1
4315
3100
Thousands
Hundreds
Tens
Units
*2
(4000 + 300 + 10 +5)
6670
5682
6426
Thousands
Hundreds
Tens
Units
8723
1873
6150
Thousands
Hundreds
Tens
Units
9902
8953
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Date
Objective 5
Number
Order and compare numbers beyond 1000
Can you say which is the greater and
the smaller number?
Greater
Smaller
*1
Can you order these numbers (smallest
first)?
206, 1340, 980
1432 or 2135
2012, 1506, 1113
6132 or 5690
267, 9280, 1227
6357 or 2234
8303, 3296, 1305
1139 or 2393
2430, 4788, 9824
1095 or 2091
1155, 578, 5902
1000 or 908
675, 958, 5230
207 or 7023
6119, 6657, 5458
6626 or 4404
2015, 5806, 5961
175 or 7670
2075, 2970, 2576
© Focus Education (UK) Ltd 2014
*2
213
Focus on Mathematics: Year 4
Name
Date
Objective 6
Number
Identify, represent and estimate numbers using different representations
Can you put each digit in the correct
column?
Th
H
T
U
Can you write these as £ and p or as
m and cm?
*1
551
*3
1728cm
663
7579
8323cm
1086
9411p
7960
Which is the greater?
4913p
*2
1145p or £31.21
3785cm
6208p
1167p or £1.23
1374p
450cm or 1m 19cm
4m 78cm or 587cm
878cm
61m or 5567cm
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Date
Objective 7
Number
Round any number to the nearest 10, 100 or 1000
Can you round these numbers to the nearest 10, 100 or 1000?
67 to the
nearest 10
*1
771 to the
nearest 100
72 to the
nearest 10
1987 to the
nearest 1000
145 to the
nearest 10
8756 to the
nearest 1000
567 to the
nearest 10
9385 to the
nearest 1000
234 to the
nearest 100
*2
*3
3567 to the
nearest 1000
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 8
Date
Number
Count backwards through zero to include negative numbers.
Can you tell me which is the
greatest?
0, 2, -2
*1
What comes next in these
sequences?
3, 2, 1, 0, -1,
-4, 0, -5
-5, -4, -3, -2, -1
9, -4, 0, -14
-2, -3, -4, -5
-8, 0, 6, -3
1, 0, -1, -2, -3
*2
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Date
Objective 10
Number
Read Roman numerals to 100 (1 to C) and know that over time, the
numeral system changed to include the concept of zero and place value
Can you write these numbers as Roman numerals?
5
*1
23
9
19
3
75
10
92
6
100
© Focus Education (UK) Ltd 2014
*2
217
Focus on Mathematics: Year 4
Name
Date
Objective 11
Number
Add and subtract numbers with up to 4-digits using the formal written
methods of columnar addition and subtraction where appropriate
Can you calculate these accurately?
1323
1234+
1135
1412+
1062
2025+
1172
4123+
1237
1459+
1648
1225+
2723
1645+
1175
1236+
3451
2429+
2356
3482+
1273
3566+
3291
3251+
5672
1345
1436+
7562
2386
4375+
8943
1923
4578+
9532
7321
5659+
*1
3276
1033-
3459
1246-
1569
2163-
4777
1555-
*3
*2
3450
1126-
7892
3569-
3819
2720-
4279
3458-
*4
5353
2466-
6211
3736-
7351
5675-
8432
4677-
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 13
Date
Number
Estimate and use inverse operations to check answers to a calculation
Can you quickly estimate the answers
to these calculations to the nearest 10?
27 + 65
*1
39 - 13
What do you notice about these
calculations?
67 + 35
*3
102 - 67
35 + 56
26 + 19
135 + 121
256 - 135
Can you quickly estimate the
answers to these calculations to the
nearest 100?
345 - 190
*2
729 + 260
760 - 205
845 + 190
205 + 555
724 - 128
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Objective 15
Date
Number
Recall multiplication and division facts for tables up to 12 x 12
Can you complete these very quickly?
(2 minutes maximum)
5x7
*1
Can you complete these very quickly?
(2 minutes maximum)
How many 7s in 35?
9x3
How many 12s in 24?
11 x 8
How many 2s in 36?
6 x 10
How many 8s in 64?
7 x 12
How many 9s in 27?
9x4
How many 11s in 33?
4x8
How many 3s in 27?
10 x 9
How many 8s in 88?
10 x 10
How many 6s in 42?
© Focus Education (UK) Ltd 2014
*2
220
Focus on Mathematics: Year 4
Name
Date
Objective 17
Number
Multiply and divide 2-digit and 3-digit numbers by 1-digit number using
formal written layout
Can you multiply or divide these accurately?
200
3x
400
5x
600
4x
300
8x
37
9x
48
5x
72
6x
75
8x
51
9x
56
7x
73
6x
91
5x
672
6x
562
7x
943
8x
532
9x
*1
90 ÷ 9
50 ÷ 2
60 ÷ 3
80 ÷ 4
*3
*2
12 ÷ 6
87 ÷ 3
84 ÷ 7
56 ÷ 8
*4
324 ÷ 4
720 ÷ 9
865 ÷ 5
658 ÷ 7
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 4
Name
Date
Objective 20
Number
Recognise and show, using diagrams, families of common equivalent
fractions with denominators up to and including 12
Can you work out the missing numbers to complete these fractions?
2
4
=
3
= 6
2
8
=
3
=
6
8
=
9
= 3
2
6
=
3
=
4
4
6
=
6
=
8
= 1
*1
1
3
6
=
3 =
12
*2
9 =
12
= 1
*3
3
9
=
= 2
*4
6
9
=
=
4
8
8
=
=
=
6
6
© Focus Education (UK) Ltd 2014
=
12
=
2
*1
4
*2
4
12
12
=
=
3
3
*3
*4
222
Focus on Mathematics: Year 4
Name
Date
Objective 25
Number
Add and subtract 2 fractions with the same denominator
Can you work out the missing numbers to complete these fractions?
2
4
+1
4
=
3
6
-
1
6
=
1
6
+ 2
6
=
3
4
-
1
4
=
3
10
+
1
10
=
7
10
-
3
10
=
1
5
+
3
5
=
3
5
-
1
5
=
1
6
+ 5
6
=
9
10
-
*1
© Focus Education (UK) Ltd 2014
4
10
*2
=
223
Focus on Mathematics: Year 4
Name
Date
Objective 26
Number
Recognise and write decimal equivalents of any number of tenths and
hundredths
Can you write the decimal equivalents of these fractions?
1/10
*1
3/100
3/10
6/100
7/10
5/100
9/10
7/100
5/10
8/100
© Focus Education (UK) Ltd 2014
*2
224
Focus on Mathematics: Year 4
Name
Objective 28
Date
Number
Find the effect of dividing a 1 or 2-digit number by 10 and 100; identify
the value of the digits in the answer as ones, tenths and hundredths
Can you work out the answers to these divisions?
60 ÷ 10
*1
300 ÷ 100
700 ÷ 10
62 ÷ 100
7 ÷ 10
5÷ 100
91 ÷ 10
79 ÷ 100
85 ÷ 10
87 ÷ 100
© Focus Education (UK) Ltd 2014
*2
225
Focus on Mathematics: Year 4
Name
Date
Objective 30
Number
Compare numbers with the same number of decimal places up to 2
decimal places
Can you tell me which is the greatest; and then order them?
4.2; 5.3; 2.7
*1
13.3; 2.17; 2.9,
6.8; 3.1; 9.4
45.1; 4.51; 1.45
5.3; 5.2; 6.1
7.2; 7.19; 7.17
7.27; 7.15; 7.16
8.23; 7.34; 7.43
*2
*3
31.3; 6.17; 3.13
7.21; 5.5; 3.23
Starting Position:
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 4 Group Objectives
Measurement, Geometry and
Statistics
Year 4 Objectives : Measurement 1
MEASUREMENT
MEASUREMENT
Objective 1m: Convert between different
units of measure e.g. km to m; m to cm; cm
to mm; kg to g; l to ml; hour to min; min to
sec; year to month; week to days
Objective 2m: Measure and calculate the
perimeter of composite rectilinear shapes in
centimetres and metres
Revise relationships between measure, ie.
1000m = 1Km; 100cm = 1m; 10mm = 1cm; 1000g
= 1kg; 60 min = 1 hour; 60sec = 1 min; 12 month =
1 year; etc.
Know that the perimeter of a rectangle can be
measured by a simple formula of 2 x length + 2 x
width
Express a distance of more than 1Km in metres
Express a distance of more than 1 cm in mm
Know the term ‘perimeter’
Know that the perimeter of an irregular shape can
be measured by adding each individual side
together
Express a weight of more than 1Kg in grams
Objective 3m: Find area of rectilinear shapes
by counting squares
Express an amount of more than 1l in ml
Know that the area of a square is measured in
squared cm or squared meters, etc.
Express the passing of time of more than 1 hour
in minutes
Express the passing of time of more than 1
minute in seconds
Know the formula for measuring the area of a
square and the area of a rectangle
Objective 4m: Estimate, compare and
calculate different measures, including
money in pounds and pence
Carry out simple problems involving money,
length, weight, and time
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Measurement 2
MEASUREMENT
Objective 5m: Read, write and convert time between analogue
and digital 12- and 24- hour clocks
Know how to set out each analogue time in digital format, eg.
ten past two = 02:10
Can convert between analogue and digital in this way
Know how a 24 hour clock system works, eg. ten past two in the
afternoon = 02:10pm = 1410 hours
Objective 6m: Solve problems involving converting
from hours to minutes; minutes to seconds; years to
months; weeks to days
Convert hours into minutes, eg, 4 hours = 240 minutes
Convert minutes to seconds, eg, 10 minutes = 600 seconds
Convert years to months, eg, 3 years = 36 months
Convert weeks to days, eg, 8 weeks = 56 days
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Geometry
PROPERTIES AND SHAPE
PROPERTIES AND SHAPE
Objective 1g: Compare and classify
geometric shapes, including quadrilaterals
and triangles, based on their properties and
sizes
Objective 3g: Identify lines of symmetry in
2D shapes presented in different orientations
Relate number of angles and sides associated
with triangles; squares; oblongs; circles
Objective 2g: Identify acute and obtuse
angles and compare and order angles up to
two right angles by size
Know what the term symmetry is
Show lines of symmetry in a equilateral or
isosceles triangle
Show lines of symmetry in a square and oblong
Understand about lines of symmetry within a
circle
Know how to describe an acute angle
Know how to describe an obtuse angle
Recognise how angles are measured
Compare angles by size
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Geometry 2
Objective 4g: Complete a simple symmetric figure
with respect to a specific line of symmetry
Create simple symmetrical figures and show line of
symmetry
Recognise line/s of symmetry in given shapes
POSITION AND DIRECTION
Objective 5g: Describe positions on a 2-D grid as
coordinates in the first quadrant
Pinpoint a position on a quadrant using numbers along
the axes
Objective 6g: Describe movements
between positions as translations of a given
unit to the left/right and up/down
Explain a change in a given position by the movement
made along each axes of the quadrant
Objective 7g: Plot specified points and draw sides
to complete a given polygon
Use the numbers along the axes of a quadrant to
complete a given polygon
© Focus Education (UK) Ltd 2014
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Year 4 Objectives : Statistics
STATISTICS
Objective 1s: Interpret and present
discrete and continuous data using
appropriate graphical methods,
including bar charts and time graphs
Read a bar chart accurately with no
scales on the axes
Read a bar chart accurately with scales
on the axes
Read a time graph accurately with no
scales on the axes
Read a time graph accurately with
scales on the axes
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Step up to the Challenge
Year 4
Number
Year 4: Can you challenge yourself to meet the Objective?
Objective 1: Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000
from any given number.
Me
My
Teacher
Can you count on in 6s from 0 to 1000 starting at any given number?
Can you count on in 7s from 0 to 1000 starting at any given number?
Can you count on in 8s from 0 to 1000 starting at any given number?
Can you count on and back in 9s from 0 to 1000 starting at any given
number?
Can you count on and back in 25s from 0 to 1000 starting at any given
number?
Can you count on and back in 50s from 0 to 1000 starting at any
given number?
Can you count on and back in 100s from 0 to 10,000?
Can you count on and back in 10s from any given number
between 0 and 10,000?
Can you count on and back in 100s from 0 to 1000?
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Year 4: Can you challenge yourself to meet the Objective?
Objective 2: Read and write numbers to at least 10,000
Me
My
Teacher
Can you write all numbers in words up to 10,000?
Can you write all numbers in numerals up to 10,000?
Can you write all numbers to 5,000 in words?
Can you write all numbers in numerals up to 5,000?
Can you remember how to write all numbers up to 1,000 in
numerals and in words?
Can you remember how to write all numbers up to 100 in
numerals and in words?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 3: Find1000 more or less than a given number
Me
My
Teacher
Can you find 1000 more than any 2 or 3-digit number
Can you find 1000 less than any 4-digit number?
Can you find 1000 more than any 4-digit number?
Can you find 100 less than any 4-digit number?
Can you find 100 more than any 4-digit number?
Can you find 100 less than any 3-digit number?
Can you find 100 more than any 3-digit number?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 4: Recognise the place value of each digit in a 4-digit
number (thousands, hundreds, tens and ones)
Me
My
Teacher
Me
My
Teacher
Can you partition any number up to 9,999 showing the value of
each digit?
Do you know and use terms: units, ones, tens, hundreds and
thousands correctly?
Objective 5: Order and compare numbers beyond 1000
Can you order a set of 4-digit numbers from largest to smallest?
Can you order a set of 4-digit numbers from smallest to largest?
Can you work out which of two 4-digit numbers is the greater
and smaller?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 6: Identify, represent and estimate numbers using different
representations
Me
My
Teacher
Me
My
Teacher
Do you know that 9042ml is 9.042 l?
Do you know that 8562cm is 85.62m?
Do you know that an object of 74.8m is longer than one of 476cm?
Do you know that 6 thousands, 3 hundreds, 2 tens and 5 ones is
6325?
Do you that 5 hundred, 6 tens and 3 ones is 563?
Objective 7: Round any number to the nearest 10, 100 or 1000
Can you round any number up to 10,000 to the nearest 1000?
Can you round any number up to 1000 to the nearest 100?
Can you round any number up to 1000 to the nearest 10?
Can you round any number up to 100 to the nearest 10?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 8: Count backwards through zero to include negative
numbers
Me
My
Teacher
Can you order a set of negative and positive numbers showing largest
or smallest first?
Can you count accurately backwards from any positive number to
any negative number, moving across the 0?
Can you count accurately forwards from any negative number to
any positive number, moving across the 0?
Do you know which of 2 negative numbers is the smaller, e.g. -7 is
smaller than -4?
Do you know which of 2 negative numbers is the greater, e.g. -2 is
greater than -5?
Do you know that the value of any negative number is less than
0?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 10: Read Roman numerals to 100 (1 to C) and know that
over time, the numeral system changed to include the concept of
zero and place value
Me
My
Teacher
Can you write out all Roman numerals between 0 and 100?
Do you know the Roman numerals for 100?
Can you write out all Roman numerals between 0 and 50?
Do you know the Roman numerals for 50?
Do you know the Roman numerals from 1 to 10?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 11: Add and subtract numbers with up to 4-digits using the
formal written methods of columnar addition and subtraction where
appropriate
Me
My
Teacher
Can you subtract a 4-digit number from another using columnar subtraction
which requires exchange between the units, tens, hundreds or thousands (or
any two of these)?
Can you subtract a 4-digit number from another using columnar
subtraction which requires no exchange between the units, tens, hundreds
or thousands?
Can you add 3 numbers with 4-digits using columnar addition
where the units, tens or hundreds make more than 10?
Can you add 2 numbers with 4-digits together using columnar addition,
where the units, tens or hundreds when added make more than 10?
Can you add 2 numbers with 4-digits together using columnar
addition without exchange between units and tens?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 12: Add and subtract numbers mentally including two 2digit numbers (with increasingly larger numbers)
(Non- statutory)
Me
My
Teacher
Can you subtract any 1000s number from a 4-digit number?
Can you add together mentally any 1000s number and any 4-digit
number?
Can you subtract mentally any two 2-digit numbers?
Can you add together mentally any two 2-digit numbers?
Can you subtract any single-digit number from a 3-digit number?
Can you add together mentally any single-digit and any 3-digit
number?
Can you subtract any single-digit number from a 2-digit number?
Can you add together mentally any single-digit and any 2-digit
number?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 13: Estimate and use inverse operations to check answers
to a calculation
Me
My
Teacher
Can you check the answer to any given subtraction by using the inverse
method?
Can you check the answer to any given addition involving 2 numbers by
using the inverse method?
Do you know the meaning of the term ‘inverse’?
Can you estimate the answer to any given subtraction involving two 3digit numbers to the nearest 10?
Can you estimate the answer to any given subtraction involving two
3-digit numbers to the nearest 100?
Can you estimate the answer to any given subtraction involving two
2-digit numbers to the nearest 10?
Can you estimate the answer to any given addition involving two 3digit numbers to the nearest 10?
Can you estimate the answer to any given addition involving two
3-digit numbers to the nearest 100?
Can you estimate the answer to any given addition involving
two 2-digit numbers to the nearest 10?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 14: Solve addition and subtraction two-step problems in
contexts, deciding which operations to use and why
Me
My
Teacher
Can you solve two-step word problems involving addition and
subtraction with numbers up to 1000?
Can you solve two-step word problems involving subtraction with
numbers up to 1000?
Can you solve two-step word problems involving addition with
numbers up to 1000?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 15: Recall multiplication and division facts for tables up to
12 x 12
Me
My
Teacher
Do you know the inverse of all table facts involving 6, 7, 9, 11 and 12x
table, e.g. how many 7s in 63?
Can you recall all number facts for the 6, 7, 9, 11 and 12x table out of
sequence?
Can you recite all multiplication facts for the x12 table?
Can you recite all multiplication facts for the x11 table?
Can you recite all multiplication facts for the x9 table?
Can you recite all multiplication facts for the x7 table?
Can you recite all multiplication facts for the x6 table?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 16: Use place value, known and derived facts to multiply
and divide mentally, including multiplying by 0 and 1; dividing by 1;
multiplying together three numbers
Me
My
Teacher
Do you know what happens when 3 numbers are multiplied together?
Do you know what happens when dividing by 1?
Do you know what happens when multiplying by 0 or 1?
Can you use all table facts up to 12x in calculations involving
multiplication and division?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 17: Multiply and divide 2-digit and 3-digit numbers by 1digit number using formal written layout
Me
My
Teacher
Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 3-digit number (no
remainder) ?
Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 2-digit number (no
remainder) ?
Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 10s number (no
remainder) ?
Can you multiply a 3-digit number by a single-digit number using 2,
3, 4, 5, 6, 7, 8, and 9x ?
Can you multiply a 2-digit number by a single-digit number using
2, 3, 4, 5, 6, 7, 8, and 9x ?
Can you multiply a 100s number by a single-digit number
mentally, using 2, 3, 4, 5, 6, 7, 8, and 9x ?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 18: Recognise and use factor pairs and commutativity in
mental calculations
Me
My
Teacher
Do you know the term ‘square number’ and know all the square numbers
associated with numbers 1 to 144 ?
Can you work out all the factors within any number up to 144?
Do you know all the factors within all numbers to 10?
Do you know the term ‘prime factor’ and what it means?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 19: Solve problems involving multiplying and dividing
including using the distributive law to multiply two digits by one digit,
integer scaling problems and harder correspondence problems such
as n objects are connected to m objects
Me
My
Teacher
Can you solve a range of two-step problems, choosing the appropriate
operation?
Can you solve mental and written calculations, eg. 2 x 6 x 5 = 10 x 6 =
60?
Can you use the associative law to solve problems, eg. (2x3) x 4 = 2 x
(3x4)?
Can you use the distributive law to solve problems, eg. 39 x 7 = 30 x
7 + 9 x 7?
Can you solve word problems involving division with numbers up
to 1000?
Can you solve word problems involving multiplication with
numbers up to 1000?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 20: Recognise and show, using diagrams, families of
common equivalent fractions with denominators up to and including
12
Me
My
Teacher
Do you know all the equivalent fractions of ⅔ up to and including the
denominator 12?
Do you know all the equivalent fractions of ⅓ up to and including
the denominator 12?
Do you know all the equivalent fractions of ¾ up to and including
the denominator 12?
Do you know all the equivalent fractions of ¼ up to and
including the denominator 12?
Do you know all the equivalent fractions of ½ up to and
including the denominator 12?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 26: Recognise and write decimal equivalents of any
number of tenths and hundredths
Me
My
Teacher
Me
My
Teacher
Do you know that 3/100 is 0.03?
Do you know that 0.01 is 1/100?
Do you know that 6/10 is 0.6?
Do you know that 1/10 is 0.1?
Objective 27: Recognise and write decimal equivalents to ¼, ½, ¾
Do you know that ¾ is 0.75?
Do you know that ¼ is 0.25?
Do you know that ½ is 0.5?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 28: Find the effect of dividing a 1 or 2-digit number by 10
Me
My
Teacher
Me
My
Teacher
and 100; identify the value of the digits in the answer as ones, tenths
and hundredths
Can you divide any 2-digit number by 100 and express answer in
terms of tenths and hundredths?
Can you divide any 2-digit number by 10 and express answer in
terms of tenths?
Objective 30: Compare numbers with the same number of decimal
places up to 2 decimal places
Given a set of numbers with either 1 or 2 decimal places can you
put them in order of either largest first or smallest first?
Given 3 numbers with two decimal places, eg. 15.67, 19.56, 12.78,
can you work out the smallest and largest number and put them
in order?
Given 3 numbers with one decimal place, eg. 34.2, 45.7, 12.8,
can you work out the smallest and largest number and put them
in order?
© Focus Education (UK) Ltd 2014
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Making Mathematics Work
Step up to the Challenge
Year 4
Measurement, Geometry and Statistics
Year 4: Can you challenge yourself to meet the Objective?
Objective 1m: Convert between different units of measure e.g. km to
m; m to cm; cm to mm; kg to g; l to ml; hour to min; min to sec; year
to month; week to days
Me
My
Teacher
Can you express the passing of time of more than 1 minute in seconds?
Can you express the passing of time of more than 1 hour in minutes?
Can you express an amount of more than 1l in ml?
Can you express a weight of more than 1Kg in grams?
Can you express a distance of more than 1 cm in mm?
Can you express a distance of more than 1Km in metres?
Do you remember that: 1000m = 1Km; 100cm = 1m; 10mm =
1cm; 1000g = 1kg; 60 min = 1 hour; 60sec = 1 min; 12 month = 1
year; etc.?
© Focus Education (UK) Ltd 2014
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Year 4: Can you challenge yourself to meet the Objective?
Objective 2m: Measure and calculate the perimeter of a rectilinear
shape (including squares) in centimetres and metres
Me
My
Teacher
Me
My
Teacher
Do you know that the perimeter of an irregular shape can be
measured by adding each individual side together?
Do you know that the perimeter of a rectangle can be measured
by a simple formula of 2 x length + 2 x width?
Do you know the term ‘perimeter’?
Objective 3m: Find area of rectilinear shapes by counting squares
Do you know the formula for measuring the area of a square and
the area of a rectangle?
Do you know that the area of a square is measured in squared
cm or squared meters, etc.?
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Year 4: Can you challenge yourself to meet the Objective?
Objective 5m: Read, write and convert time between analogue
Me
My
Teacher
Me
My
Teacher
and digital 12- and 24- hour clocks
Do you know how a 24 hour clock system works, e.g. ten past two
in the afternoon = 02:10pm = 14:10 hours?
Can you convert between analogue and digital in this way?
Do you know how to set out each analogue time in digital
format, eg. ten past two = 02:10?
Objective 6m: Solve problems involving converting from hours to
minutes; minutes to seconds; years to months; weeks to days
Can you convert weeks to days?
Can you convert years to months?
Can you convert minutes to seconds?
Can you convert hours into minutes?
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Year 4: Can you challenge yourself to meet the Objective?
Objective 2g: Identify acute and obtuse angles and
compare and order angles up to two right angles by size
Me
My
Teacher
Me
My
Teacher
Can you compare angles by size?
Do you know how angles are measured?
Do you know how to describe an obtuse angle?
Do you know how to describe an acute angle?
Objective 3g: Identify lines of symmetry in 2D shapes
presented in different orientations
Do you understand about lines of symmetry within a circle?
Can you show lines of symmetry in a square and oblong?
Can you show lines of symmetry in a equilateral or isosceles
triangle?
Can you explain what the term symmetry is?
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Year 4: Can you challenge yourself to meet the Objective?
Objective 1s: Interpret and present discrete and continuous
data using appropriate graphical methods, including bar
charts and time graphs
Me
My
Teacher
Can you read a time graph accurately with scales on the axes?
Can you read a time graph accurately with no scales on the axes?
Can you read a bar chart accurately with scales on the axes?
Can you read a bar chart accurately with no scales on the
axes?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Non-Negotiables
Year 4 Possible Planning Outline
Year 4 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
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Year 4 Mathematics Non-Negotiables
• Count backwards through zero to include
negative numbers.
• Compare and order numbers beyond
1000.
• Compare and order numbers with 2
decimal places.
• Read Roman numerals to 100.
• Find 1000 more/less than a given number.
• Count in multiples of 6, 7, 8, 9, 25 & 1000.
• Recall and use multiplication and division
facts all tables to 12x12.
• Recognise place value of any 4-digit
number.
• Round any number to the nearest 10, 100
or 1000.
• Round decimals with 1decimal place (dp)
to nearest whole number.
• Add and subtract:
o Numbers with up to 4-digits using
efficient written method (column).
o Numbers with up to 1dp.
• Multiply:
o 2-digit by 1-digit
o 3-digit by 1-digit
• Divide:
o 3-digit by 1-digit
• Count up/down in hundredths.
• Write equivalent fractions
• Add and subtract fractions with same
denominator.
• Read, write and convert time between
analogue and digital 12 and 24 hour
clocks.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
The following 3 pages suggest a planning outline for delivering the non-negotiables in
classrooms. There should be some element of teaching of these each day.
Autumn Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s and 9s (through
zero to include negative numbers)
Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived division
facts
Count on/back in multiples of 6 and 9 from 0
Count on/back in 25s, 50s, 100s from 0 to 5000 and in 1000s from
0 to 10,000 and beyond
Find 10/100/1000 more or less than a given number beyond 1000
Read and write all numbers to at least 10,000 in both numerals
and words
Partition 4 digit numbers (thousands, hundreds, tens and ones)
Partition in different ways
Order a set of numbers (4 and/or 5 ) to 10,000 and beyond in
increasing and decreasing value
Compare numbers up to 10,000 and beyond using =, <, > symbols
Round numbers up to 10,000 to the nearest 10, 100 or 1000
Count in tenths, read and write numbers with 1 decimal place
and compare numbers with one decimal place
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and 3
digit numbers
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 =
100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
Double any number up to 100; double any multiple of 50 up to
500 and halve any number up to 200
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s
Count on/back in multiples of 6 and 9 from 0
Recall the 2, 3, 4, 5, 6, 8 and 10 times tables and the derived
division facts
Count on/back in 25s, 50s, 100s from 0 to 5000 and in 1000s
from 0 to 10,000 and beyond
Find 10/100/1000 more or less than a given number beyond
1000
Read and write all numbers to at least 10,000 in both numerals
and words
Order a set of numbers (4 and/or 5 ) to 10,000 and beyond in
increasing and decreasing value
Compare numbers up to 10,000 and beyond using =, <, >
symbols
Round numbers up to 10,000 to the nearest 10, 100 or 1000
Count in tenths, hundredths, read and write numbers with up
to 2 decimal places and compare numbers with the same
number of decimal places up to 2 decimal places
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number
and tens and a 3-digit number and hundreds, combinations of
2 and 3 digit numbers
Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions
including on a number line
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 =
100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
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Planning to meet the requirement of the nonnegotiables
Spring Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s
Recall the 2, 3, 4, 5, 6, 8, 9 and 10 times tables and the derived
division facts
Count on/back in multiples of 7 from 0
Count on/back in 25s, 50s, 100s from 0 to 10,000 and in 1000s
from 0 to 10,000 and beyond
Find 10/100/1000 more or less than a given number beyond 5000
Read and write all numbers to at least 10,000 in both numerals
and words
Partition 4 digit numbers (thousands, hundreds, tens and ones)
Partition in different ways
Order a set of numbers (4 and/or 5) to 50,000 and beyond in
increasing and decreasing value
Compare numbers up to 50,000 and beyond using =, <, >
symbols
Round numbers up to and beyond 10,000 to the nearest 10, 100
or 1000
Count in tenths, hundredths, read and write numbers with up to
2 decimal places and compare numbers with the same number
of decimal places up to 2 decimal places
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and
3 digit numbers
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 =
100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s
Recall the 2, 3, 4, 5, 6, 8, 9 and 10 times tables and the derived
division facts
Count on/back in multiples of 7 from 0
Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in
1000s from 0 to 10,000 and beyond
Count in tenths, hundredths, read and write numbers with up to
2 decimal places and compare numbers with the same number
of decimal places up to 2 decimal places
Find 10/100/1000 more or less than a given number beyond 5000
Read and write all numbers to at least 10,000 in both numerals
and words
Order a set of numbers (4 and/or 5) to 50,000 and beyond in
increasing and decreasing value
Compare numbers up to 50,000 and beyond using =, <, >
symbols
Round numbers up to and beyond 10,000 to the nearest 10, 100
or 1000
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and
3 digit numbers
Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions
including on a number line
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 =
100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
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Planning to meet the requirement of the nonnegotiables
Summer Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s, 7s
Recall the 2, 3, 4, 5, 6, 7, 8, 9 and 10 times tables and the derived
division facts
Multiply and divide numbers mentally using place value and
known facts including multiplying by 1 and 0 and dividing by 1
Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in
1000s from 0 to 10,000 and beyond
Count in tenths, hundredths, read and write numbers with up to
2 decimal places and compare numbers with the same number
of decimal places up to 2 decimal places
Find 10/100/1000 more or less than a given number up to 10,000
Read and write all numbers to at least 10,000 in both numerals
and words
Partition 4 and begin to partition 5 digit numbers (thousands,
hundreds, tens and ones) Partition in different ways
Order a set of numbers (4 and/or 5)up to 100,000 in increasing
and decreasing value
Compare numbers up to 100,000 using =, <, > symbols
Round numbers up to 50,000 to the nearest 10, 100 or 1000
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and
3 digit numbers
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 =
100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
Count on/back in steps of 11 and 12
Recall the 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 times tables and the
derived division facts
Multiply and divide numbers mentally using place value and
known facts including multiplying by 1 and 0 and dividing by 1
Multiply together three numbers by using place value and known
facts
Partition 4 and begin to partition 5 digit numbers
Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in 1000s
from 0 to 10,000 and beyond
Count in tenths, hundredths, read and write numbers with up to 2
decimal places and compare numbers with the same number of
decimal places up to 2 decimal places
Find 10/100/1000 more or less than a given number beyond 10,000
Read and write all numbers to at least 10,000 in both numerals and
words
Order a set of numbers (4 and/or 5) to 100,000 and beyond in
increasing and decreasing value
Compare numbers up to 100,000 and beyond using =, <, > symbols
Round numbers up to and beyond 100,000 to the nearest 10, 100 or
1000
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and 3
digit numbers
Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions
including on a number line
Find complements to 100 and to 1000 and recall addition and
subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100,
100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000)
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 4 Assessment
Assessment: Meeting Year 4 Expectations
•
•
•
•
•
•
The main focus on assessment will be
measuring a pupil’s journey towards and
beyond the Year 4 expectations. The Year 4
expectations for number are set out on the
right hand side of this page.
To meet the Year 4 expectations a pupil
must be able to meet all of the statements
outlined in the table, plus the ones for
measurement and geometry, shown later.
If they have not met all the statements then
they will be deemed to be emerging.
If a pupil is meeting the expectations then
an assessment needs to made as to
whether a pupil is exceeding the
expectations.
The next page sets out how to assess
whether a pupil is exceeding this
expectation or whether a pupil is at the
emerging stage.
The next page also provides you with a 9point scale for deeper analysis, if required.
Year 4 Expectations: Number
• Recall all multiplication facts to 12 x 12
• Round any number to the nearest 10, 100 or 1000 and
decimals with one decimal place to the nearest whole
number
• Count backwards through zero to include negative
numbers
• Compare numbers with the same number of decimal
places up to 2 decimal places
• Recognise and write decimal equivalents of any number
of tenths or hundredths
• Add and subtract with up to 4 decimal places using formal
written methods of columnar addition and subtraction
• Divide a 1 or 2-digit number by 10 or 100 identifying the
value of the digits in the answer as Units, tenths and
hundredths
• Multiply 2-digit and 3-digit numbers by a 1-digit number
using formal written layout
• Solve addition and subtraction two-step problems in context
and solve problems involving multiplication and division
• Solve simple measures and money problems involving fractions
and decimals to 2 decimal places
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Assessment: Meeting Year 4 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
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Assessment: Meeting Year 4 Expectations
A pupil will be deemed to be
meeting the expectations only if
they can satisfy their teacher
that they meet all the
expectations for their age
A pupil will be deemed to be
emerging towards the
expectations if they do not meet
all of the statements outlined for
that year group
•Meeting the expectations (Stage
C) – Point 4
•It is accepted that a pupil might
make the occasional error if they
are at this stage. However,
despite that, the teacher needs
to be satisfied that they
understand the concept fully.
•Meeting the expectations (Stage
B) - Point 5
•At this stage a pupil will rarely
make mistakes and is very
confident at meeting the
statements.
•Meeting the expectation (Stage
A)- Point 6
•At this stage, not only is the pupil
confident at meeting the
statements but works at a rapid
rate. However, they are not yet
meeting all the statements for
exceeding.
•If they meet more than 75% of
the statements but not all then
they will be described as:
•Emerging towards the
expectations (Stage C) – Point 3
•If they meet between 50% and
75% of the statements then they
will be described as:
•Emerging towards the
expectations (Stage B) – Point 2
•However if they are not meeting
50% of the expectations they will
be described as:
•Emerging towards the
expectations (Stage A) – Point 1
•There is, therefore, no
requirement to write a set of
emerging statements
© Focus Education (UK) Ltd 2014
A pupil will be deemed to be
exceeding the expectations when, in
addition to the statements set out for
meeting the expectation (Stage
A)they meet one or more of three sets
of further expectations
•Pupils will be deemed to be exceeding
expectations if, in addition to what is
outlined as Point 6, they show evidence
of:
•Accessing some of the following year
group’s objectives
•Being able to use the year group’s
expectation within context
•Being able to consistently apply the year
group objectives in a range of situations.
•A set of exceeding statements are set out
for you to feel secure about your
judgements.
•If a pupil is meeting the exceeding
statements, they will be deemed to be at
Point 7 (Stage C)
•If they are very confident and rarely
make a mistake in relation to the
‘exceeding’ statements then they will be
judged at Point 8 (Stage B)
•A few pupils will be judged at Point 9
(Stage A). These will be pupils who are
exceptionally confident in handling the
exceeding statements and show
exceptional mathematical ability for their
age
268
Assessment: Meeting Year 4 Expectations
Year 4 Expectations: Number
Year 4 Expectations: Measurement,
Geometry and Statistics
• Recall all multiplication facts to 12 x 12
• Round any number to the nearest 10, 100 or 1000 and
decimals with one decimal place to the nearest whole
number
• Compare and classify geometrical shapes,
including quadrilaterals and triangles, based on
their properties and sizes
• Count backwards through zero to include negative
numbers
• Know that angles are measured in degrees and
identify acute and obtuse angles and compare
and order angles up to two right angles by size
• Compare numbers with the same number of decimal
places up to 2 decimal places
• Measure and calculate the perimeter of a
rectilinear shape in centimetres and metres
• Recognise and write decimal equivalents of any
number of tenths or hundredths
• Read, write and convert between analogue and
digital 12 and 24 hour clocks
• Add and subtract with up to 4 decimal places using
formal written methods of columnar addition and
subtraction
• Interpret and present discrete and continuous
data using appropriate graphical methods,
including bar charts and time graphs
• Divide a 1 or 2-digit number by 10 or 100 identifying the
value of the digits in the answer as units, tenths and
hundredths
• Multiply 2-digit and 3-digit numbers by a 1-digit number
using formal written layout
• Solve addition and subtraction two-step problems in context
and solve problems involving multiplication and division
• Solve simple measures and money problems involving
fractions and decimals to 2 decimal places
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Assessment: Exceeding Year 4 Expectations
Year 4 Exceeding Expectations:
• Use tenths, hundredths and thousandths when comparing
values and solving addition and subtraction problems
• Round any number to 100,000 to the nearest 10, 100, 1,000 or
10,000
• Relate tenths and hundredths to fractional values
• Rapidly recall answer when multiplying and dividing a whole
or decimal number by 10
• Solve multi-step problems involving more than one of the
operations
• Work out simple percentage values of whole numbers as is
related to on-going learning in science, history and
geography
• Compare and add fractions whose denominators are all
multiples of the same number
• Use a 24-hour timetable to find out times for a journey
between various places
• Use knowledge of perimeter to work out perimeter of large areas
around school using meters and centimetres
• Collect own data on given project and present information in
graphical formats of their choosing
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Focus on Mathematics
Year 4 Parents’ Guide
Parents’ Guide
‘Must Dos’ by the end of Year 4
Number
•
•
•
•
•
•
•
•
•
•
•
Number
Read and write all numbers to 10,000
Know place value of each digit in a 4digit number
Order a set of 4-digit numbers: greatest
first, smallest first
Count on and back from any number in
2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s,10s, 25s, 50s,
100s and 1000s up to 10,000
Round a number to the nearest 10 or
100
Read and write negative numbers
Count on and back in negative
numbers
Add a number of 4-digit numbers using
formal methods
Subtract 2, 4-digit numbers using formal
methods
Estimate the answer to additions with up
to 3-digit numbers
Estimate the answer to subtractions with
up to 3-digit numbers
•
•
•
•
•
•
•
•
•
Rapid Recall: All table facts up to 12x,
including their inverses
Multiply 2-digit and 3-digit numbers by a
1-digit number
Divide 2-digit numbers by a 1-digit
number
Recognise and use factor pairs within
144
Fractions: Identify and name equivalent
fractions with the same denominator up
to and including 12
Add and subtract fractions with the
same denominator (within 1 whole)
Decimal Fractions: Order decimal
fractions up to tenths and hundredths
Multiply and divide decimal fractions by
10 and 100
Recognise fractional value of decimal
fractions
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year Group Objectives
Year 5
Year 5 Objectives: Number
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 1: Read, write, order and
compare numbers to at least 1,000,000 and
determine the value of each digit
Objective 2: Count forwards and backwards
in steps of powers of 10 (100, 1000, 10,000 )
for any given number up to 1,000,000
Revise reading and writing numbers to: 1000
and then to 10,000.
*1
Read and write numbers to 50,000
Read and write numbers to 1,000,000
Recognise the value of each digit up to
1,000,000
Know and use terms: units; tens, hundreds,
thousands, ten thousands, hundred thousands
and one million correctly
*2
Count onwards and backwards from a given
number in steps of 100s
*1
Count onwards and backwards from a given
number in steps of 1000s
*2
Count onwards and backwards from a given
number in steps of 10,000s
*3
Count onwards and backwards from a given
number in steps of 100,000s
*4
Count onwards and backwards from a given
number in steps of 1,000,000s
Partition any number up to 1,000,000 showing
the value of each digit
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Year 5 Objectives : Number 2
NUMBER AND PLACE VALUE
NUMBER AND PLACE VALUE
Objective 3: Interpret negative numbers in
context, count forwards and backwards with
positive and negative whole numbers,
including through zero
Objective 5: Estimate the answers to
calculations involving addition, subtraction,
multiplication and division
Interpret temperatures at minus ⁰C on a
thermometer
*1
Count forwards from - 20 to + 20
*2
Count backwards from + 30 to -30
Objective 4: Round any number up to
1,000,000 to the nearest 10, 100, 1,000, 10,000
and 100,000
Round any number up to 100 to the nearest 10
*1
Round any number up to 1000 to the nearest 10
Round any number up to 100,000 to the nearest
10,000, 1000, 100 or 10
Round any number up to 1,000,000 to the nearest
100,000, 10,000, 1000, 100 or 10
*1
Estimate the answer to any given addition or
subtraction involving two 3-digit numbers to the
nearest 100
*2
Estimate the answer to any given addition or
subtraction involving two 3-digit numbers to the
nearest 10
*3
Estimate the answer to any given multiplication
involving two 2-digit numbers to the nearest 10
*4
Estimate the answer to any given multiplication
involving two 3-digit numbers to the nearest 100
Estimate the answer to any given multiplication
involving two 3-digit numbers to the nearest 10
Round any number up to 1000 to the nearest 100
Round any number up to 10,000 to the nearest 1,000,
100 or 10
Estimate the answer to any given addition or
subtraction involving two 2-digit numbers to the
nearest 10
*2
Estimate the answer to any given division involving a 2digit number divided by a 1-digit number to the
nearest 10
Estimate the answer to any given division involving a 3digit number divided by a 1-digit number to the
nearest 100
Estimate the answer to any given division involving a 3digit number divided by a 1-digit to the nearest 10
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Year 5 Objectives : Number 3
NUMBER AND PLACE VALUE
ADDITION AND SUBTRACTION
Objective 6: Solve number problems and
practical problems that involve all of the
above, including addition, subtraction,
multiplication and division
Objective 8: Add and subtract whole
numbers with more than 4 digits, including
using formal written methods (columnar
addition and subtraction)
Calculate the answer to any given addition
involving two 2-digit numbers to the nearest 10
Add 2 numbers with 5-digits together using
column addition without exchange between
units and tens
*1
Calculate the answer to any given addition
involving two 3-digit numbers to the nearest 10
Add 2 numbers with 5-digits together using
column addition, where the units, tens or
hundreds when added make more than 10.
*2
Objective 7: Read Roman numerals to 1000
(M) and recognise years written in Roman
numerals
Add 3 numbers with 5-digits using column
addition where the units, tens or hundreds make
more than 10
Calculate the answer to any given addition
involving two 3-digit numbers to the nearest 100
Remember the Roman numerals from 1 to 10
*1
Remember the Roman numerals for 50
*2
Remember the Roman numerals for 100
*3
Know all Roman numerals up to 1000
*4
Subtract a 5-digit number from another using
column subtraction which requires no exchange
between the units, tens, hundreds or thousands
*3
Subtract a 5-digit number from another using
column subtraction which requires exchange
between the units, tens, hundreds or thousands
(or any two of these)
*4
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Year 5 Objectives : Number 4
ADDITION AND SUBTRACTION
ADDITION AND SUBTRACTION
Objective 9: Add and subtract numbers
mentally with increasingly large numbers
Objective 10: Use rounding to check
answers to calculations and determine, in
the context of a problem, levels of
accuracy
Add together mentally any two 2-digit numbers
*1
Subtract any 2-digit number from a 2 or 3-digit
number
Use rounding to add together mentally any two
2-digit numbers, eg. 29 + 39 = 30 + 40 – 2 =
Add together mentally any 2-digit and any 3digit number
Subtract any 2-digit number from a 3 or 4-digit
number
*2
Use rounding to subtract any 2-digit number
from a 2 or 3-digit number, eg. 321 – 19 = 320 –
20
Add together mentally any two 3-digit numbers
*3
Use rounding to add together mentally any two
3-digit numbers, eg. 398 + 449 = 400 + 450 – 3 =
Use rounding to add together mentally any
1000s number and any 5-digit number, eg. 4203
+ 58502 = 4200 + 58500 + 5
Subtract mentally any two 3-digit numbers
Add together mentally any 1000s number and
any 5-digit number
Subtract any 1000s number from a 5-digit
number
*4
Objective 11: Solve addition and
subtraction multi-step problems in
contexts, deciding which operations
and methods to use and why
Solve a range of addition and subtraction multistep problems involving numbers to at least
1, 000, 000
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Year 5 Objectives : Number 5
MULTIPLICATION AND DIVISION
Objective 12: Identify multiples and factors,
including finding all factor pairs of a number
and common factors of two numbers
Identify all multiples of numbers up to 100
Know all factors that make up all numbers to
100
MULTIPLICATION AND DIVISION
Objective 15: Multiply numbers up to 4-digits
by a 1 or 2-digit number using a formal
written method, including long
multiplication for 2-digit numbers
Multiply any number with 3-digits by a single
digit number
*1
Multiply any number with 4-digits by a single
digit number
*2
Multiply any number with 3-digits by a 2-digit
number
*3
Describe what a prime number is
Recognise all prime numbers to 100
Multiply any number with 4-digits by a 2-digit
number
*4
Explain why a number is not a prime number
Objective 16: Multiply and divide mentally,
drawing upon known facts
Objective 14: Establish whether a number up
to 100 is a prime number and recall prime
numbers to 19
Use mental applications to multiply and divide
numbers making use of known number facts
included in x table between x2 and x12
Objective 13: Know and use the vocabulary
of prime numbers, prime factors and
composite (non-prime) numbers
Recognise all prime numbers to 100
Explain why a number is or is not a prime number
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Year 5 Objectives : Number 6
MULTIPLICATION AND DIVISION
MULTIPLICATION AND DIVISION
Objective 17: Divide numbers up to 4-digits
by a 1-digit number using the formal written
method of short division and interpret
remainders appropriately for the context
Divide any number with 3-digits by a single digit
number
*1
Divide any number with 4-digits by a single digit
number
Multiply any 2, 3, 4, 5 or 6-digit number by 10
*1
Divide any 2, 3, 4, 5 or 6-digit number by 10
*2
Multiply any 2, 3, 4, 5 or 6-digit number by 100
Divide any number with 3-digits by a single digit
number with remainder
*2
Divide any number with 4-digits by a single digit
number with remainder
*3
Divide any number with 3-digits by 10, showing
remainder where appropriate
Divide any number with 4-digits by 10, showing
remainder where appropriate
Objective 18: Multiply and divide numbers
by 10, 100 and 1000
Divide any 3, 4, 5 or 6-digit number by 100
Multiply any 2, 3, 4, 5 or 6-digit number by 1000
*3
Divide any 4, 5 or 6-digit number by 1000
*4
*4
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Year 5 Objectives : Number 7
MULTIPLICATION AND DIVISION
MULTIPLICATION AND DIVISION
Objective 21: Solve problems involving addition
Objective 19: Recognise and use square
numbers and cube numbers, and the
notation for squared (²) and cubed (3)
and subtraction, multiplication and division and a
combination of these, including understanding the
meaning of the equals sign
Know the square of all numbers between 2 and
12 by heart
*1
Solve problems involving subtraction with
numbers up to 1,000,000
Use the symbols (²) and (√) accurately
*2
Solve problems involving multiplication with
numbers up to 1,000,000
Know the relationship between the square of a
number and the square root of a number
*3
Solve problems involving division with numbers
up to 1,000,000
Solve problems involving a combination of the
above with numbers up to 1,000,000
Know the cube of all numbers between 2 and
12 by heart
*4
Use the symbol (3) accurately
Objective 20: Solve problems
involving multiplication and division,
including using their knowledge of
factors and multiples, squares and
cubes
Solve problems involving multiplication and division, with
numbers up to 1,000,000
Understand and use the equals sign to indicate
equivalence, including in missing number
problems, e.g. 13 + 24 = 12 + 25
Objective 22: Solve problems involving
multiplication and division including scaling by
simple fractions and problems involving simple rates
Use multiplication and division as inverses, eg.
multiply and divide by powers of 10 in scale
drawings or multiplying and dividing by powers
of a 1000 in converting between units such as
kilometres and metres
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Year 5 Objectives : Number 8
FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES)
Objective 23: Compare and order fractions whose
denominations are all multiples of the same number
Compare and order fractions with the same denominator
Compare and order fractions with denominators of 2, 4 and 8
Compare and order fractions with denominators 5 and 10
Know how to convert fractions with different denominators
into a common denominator
Order 2 different fractions with different denominators that
are multiples of the same number
Order more than 2 different fractions with different
denominators that are multiples of the same number
Objective 24: Identify, name and write equivalent
fractions of a given fraction, represented visually,
including tenths and hundredths
Identify equivalent fractions for 4/6, 5/10, 40/100
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Year 5 Objectives : Number 9
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
Objective 25: Recognise mixed numbers and
improper fractions and convert from one form to the
other and write mathematical statements › 1 as a
mixed number , e.g. ⅖ + ⅘ = 6/5 = 1 ⅕
Know that a whole number can be written as
2/2 or 4/4, etc.
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
Objective 27: Multiply proper fractions and
mixed fractions by whole numbers,
supported by material and diagrams
Know that 1and a half can be written as 3/2
Convert any improper fraction to a mixed
fraction and vice versa
Multiply a proper fraction by 10
*1
same denominator and denominators that are
multiples of the same number
Multiply a proper fraction by any whole number
up to 10
*2
Add two fractions that have the same
denominator with an answer of less than 1
Multiply a mixed fraction by 10
*3
Add two fractions that have the same
denominator with an answer of more than 1,
and then translate to a mixed number
Multiply a mixed fraction by any number up to
10
*4
Objective 26: Add and subtract fractions with the
Subtract two fractions with denominators that
are multiples of the same number
Subtract a fraction from a mixed number with
denominators that are multiples of the same
number
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Year 5 Objectives : Number 10
DECIMALS
DECIMALS
Objective 28: Read and write decimal
numbers as fractions (e.g. 0.71 = 71/100)
*1
Objective 30: Round decimals with 2 decimal
places to the nearest whole number and to
one decimal place
Write any decimal with 1 decimal place as a
fraction
*2
Round any number to the nearest whole number,
e.g. 18.23→ 18
*1
Write any decimal with 2 decimal places as a
fraction
*3
Round any number to one decimal place, eg.
17.91 → 17.9
*2
Write 0.5; 0.25; 0.1; as fractions
Objective 29: Recognise and use
thousandths and relate them to tenths,
hundreds and decimal equivalents
Objective 31: Read, write, order and compare
numbers with up to 3 decimal places
Order decimal fractions with 1 decimal place
*1
Know that 10 thousandths are equivalent to
one tenth
Order decimal fractions with 2 decimal places
*2
Work out how many thousandths there are in
any given hundredth value
Order decimal fractions with 3 decimal places
*3
Work out how many thousandths there are in
any given tenth value
Order a set of decimal fractions with between 1
and 3 decimal places
*4
Work out how many thousandths there are in
any unit value
Work out how many thousandths there are in
any number to include u, t, h and th
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Year 5 Objectives : Number 11
DECIMALS
PERCENTAGES
Objective 32: Solve problems involving
number up to three decimal places
Objective 34: Write percentages as a fraction
with denominator 100, and as a decimal
percentages (eg ½ = 50% = 0.5)
Add numbers with 1 decimal place
Know that 50% is 50/100 = one half = ½
Add numbers with 2 and then 3 decimal places
Know that 0.5 is 50%
Subtract numbers with 1 decimal place
Know that one quarter is 25% = 25/100 = ¼
Subtract numbers with 2 and then 3 decimal
places
Know that 0.25 is 25% = ¼
Solve a range of problems involving the above
Know percentage value of all tenths; fifths;
quarters and eighths
Objective 33: Recognise the %
symbol and understand that per cent
relates to ‘a part of a hundred’
Objective 35: Solve problems which
require knowing percentage and
decimal equivalents of ½, ¼, ⅕, ⅖ ⅘
Know what the % symbol stands for
Objective 36: Solve problems which
require knowing those fractions with a
denominator of a multiple of 10 or 25
Know that percentages deals with everything as
part of 100
© Focus Education (UK) Ltd 2014
*1
*2
284
Focus on Mathematics
Year 5 Pre-Learning Tasks
Number
Focus on Mathematics: Year 5
Name
Objective 1
Date
Number
Read, write, order and compare numbers to at least 1,000,000 and determine
the value of each digit
Can you write these numbers in
numerals?
Two thousand, four
hundred and
fourteen
*1
Can you write these numbers in words?
12,461
Thirteen thousand,
three hundred and
sixty-four
123,879
Two hundred and
four thousand, one
hundred and sixteen
15,247
Four hundred
thousand, three
hundred and eightythree
998,392
Sixty thousand, four
hundred and five
719,709
© Focus Education (UK) Ltd 2014
*2
286
Focus on Mathematics: Year 5
Name
Objective 2
Date
Number
Count forwards and backwards in steps of powers of 10 (100, 1000, 10,000)
for any given number up to 1,000,000
Can you count on or back as required?
100 more than 237
100 more than 327
*1
100 less than 347
100 less than 672
1000 more than 257
1000 more than 4298
100,000 more than 135,478
100,000 more than 656,625
*2
1000 less than 3478
1000 less than 6625
10,000 more than 13478
10,000 more than 65625
10,000 less than 13978
10,000 less than 63628
100,000 less than 435,878
100,000 less than 856,925
1,000,000 more than 135,478
1,000,000 more than 1,656,625
*3
*4
*5
1,000,000 less than 4,935,878
1,000,000 less than 1,856,925
Starting Position:
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Name
Objective 3
Focus on Mathematics: Year 5
Date
Number
Interpret negative numbers in context, count forwards and backwards with
positive and negative whole numbers, including through zero
Can you respond to these problems?
If Room A is 5⁰C and Room
B is 7⁰C, which is warmer?
*1
What comes next?
-3, -4, -5, -6, …
If Room A is -5⁰C and
Room B is -7⁰C, which is
warmer?
2, 1, 0, -1, …
If Room A is 10⁰C and
Room B is -7⁰C, which is
colder?
-4, -3, -2, -1, 0, ….
If Room A is -6⁰C; Room B is
7⁰C and Room c is -3⁰C,
which is warmer?
-7, -6, -5, -4, -3, -2, -1, ….
If Room A is -8⁰C; Room B is
-9⁰C and Room c is -10⁰C,
which is warmer?
3, 2, 1, 0, -1, -2, -3, …
© Focus Education (UK) Ltd 2014
*2
288
Focus on Mathematics: Year 5
Name
Objective 4
Date
Number
Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and
100,000
Can you round these numbers to the nearest 10, 100, 1000, 10,000 or 100,000?
1167 to the
nearest 10
*1
77,771 to the
nearest 1000
272 to the
nearest 10
159,987 to the
nearest 10,000
1145 to the
nearest 100
918,756 to the
nearest 10,000
5607 to the
nearest 100
391,385 to the
nearest
100,000
2134 to the
nearest 1000
357,867 to the
nearest
100,000
© Focus Education (UK) Ltd 2014
*2
289
Focus on Mathematics: Year 5
Name
Date
Objective 5
Number
Estimate the answers to calculations involving addition, subtraction,
multiplication and division
Can you first estimate and then work out these calculations?
Estimate
estimate to nearest 10
18 + 35
Calculate
Estimate
*1
estimate to nearest 10
108 + 350
*2
estimate to nearest 10
472 - 158
estimate to nearest 100
123 x 13
estimate to nearest 100
672 - 158
108 + 650
*4
25 x 14
estimate to nearest 100
estimate to nearest 10
12 x 13
estimate to nearest 10
67 - 15
estimate to nearest 100
estimate to nearest 10
Calculate
250 x 14
*3
estimate to nearest 10
186 ÷ 8
estimate to nearest 10
122 ÷ 6
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Focus on Mathematics: Year 5
Name
Date
Objective 7
Number
Read Roman numerals to 1000 (M) and recognise years written in Roman
numerals
Can you write these numbers as Roman numerals?
5
*1
213
50
*2
199
100
*3
175
406
*4
925
604
288
© Focus Education (UK) Ltd 2014
291
Focus on Mathematics: Year 5
Name
Date
Objective 8
Number
Add and subtract whole numbers with more than 4 digits, including using
formal written methods (columnar addition and subtraction)
Can you calculate these accurately?
13232
12334+
11325
14123+
10462
20257+
11727
41231+
12437
14659+
16448
12255+
27223
16465+
11795
12836+
34571
24259+
23456
34862+
12973
35686+
32971
32519+
56732
13545
14376+
75682
23876
43975+
89943
19243
45778+
95832
73271
56659+
*1
32876
10323-
34599
12416-
15689
21643-
47787
15535-
*3
*2
34450
11326-
78592
35869-
38419
27260-
42879
34588-
*4
53653
24676-
62181
37336-
73581
56775-
84932
46737-
© Focus Education (UK) Ltd 2014
292
Focus on Mathematics: Year 5
Name
Objective 9
Date
Number
Add and subtract numbers mentally with increasingly large numbers
Can you complete these very quickly?
(2 minutes maximum)
23 + 37
*1
16 + 54
106 - 67
Can you complete these very quickly?
(2 minutes maximum)
456 + 345
*3
235 + 765
*2
235 - 156
230 - 34
347 - 289
78 - 34
23,789 + 2,000
348 - 78
16, 987 + 6,000
345 - 67
56,732 - 8,000
1234 - 78
89,765 - 5,000
2346 - 98
72,367- 6,000
© Focus Education (UK) Ltd 2014
*4
293
Focus on Mathematics: Year 5
Name
Date
Objective 15
Number
Multiply numbers up to 4-digits by a 1 or 2-digit number using a formal
written method, including long multiplication for 2-digit numbers
Can you multiply these accurately?
230
3x
405
5x
670
4x
302
8x
317
9x
448
5x
752
6x
785
8x
5231
9x
5645
7x
7223
6x
9541
5x
6723
6x
5662
7x
9413
8x
5532
9x
*1
*2
902
x12
506
x26
607
x24
809
x32
126
x25
873
x45
847
x26
568
x34
3244
x34
7209
x24
8655
x45
6587
x34
© Focus Education (UK) Ltd 2014
*3
*4
294
Focus on Mathematics: Year 5
Name
Date
Objective 17
Number
Divide numbers up to 4-digits by a 1-digit number using the formal written
method of short division and interpret remainders appropriately for the
context
Can you divide these accurately?
235 ÷ 5
348 ÷ 6
248 ÷ 4
237 ÷ 3
3372÷ 6
2645÷5
1036÷7
5154÷6
566÷5
349÷6
247÷8
345÷7
873÷5
567÷9
239÷7
987÷4
*1
*2
9150 ÷ 9
5720 ÷ 7
6076 ÷ 3
1452 ÷ 7
8987 ÷ 6
8114 ÷ 7
3247 ÷ 10
7209 ÷ 10
8656 ÷ 10
© Focus Education (UK) Ltd 2014
*3
*4
295
Focus on Mathematics: Year 5
Name
Objective 18
Date
Number
Multiply and divide numbers by 10, 100 and 1000
Can you multiply or divide as needed?
23 X 10
*1
45456 ÷ 100
345 x 10
25435 ÷ 100
94723 x 10
675345 ÷ 100
235 ÷ 10
*2
34987 x 1000
67543 ÷ 10
23789 x 1000
348761 ÷ 10
16,987 x 1000
3476 X100
562,732 ÷ 1000
123,454 x 100
189,765 ÷ 1000
213,496 x 100
72367÷ 1000
© Focus Education (UK) Ltd 2014
*3
*4
296
Focus on Mathematics: Year 5
Name
Objective 19
Date
Number
Recognise and use square numbers and cube numbers, and the notation
for squared (²) and cubed (3)
Can you write the square number; the square root of the number or the cube of the
number as indicated?
5²
*1
10²
²√100
If the square of a number
is 64, what is its square
root?
*3
If the square of a number
is 81, what is its square
root?
*2
3(3)
²√81
4(3)
²√64
5(3)
© Focus Education (UK) Ltd 2014
*4
297
Focus on Mathematics: Year 5
Name
Date
Objective 26
Number
Add and subtract 2 fractions with the same denominator
Can you put these fractions in order
(smallest first)?
2
4
1
4
3
4
1
6
5
6
4
6
3
4
1
2
3
8
1
5
3
10
6
10
1
2
4
5
*1
3
6
7
10
*2
Can you reorganise these fractions so
that they have the same denominator?
2
3
5
6
7
8
1
2
1
2
*3
3
4
Can you reorganise these fractions so that
they have the same denominator and then
order them (smallest first)?
1
2
3
4
5
8
7
8
1
5
1
2
7
10
9
10
© Focus Education (UK) Ltd 2014
*4
3
5
298
Focus on Mathematics: Year 5
Name
Date
Objective 27
Number
Multiply proper fractions and mixed fractions by whole numbers, supported
by material and diagrams
Can you work out the following calculations?
¾ x 10
*1
2¾ x 10
5/8 x 10
45/8 x 10
2/3 x 10
62/3 x 10
1/6 x 6
*2
71/6 x 6
2/5 x 8
82/5 x 8
¾x7
7¾ x 7
3/5 x 9
53/5 x 9
1/8 x 9
91/8 x 9
© Focus Education (UK) Ltd 2014
*3
*4
299
Focus on Mathematics: Year 5
Name
Date
Objective 28
Number
Read and write decimal numbers as fractions (e.g. 0.71 = 71/100)
Can you write the following decimal numbers as fractions?
0.25
*1
0.15
0.5
2.5
0.1
1.25
0.3
3.75
4.1
*2
*3
6.83
7.3
9.45
6.9
10.75
8.5
3.78
© Focus Education (UK) Ltd 2014
300
Focus on Mathematics: Year 5
Name
Date
Objective 30
Number
Round decimals with 2 decimal places to the nearest whole number and
to one decimal place
Can you round these decimal numbers
to one whole number?
6.25
*1
Can you round these decimal numbers
to one decimal place number?
0.15
7.5
2.58
8.1
1.25
9.3
3.75
11.1
6.83
9.3
9.45
6.9
10.75
8.5
3.78
© Focus Education (UK) Ltd 2014
*2
301
Focus on Mathematics: Year 5
Name
Date
Objective 31
Number
Read, write, order and compare numbers with up to 3 decimal places
Can you order these decimal numbers (smallest first)?
6.2; 7.3; 2.7
*1
0.153; 0.234; 0.765
7.5; 6.1; 4.6
2.584; 6.786; 2.345
8.1; 7.2; 7.7
1.254; 2.319; 1.255
9.3; 8.2; 6.5
3.753; 4.845; 2.735
11.12; 2.65; 7.12
*2
6.83; 1.2; 6.634
9.13; 6.98; 7.45
3.2; 9.45; 3.342
6.93; 5.23; 8.45
10.5; 10.75; 10.456
8.56; 6.78; 5.54
1.9; 3.78 1.659
© Focus Education (UK) Ltd 2014
*3
*4
302
Focus on Mathematics: Year 5
Name
Date
Objective 34
Number
Write percentages as a fraction with denominator 100, and as a decimal
(e.g. ½ = 50% = 0.5)
Can you complete the missing values?
Percentage
(%)
Decimal
Fraction
*1
Percentage
(%)
Decimal
Fraction
50%
3/4
25%
5/6
33%
3/10
0.3
*2
0.6
1/4
2/9
0.75
0.2
© Focus Education (UK) Ltd 2014
303
Focus on Mathematics
Year 5 Group Objectives
Measurement, Geometry and
Statistics
Year 5 Objectives : Measurement
MEASUREMENT
MEASUREMENT
Objective 1m: Convert between different units
of metric measure, e.g. kilometre and metre;
centimetre and metre; centimetre and
millimetre; gram and kilogram; litre and
millilitre
Objective 3m: Measure and calculate the
perimeter of composite rectilinear shapes in
centimetres and metres
Express a distance of more than 1Km in metres
Express a distance of more than 1 cm in mm
Express a weight of more than 1Kg in grams
Express an amount of more than 1l in ml
Objective 2m: Understand and use
approximate equivalences between metric
and common imperial units such as inches,
pounds and pints
Know the approximate number of metres in 1 mile
Know the approximate relationship between inches
and centimetres
Know the approximate relationship between a
pound and a gram
Know that the perimeter of a composite
rectilinear shape is measured by calculating the
length of all the different sides
Objective 4m: Calculate and compare the
area of rectangles (including squares) and
including using standard units, square
centimetres (cm²) and square metres (m²)
and estimate the area of irregular shapes
Know that the area of a square or a rectangle is
measured in cm² or m²
Know that the area of a square is measured by
multiplying the length of a side by itself
Know that the area of a rectangle is measured
by multiplying the length of the longer side by
the shorter
Use this information about calculating the area
of a square or rectangle to work out the area of
irregular shapes that can be divided up into
squares and rectangles
Know the approximate relationship between a pint
and a litre
© Focus Education (UK) Ltd 2014
305
Year 5 Objectives : Measurement 2
MEASUREMENT
MEASUREMENT
Objective 5m: Estimate volume, e.g. Using
1cm³ blocks to build cuboids (including
cubes) and capacity, e.g. using water
Know that volume is measured in cm³ or m³
Objective 7m: Use all four operations to
solve problems involving measure (e.g.
length, mass, volume, money) using
decimal notation, including scaling
Use cubes to work out volume of a given shape
Carry out addition problems which relate to
measurement as in money; length; weight; volume
Use water to estimate and work out the capacity
of a given container
Objective 6m: Solve problems
involving converting between units of
time
Carry out subtraction problems which relate to
measurement as in money; length; weight; volume
Carry out multiplication problems which relate to
measurement as in money; length; weight; volume
Carry out division problems which relate to
measurement as in money; length; weight; volume
Solve problems involving days and weeks, expressing the
answer as weeks and days
© Focus Education (UK) Ltd 2014
306
Year 5 Objectives : Geometry
PROPERTIES of SHAPES
PROPERTIES of SHAPES
Objective 1g: Identify 3-D shapes, including
cubes and other cuboids, from 2–D
representations
Objective 4g: Recognise and compare
different triangles, including isosceles,
equilateral and right angles triangles
Understand relationship between square and
cube; rectangle and cuboid; triangle and prism
and triangle and square based pyramid
Describe an equilateral triangle
Objective 2g: Know angles are measured in
degrees and identify right angles as ¼ turn
(total 90˚); straight line as half turn = 180˚;
whole turn = 360˚
Know that 90˚ is equivalent to quarter a turn
Describe an isosceles triangle
Describe a right angle triangle
Objective 5g: Identify and name
parallelogram; rhombus and trapezium
Know what a parallelogram is and describe it in
mathematical terms
Know that 180˚ is equivalent to half a turn
Know what a rhombus is and describe it in
mathematical terms
Know that 360˚ is equivalent to a full turn
Objective 3g: Estimate and compare
acute, obtuse and reflex angles
Know what a trapezium is and describe it in
mathematical terms
* Objective 3g, 4g, and 5g are non statutory
Estimate and compare acute, obtuse and reflex
angles in a range of drawings
© Focus Education (UK) Ltd 2014
307
Year 5 Objectives : Geometry 2
PROPERTIES of SHAPES
Objective 6g: Draw given angles, and measure them
in degrees (˚)
Draw and be able to measure an angle of 90˚
Draw and be able to measure an angle of 45˚
Draw a given angle using a protractor and label it
appropriately
Objective 7g: Identify angles at a point and one
whole turn (total 360˚)
Objective 8g: Identify angles at a point on a straight
line and ½ a turn (total 180˚)
Identify other multiples of 90 ˚
Objective 9g: Distinguish between regular and
irregular polygons based on reasoning about equal
sides and angles
Explain that a hexagon has more sides and smaller angles
than a pentagon
© Focus Education (UK) Ltd 2014
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Year 5 Objectives : Geometry 3
PROPERTIES of SHAPES
POSITION and DIRECTION
Objective 10g; Use the properties of
rectangles to deduce related facts and find
missing lengths and angles
Draw a square accurately having been given
the length of the side
Draw a rectangle accurately having been
given the length and breadth
Draw an equilateral triangle with a given length
Draw an isosceles triangle accurately given the
length of side and the base
Draw a triangle to a given set of angles and
sides
Objective 11g: Identify, describe and
represent the position of a shape following a
reflection or translation, using the appropriate
language and know that the shape has not
changed
Use a 2-D grid and coordinates in the first
quadrant to reflect and translate different shapes
Use four quadrants to reflect and translate
different shapes
Reflect the shapes in lines that are parallel to the
axes
© Focus Education (UK) Ltd 2014
309
Year 5 Objectives : Statistics
STATISTICS
Objective 2s: Complete, read and interpret
information in tables, including timetables
STATISTICS
Know how to construct a table from a set of
given information
Objective 1s: Solve comparison, sum and
difference problems using information
presented in a line graph
Can read tables with given axes
Can construct own table and make decisions
about the axes
Can compare information on line graphs to
answer questions
Know what a pie chart is
Can solve sum problems using information on
line graphs to answer questions
Can read a simple pie chart with segments that
are divisible by 10
Can solve difference problems using information
on line graphs to answer questions
Can interpret timetables to answer questions
Know how to construct a bar graph from a set
of given information
Know how to apply scales on the axes of a bar
graph
Can read bar graphs with scales
Can construct own bar graph and make
decisions about the scales for the axes
© Focus Education (UK) Ltd 2014
310
Focus on Mathematics
Step up to the Challenge
Year 5
Number
Year 5: Can you challenge yourself to meet the Objective?
Objective 1: Read, write, order and compare numbers to at least
1,000,000 determine the value of each digit
Me
My
Teacher
Can you partition any number up to 1,000,000 showing the value of
each digit?
Do you know and use terms: units; tens, hundreds, thousands, ten
thousands, hundred thousands and one million correctly?
Can you recognise the value of each digit up to 1,000,000?
Can you read and write numbers to 1,000,000?
Can you read and write number to 50,000?
Can you remember how to read and write numbers to: 1000 and
then to 10,000?
© Focus Education (UK) Ltd 2014
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Year 5: Can you challenge yourself to meet the Objective?
Objective 2: Count forwards and backwards in steps of powers of 10
(100, 1000, 10,000 ) for any given number up to 1,000,000
Me
My
Teacher
Me
My
Teacher
Can you count onwards and backwards from a given number in steps
of 1,000,000s?
Can you count onwards and backwards from a given number in
steps of 100,000s?
Can you count onwards and backwards from a given number in
steps of 10,000s?
Can you count onwards and backwards from a given number in
steps of 1000s?
Can you count onwards and backwards from a given number in
steps of 100s?
Objective 3: Interpret negative numbers in context, count forwards
and backwards with positive and negative whole numbers, including
through zero
Can you count backwards from + 30 to -30?
Can you count forwards from - 20 to + 20?
Can you interpret temperatures at minus ⁰C on a thermometer?
© Focus Education (UK) Ltd 2014
313
Year 5: Can you challenge yourself to meet the Objective?
Objective 4: Round any number up to 1,000,000 to the nearest 10,
100, 1,000, 10,000 and 100,000
Me
My
Teacher
Can you round any number up to 1,000,000 to the nearest 100,000,
10,000, 1000, 100 or 10?
Can you round any number up to 100,000 to the nearest 10,000, 1000,
100 or 10?
Can you round any number up to 10,000 to the nearest 1,000, 100 or
10?
Can you round any number up to 1000 to the nearest 100?
Can you round any number up to 1000 to the nearest 10?
Can you round any number up to 100 to the nearest 10?
© Focus Education (UK) Ltd 2014
314
Year 5: Can you challenge yourself to meet the Objective?
Objective 5: Estimate the answers to calculations involving addition,
subtraction, multiplication and division
Me
My
Teacher
Can you estimate the answer to any given division involving a 3-digit
number divided by a 1-digit to the nearest 10?
Can you estimate the answer to any given division involving a 3-digit
number divided by a 1-digit number to the nearest 100?
Can you estimate the answer to any given division involving a 2-digit
number divided by a 1-digit number to the nearest 10?
Can you estimate the answer to any given multiplication involving two
3-digit numbers to the nearest 10?
Can you estimate the answer to any given multiplication involving two
3-digit numbers to the nearest 100?
Can you estimate the answer to any given multiplication involving
two 2-digit numbers to the nearest 10?
Can you estimate the answer to any given addition or subtraction
involving two 3-digit numbers to the nearest 10?
Can you estimate the answer to any given addition or subtraction
involving two 3-digit numbers to the nearest 100?
Can you estimate the answer to any given addition or
subtraction involving two 2-digit numbers to the nearest 10?
© Focus Education (UK) Ltd 2014
315
Year 5: Can you challenge yourself to meet the Objective?
Objective 6: Solve number problems and practical problems that
involve all of the above, including addition, subtraction,
multiplication and division
Me
My
Teacher
Me
My
Teacher
Can you calculate the answer to any given addition involving two
3-digit numbers to the nearest 10?
Can you calculate the answer to any given addition involving
two 3-digit numbers to the nearest 100?
Can you calculate the answer to any given addition involving
two 2-digit numbers to the nearest 10?
Objective 7: Read Roman numerals to 1000 (M) and recognise years
written in Roman numerals
Do you know all the Roman numerals to 1000?
Do you know the Roman numerals for 100?
Do you know the Roman numerals for 50?
Can you remember the Roman numerals from 1 to 10?
© Focus Education (UK) Ltd 2014
316
Year 5: Can you challenge yourself to meet the Objective?
Objective 8: Add and subtract whole numbers with more than 4
digits, including using formal written methods (columnar addition and
subtraction)
Me
My
Teacher
Can you subtract a 5-digit number from another using column
subtraction which requires exchange between the units, tens,
hundreds or thousands (or any two of these)?
Can you subtract a 5-digit number from another using column
subtraction which requires no exchange between the units, tens,
hundreds or thousands?
Can you add 3 numbers with 5-digits using column addition where
the units, tens or hundreds make more than 10?
Can you add 2 numbers with 5-digits together using column
addition, where the units, tens or hundreds when added make
more than 10.?
Can you add 2 numbers with 5-digits together using column
addition without exchange between units and tens?
© Focus Education (UK) Ltd 2014
317
Year 5: Can you challenge yourself to meet the Objective?
Objective 9: Add and subtract numbers mentally with increasingly
large numbers
Me
My
Teacher
Can you subtract any 1000s number from a 5-digit number?
Can you add together mentally any 1000s number and any 5-digit
number?
Can you subtract mentally any two 3-digit numbers?
Can you add together mentally any two 3-digit numbers?
Can you subtract any 2-digit number from a 3 or 4-digit number?
Can you add together mentally any 2-digit and any 3-digit
number?
Can you subtract any 2-digit number from a 2 or 3-digit number?
Can you add together mentally any two 2-digit numbers?
© Focus Education (UK) Ltd 2014
318
Year 5: Can you challenge yourself to meet the Objective?
Objective 10: Use rounding to check answers to calculations and
determine, in the context of a problem, levels of accuracy
Me
My
Teacher
Me
My
Teacher
Can you use rounding to add together mentally any 1000s number
and any 5-digit number, e.g. 4203 + 58502 = 4200 + 58500 + 5?
Can you use rounding to add together mentally any two 3-digit
numbers, e.g. 398 + 449 = 400 + 450 – 3 =?
Can you use rounding to subtract any 2-digit number from a 2 or
3-digit number, e.g. 321 – 19 = 320 – 20?
Can you use rounding to add together mentally any two 2-digit
numbers, e.g. 29 + 39 = 30 + 40 – 2 = ?
Objective 12 and 13: Identify multiples and factors, including finding
all factor pairs of a number and common factors of two numbers;
know and use the vocabulary of prime numbers, prime factors and
composite (non-prime) numbers
Can you recognise all prime numbers to 100?
Can you describe what a prime number is?
Do you know all factors that make up all numbers to 100?
Can you identify all multiples of numbers up to 100?
© Focus Education (UK) Ltd 2014
319
Year 5: Can you challenge yourself to meet the Objective?
Objective 15: Multiply numbers up to 4-digits by a 1 or 2-digit number
using a formal written method, including long multiplication for 2digit numbers
Me
My
Teacher
Can you multiply any number with 3-digits by a single digit number?
Can you multiply any number with 4-digits by a single digit number
Can you multiply any number with 3-digits by a 2-digit number?
Can you multiply any number with 4-digits by a 2-digit number?
© Focus Education (UK) Ltd 2014
320
Year 5: Can you challenge yourself to meet the Objective?
Objective 17: Divide numbers up to 4-digits by a 1-digit number
using the formal written method of short division and interpret
remainders appropriately for the context
Me
My
Teacher
Can you divide any number with 4-digits by 10, showing remainder
where appropriate?
Can you divide any number with 3-digits by 10, showing remainder
where appropriate?
Can you divide any number with 4-digits by a single digit number
with remainder?
Can you divide any number with 3-digits by a single digit number
with remainder?
Can you divide any number with 4-digits by a single digit number?
Can you divide any number with 3-digits by a single digit
number?
© Focus Education (UK) Ltd 2014
321
Year 5: Can you challenge yourself to meet the Objective?
Objective 18: Multiply and divide numbers by 10, 100 and 1000
Me
My
Teacher
Can you divide any 4, 5 or 6-digit number by 1000?
Can you multiply any 2, 3, 4, 5 or 6-digit number by 1000?
Can you divide any 3, 4, 5 or 6-digit number by 100?
Can you multiply any 2, 3, 4, 5 or 6-digit number by 100?
Can you divide any 2, 3, 4, 5 or 6-digit number by 10?
Can you multiply any 2, 3, 4, 5 or 6-digit number by 10?
© Focus Education (UK) Ltd 2014
322
Year 5: Can you challenge yourself to meet the Objective?
Objective 19: Recognise and use square numbers and cube
numbers, and the notation for squared (²) and cubed (3)
Me
My
Teacher
Can you use the symbols (3) (cubed) accurately?
Do you know the cube of all numbers between 2 and 12 by heart?
Do you know the relationship between the square of a number and
the square root of a number?
Can you use the symbols (²) and (√) accurately?
Do you know the square of all numbers between 2 and 12 by
heart?
© Focus Education (UK) Ltd 2014
323
Year 5: Can you challenge yourself to meet the Objective?
Objective 21: Solve problems involving addition and subtraction,
multiplication and division and a combination of these, including
understanding the meaning of the equals sign
Me
My
Teacher
Can you understand and use the equals sign to indicate equivalence,
including in missing number problems, e.g. 13 + 24 = 12 + 25;
33 = 5 x
?
Can you solve problems involving a combination of the above with
numbers up to 1,000,000?
Can you solve problems involving division with numbers up to
1,000,000?
Can you solve problems involving multiplication with numbers up
to 1,000,000?
Can you solve problems involving subtraction with numbers up to
1,000,000?
© Focus Education (UK) Ltd 2014
324
Year 5: Can you challenge yourself to meet the Objective?
Objective 23: Compare and order fractions whose denominations
are all multiples of the same number
Me
My
Teacher
Can you order more than 2 different fractions with different
denominators that are multiples of the same number?
Can you order 2 different fractions with different denominators that
are multiples of the same number?
Do you know how to convert fractions with different denominators
into a common denominator?
Can you compare and order fractions with denominators of 5 and
10?
Can you compare and order fractions with denominators of 2, 4
and 8?
Can you compare and order fractions with the same
denominator?
© Focus Education (UK) Ltd 2014
325
Year 5: Can you challenge yourself to meet the Objective?
Objective 25: Recognise mixed numbers and improper fractions and
convert from one form to the other and write mathematical
statements › 1 as a mixed number , e.g. ⅖ + ⅘ = 6/5 = 1 ⅕
Me
My
Teacher
Me
My
Teacher
Can you convert any improper fraction to a mixed fraction and vice
versa?
Do you know that 1and a half can be written as 3/2?
Do you know that a whole number can be written as 2/2 or 4/4,
etc.?
Objective 26: Add and subtract fractions with the same denominator
and denominators that are multiples of the same number
Can you subtract a fraction from a mixed number with
denominators that are multiples of the same number?
Can you subtract two fractions with denominators that are
multiples of the same number?
Can you add two fractions that have the same denominator with
an answer of more than 1, and then translate to a mixed number?
Can you add two fractions that have the same denominator
with an answer of less than 1?
© Focus Education (UK) Ltd 2014
326
Year 5: Can you challenge yourself to meet the Objective?
Objective 27: Multiply proper fractions and mixed fractions by whole
numbers, supported by material and diagrams
Me
My
Teacher
Me
My
Teacher
Can you multiply a mixed fraction by any number up to 10?
Can you multiply a mixed fraction by 10?
Can you multiply a proper fraction by any whole number up to 10?
Can you multiply a proper fraction by 10?
Objective 28: Read and write decimal numbers as fractions (e.g. 0.71
= 71/100)
Can you write any decimal with 2 decimal places as a fraction?
Can you write any decimal with 1 decimal place as a fraction?
Can you write 0.5; 0.25; 0.1; as fractions?
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Year 5: Can you challenge yourself to meet the Objective?
Objective 29: Recognise and use thousandths and relate them to
tenths, hundreds and decimal equivalents
Me
My
Teacher
Me
My
Teacher
Can you work out how many thousandths there are in any number to
include u, t, h and th?
Can you work out how many thousandths there are in any unit
value?
Can you work out how many thousandths there are in any given
tenth value?
Can you work out how many thousandths there are in any given
hundredth value?
Do you know that 10 thousandths are equivalent to one tenth?
Objective 30: Round decimals with 2 decimal places to the nearest
whole number and to one decimal place
Can you round any number to one decimal place, e.g. 17.91 →
17.9?
Can you round any number to the nearest whole number, eg.
18.23→ 18?
© Focus Education (UK) Ltd 2014
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Year 5: Can you challenge yourself to meet the Objective?
Objective 31: Read, write, order and compare numbers with up to 3
decimal places
Me
My
Teacher
Me
My
Teacher
Can you order a set of decimal numbers with between 1 and 3 decimal
places?
Can you order decimal numbers with 3 decimal places?
Can you order decimal numbers with 2 decimal places?
Can you order decimal numbers with 1 decimal place?
Objective 32: Solve problems involving number up to three decimal
places
Can you solve a range of problems involving the above?
Can you subtract numbers with 2 and then 3 decimal places?
Can you subtract numbers with 1 decimal place?
Can you add numbers with 2 and then 3 decimal places?
Can you add numbers with 1 decimal place?
© Focus Education (UK) Ltd 2014
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Year 5: Can you challenge yourself to meet the Objective?
Objective 34: Write percentages as a fraction with denominator 100,
and as a decimal (e.g. ½ = 50% = 0.5)
Me
My
Teacher
Do you know percentage value of all tenths; fifths; quarters and
eighths?
Do you know that 0.25 is 25% = ¼?
Do you know that one quarter is 25% = 25/100 = ¼ ?
Do you know that 0.5 is 50%?
Do you know that 50% is 50/100 = one half = ½?
© Focus Education (UK) Ltd 2014
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Making Mathematics Work
Step up to the Challenge
Year 5
Measurement, Geometry and Statistics
Year 5: Can you challenge yourself to meet the Objective?
Objective 1m: Convert between different units of metric measure,
e.g. kilometre and metre; centimetre and metre; centimetre and
millimetre; gram and kilogram; litre and millilitre
Me
My
Teacher
Me
My
Teacher
Can you express an amount of more than 1l in ml?
Can you express a weight of more than 1Kg in grams?
Can you express a distance of more than 1 cm in mm?
Can you express a distance of more than 1Km in metres?
Objective 2m: Understand and use approximate equivalences
between metric and common imperial units such as inches, pounds
and pints
Do you know the approximate relationship between a pint and a
litre?
Do you know the approximate relationship between a pound
and a gram?
Do you know the approximate relationship between
inches and centimetres?
Do you know the approximate number of metres in 1
mile?
© Focus Education (UK) Ltd 2014
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Year 5: Can you challenge yourself to meet the Objective?
Objective 4m: Calculate and compare the area of rectangles
(including squares) and including using standard units, square
centimetres (cm²) and square metres (m²) and estimate the area of
irregular shapes
Me
My
Teacher
Me
My
Teacher
Can you use information about calculating the area of a square or
rectangle to work out the area of irregular shapes that can be divided up
into squares and rectangles?
Do you know that the area of a rectangle is measured by multiplying
the length of the longer side by the shorter?
Do you know that the area of a square is measured by multiplying
the length of a side by itself?
Do you know that the area of a square or a rectangle is
measured in cm² or m²?
Objective 5m: Estimate volume, e.g. Using 1cm³ blocks to build
cuboids (including cubes) and capacity, e.g. using water
Can you use water to estimate and work out the capacity of a
given container?
Can you use cubes to work out volume of a given shape?
Do you know that volume is measured in cm³ or m³?
© Focus Education (UK) Ltd 2014
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Year 5: Can you challenge yourself to meet the Objective?
Objective 7m: Use all four operations to solve problems involving
measure (e.g. length, mass, volume, money) using decimal notation,
including scaling
Me
My
Teacher
Me
My
Teacher
Can you carry out addition problems which relate to measurement as in
money; length; weight; volume ?
Can you carry out subtraction problems which relate to
measurement as in money; length; weight; volume?
Can you carry out multiplication problems which relate to
measurement as in money; length; weight; volume?
Can you carry out division problems which relate to measurement
as in money; length; weight; volume?
Objective 2g: Know angles are measured in degrees and identify
right angles as ¼ turn (total 90˚); straight line as half turn = 180˚; whole
turn = 360˚
Do you know that 360˚ is equivalent to a full turn?
Do you know that 180˚ is equivalent to half a turn?
Do you know that 90˚ is equivalent to quarter a turn?
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Year 5: Can you challenge yourself to meet the Objective?
Objective 4g: Recognise and compare different triangles, including
isosceles, equilateral and right angles triangles
Me
My
Teacher
Me
My
Teacher
Can you describe a right angle triangle?
Can you describe an isosceles triangle?
Can you describe an equilateral triangle?
Objective 5g: Identify and name parallelogram; rhombus and
trapezium
Do you know what a parallelogram is and can you describe it in
mathematical terms?
Do you know what a rhombus is and can you describe it
in mathematical terms?
Do you know what a trapezium is and describe it in
mathematical terms?
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Year 5: Can you challenge yourself to meet the Objective?
Objective 6g: Draw given angles, and measure them in degrees (˚)
Me
My
Teacher
Me
My
Teacher
Can you draw a given angle using a protractor and label it
appropriately?
Can you draw and measure an angle of 45˚?
Can you draw and measure an angle of 90˚?
Objective 10g; Use the properties of rectangles to deduce related
facts and find missing lengths and angles
Can you draw a triangle to a given set of angles and sides?
Can you draw an isosceles triangle accurately given the length of
side and the base?
Can you draw an equilateral triangle with a given length?
Can you draw a rectangle accurately having been given
the length and breadth?
Can you draw a square accurately having been
given the length of the side?
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Non-Negotiables
Year 5 Possible Planning Outline
Year 5 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
© Focus Education (UK) Ltd 2014
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Year 5 Mathematics Non-Negotiables
• Count forwards and backward with
positive and negative numbers through
zero.
• Count forwards and backwards in steps of
powers of 10 for any given number up to
1000000.
• Compare and order numbers with 3
decimal places.
• Read Roman numerals to 1000.
• Identify all multiples and factors, including
finding all factor pairs.
• Use known tables to derive other number
facts.
• Recall prime numbers up to 19.
• Recognise place value of any number up
to 1,000,000.
• Round any number to 1,000,000 to the
nearest 10, 100, 1000, 10,000 or 100,000.
• Round decimals with 2 decimal places to
nearest whole number and 1decimal
place.
• Add and subtract:
o Numbers with more than 4-digits
using efficient written method
(column).
o Numbers with up to 2 decimal
places.
• Multiply:
o 4-digits by 1-digit/ 2-digit
• Divide:
o 4-digits by 1-digit
• Multiply and divide:
o Whole numbers and decimals by 10,
100 & 1000
• Count up/down in thousandths.
• Recognise mixed numbers and fractions
and convert from one to another.
• Multiply proper fractions by whole
numbers.
• Solve time problems using timetables and
converting between different units of time.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms.
There should some element of teaching of these each day.
Autumn Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back from a given number in steps of 100/1000/10,000
up to a 100,000
Read, write and order numbers to 100,000
Compare numbers to at least 100,000
Partition numbers to at least 100,000
Find powers of 10 more than a given number
Multiply and divide numbers mentally drawing upon known facts
Multiply and divide any whole number by 10 and 100 and
multiply and divide any decimal number by 10
Count on/back with positive and negative numbers, including
through zero
Round any number up to 50,000 to the nearest 10, 100 and 1000
Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and
tens and a 3-digit number and hundreds, combinations of 2 and
3 digit numbers
Find complements to 100 and 1000 and 10. 000
Find factors and factor pairs of each number up to 20
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back from a given number in steps of 100/1000/10,000
up to and beyond a 100,000
Read, write and order numbers to 100,000 and beyond
Compare numbers to 100,000 and beyond
Partition numbers to 100,000 and beyond
Find powers of 10 more than a given number
Read, write, order and compare decimal numbers up to 2dp
Partition decimal numbers to 2dp
Round decimals with 1dp to the nearest whole number
Multiply and divide numbers mentally drawing upon known facts
Multiply and divide any whole number by 10 and 100 and
multiply and divide any decimal number by 10 and 100
Count on/back with positive and negative numbers, including
through zero)
Count on/back in fraction and decimal sequences (e.g. 2.5 or 1
½
Round any number up to 100,000 to the nearest 10, 100 and 1000
Add/subtract: 4-digit and 1-digit numbers, a 4 digit and tens, a 4digit number and hundreds and a 4-digit number and thousands
and combinations of pairs of 2,3 or 4 digit numbers
Find factors and factor pairs of each number up to and beyond
20
Find complements to 1000
Convert units of measurement (km and m; cm and m; cm and
mm; gram and km, ml and L)
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Spring Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back from a given number in steps of
100/1000/10,000/100.000 up to 500,000
Read, write and order numbers to 500,000
Compare numbers to at least 500,000
Partition numbers to at least 500,000
Find powers of 10 more than a given number
Read, write, order and compare decimal numbers up to 3dp
Partition decimal numbers to 3dp
Round decimals with 1 and 2dp to the nearest whole number
Multiply and divide numbers mentally drawing upon known
facts
Multiply and divide any whole number by 10, 100, 1000 and
multiply and divide any decimal number by 10 and 100
Count on/back with positive and negative numbers, including
through zero
Count on/back in fraction and decimal sequences? (e.g. 2.5 or
1½
Round any number up to 500,000 to the nearest 10, 100, 1000,
10,000 and 100,000
Add/subtract: 4-digit and 1-digit numbers, a 4 digit and tens, a
4-digit number and hundreds and a 4-digit number and
thousands and combinations of pairs of 2,3 or 4 digit numbers
Mentally add and subtract tenths
Find factors and factor pairs of each number up to 50
Find complements to 100 and 1000 and to £1.00
Convert units of measurement (km and m; cm and m; cm and
mm; gram and km, ml and L)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back from a given number in steps of
100/1000/10,000/100,000 up to and beyond 500,000
Read, write and order numbers to 500,000 and beyond
Compare numbers to 500,000 and beyond
Partition numbers to 500,000 and beyond
Find powers of 10 more than a given number
Read, write, order and compare decimal numbers up to 3dp
Partition decimal numbers to 3dp
Round decimals with 1 and 2dp to the nearest whole number
Multiply and divide numbers mentally drawing upon known
facts
Multiply and divide any whole number by 10, 100, 1000 and
multiply and divide any decimal number by 10 and 100
Count on/back with positive and negative numbers, including
through zero)
Count on/back in fraction and decimal sequences (e.g. 2.5 or 1
½
Round any number up to 500,000 and beyond to the nearest 10,
100, 1000, 10,000 and 100,000
Add mentally a 4 digit number and a 3 digit number (for
example 8,345 + 230)
Subtract mentally any 4-digit number from a 3-digit number (for
example 8,345 – 230)
Find factors and factor pairs of each number up to 50 and
beyond
Find complements to 100 and 1000; £1.00 and £5.00 and to 1
using 2dp
Convert units of measurement (km and m; cm and m; cm and
mm; gram and km, ml and L)
Mentally add and subtract tenths
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the nonnegotiables
Summer Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back from a given number in steps of
100/1000/10,000/100,000 up to a 1,000,000
Read, write and order numbers to 1,000,000
Compare numbers to at least 1,000,000
Partition numbers to at least 1,000,000
Find powers of 10 more than a given number
Read, write, partition, order and compare decimal numbers up
to 3dp
Round decimals with 1 and 2dp to the nearest whole number
and to 1dp
Multiply and divide numbers mentally drawing upon known
facts
Multiply and divide any whole and decimal number by 10, 100,
1000
Count on/back with positive and negative numbers, including
through zero
Count on/back in fraction and decimal sequences (e.g. 2.5 or 1
½
Round any number up to 1,000,000 to the nearest 10, 100, 1000,
10,000 and 100,000
Add mentally a 4 digit number and 3 digit numbers (for example
8,345 + 230)
Subtract mentally any 4-digit number from a 3-digit number
(e.g. 8,345 – 230)
Mentally add and subtract tenths and one-digit whole numbers
and tenths
Find factors and factor pairs of each number up to 100
Find complements to 100 and 1000; £1.00 and £5.00 and to 1
using 2dp
Convert units of measurement (km and m; cm and m; cm and
mm; gram and km, ml and L)
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back from a given number in steps of
100/1000/10,000/100,000 to a 1,000,000 and beyond
Read, write, and order numbers to 1,000,000 and beyond
Compare numbers to 100,000 and beyond
Partition numbers to 1,000,000 and beyond
Find powers of 10 more than a given number
Read, write, partition, order and compare decimal numbers up
to 3dp
Round decimals with 1 and 2dp to the nearest whole number
and to 1dp
Multiply and divide numbers mentally drawing upon known
facts
Multiply and divide any whole and decimal number by 10, 100,
1000
Count on/back with positive and negative numbers, including
through zero
Count on/back in fraction and decimal sequences (e.g. 2.5 or 1
½
Round any number to 1,000,000 and beyond to the nearest 10,
100, 1000, 10,000 and 100,000
Add mentally a 5-digit number and 4- digit numbers (e.g. 15,345
+ 2300)
Mentally add and subtract tenths and one-digit whole numbers
and tenths
Find complements to 100. 1000, 10,000; £1.00, £5.00 and £10.00;
and to 1 using 3dp
Find factors and factor pairs of each number to 100
Convert units of measurement (km and m; cm and m; cm and
mm; gram and km, ml and L)
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 5 Assessment
Assessment: Meeting Year 5 Expectations
The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 5 expectations. The Year 5 expectations
for number are set out below on this page. To meet the Year 5 expectations a pupil must be able to meet all of the statements outlined in
the table, plus the ones for measurement and geometry, shown later.
If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an
assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is
exceeding the expectations or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper
analysis, if required.
Year 5 Expectations: Number
•
Count forwards and backwards in steps of power 10 for any given number up to 1,000,000
•
Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents
•
Recognise mixed numbers and improper fractions and convert from one to the other
•
Read and write decimal numbers as fractions, e.g. 0.47 = 47/100
•
Recognise the per cent symbol (%) and understand per cent relates to number of parts per hundred
•
Write percentages as a fraction with denominator hundred, and as a decimal number
•
Compare and add fractions whose denominators are all multiples of the same number
•
Multiply and divide numbers mentally drawing upon known facts up to 12 x 12
•
Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
•
Round decimals with 2dp to the nearest whole number and to 1decimal place
•
Recognise and use square numbers and cube numbers and the notation for squared (²) and cubed (³)
•
Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
•
Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including long multiplication for 2-digit numbers
•
Divide numbers up to 4-digits by 1-digit numbers
•
Solve problems involving multiplication and division where large numbers are used by decomposing them into factors
•
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why; solve
problems involving 3 decimal places and problems which require knowledge of percentages and decimal equivalents
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 5 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 5 Expectations
A pupil will be deemed to be
meeting the expectations only if
they can satisfy their teacher
that they meet all the
expectations for their age
A pupil will be deemed to be
emerging towards the
expectations if they do not meet
all of the statements outlined for
that year group
•Meeting the expectations (Stage
C) – Point 4
•It is accepted that a pupil might
make the occasional error if they
are at this stage. However,
despite that, the teacher needs
to be satisfied that they
understand the concept fully.
•Meeting the expectations (Stage
B) - Point 5
•At this stage a pupil will rarely
make mistakes and is very
confident at meeting the
statements.
•Meeting the expectation (Stage
A)- Point 6
•At this stage, not only is the pupil
confident at meeting the
statements but works at a rapid
rate. However, they are not yet
meeting all the statements for
exceeding.
•If they meet more than 75% of
the statements but not all then
they will be described as:
•Emerging towards the
expectations (Stage C) – Point 3
•If they meet between 50% and
75% of the statements then they
will be described as:
•Emerging towards the
expectations (Stage B) – Point 2
•However if they are not meeting
50% of the expectations they will
be described as:
•Emerging towards the
expectations (Stage A) – Point 1
•There is, therefore, no
requirement to write a set of
emerging statements
© Focus Education (UK) Ltd 2014
A pupil will be deemed to be
exceeding the expectations when, in
addition to the statements set out for
meeting the expectation (Stage
A)they meet one or more of three sets
of further expectations
•Pupils will be deemed to be exceeding
expectations if, in addition to what is
outlined as Point 6, they show evidence
of:
•Accessing some of the following year
group’s objectives
•Being able to use the year group’s
expectation within context
•Being able to consistently apply the year
group objectives in a range of situations.
•A set of exceeding statements are set out
for you to feel secure about your
judgements.
•If a pupil is meeting the exceeding
statements, they will be deemed to be at
Point 7 (Stage C)
•If they are very confident and rarely
make a mistake in relation to the
‘exceeding’ statements then they will be
judged at Point 8 (Stage B)
•A few pupils will be judged at Point 9
(Stage A). These will be pupils who are
exceptionally confident in handling the
exceeding statements and show
exceptional mathematical ability for their
age
346
Assessment: Meeting Year 5 Expectations
The 3 or 9-point scale
Effectively pupils will be assessed on a 3-point scale: that is pupils will be judged as
having met the expectations; emerging (or developing) towards the expectation or
exceeding the expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined
for them to use.
Assessed
position
Emerging
Stage A
Emerging
Stage B
Emerging
Stage C
Meeting
Meeting
advanced
Meeting
higher
Exceeding
Exceeding
advanced
Exceeding
higher
Points
allocation
1
2
3
4
5
6
7
8
9
•
•
•
•
•
As is illustrated Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then
it is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting expectation’ stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 5 Expectations
Year 5 Expectations: Number
•
Count forwards and backwards in steps of power 10 for any given number up to 1,000,000
•
Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents
•
Recognise mixed numbers and improper fractions and convert from one to the other
•
•
Year 5 Expectations:
Measurement, Geometry and
Statistics
•
Know angles are measured in degrees:
estimate and compare acute; obtuse and
reflex angles
Read and write decimal numbers as fractions, e.g. 0.47 = 47/100
•
Recognise the per cent symbol (%) and understand per cent relates to number of parts per
hundred
Draw given angles and measure them in
degrees (º)
•
Convert between different units of metric
measures and estimate volume and
capacity
•
Measure and calculate the perimeter of
composite rectilinear shapes in centimetres
and metres
•
Calculate and compare the area of squares
and rectangles including using standard
units (cm² and m²)
•
Solve comparison, sum and difference
problems using information presented in a
line graph
•
Write percentages as a fraction with denominator hundred, and as a decimal number
•
Compare and add fractions whose denominators are all multiples of the same number
•
Multiply and divide numbers mentally drawing upon known facts up to 12 x 12
•
Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
•
Round decimals with 2dp to the nearest whole number and to 1decimal place
•
Recognise and use square numbers and cube numbers and the notation for squared (²) and
cubed (³)
•
Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
•
Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including
long multiplication for 2-digit numbers
•
Divide numbers up to 4-digits by 1-digit numbers
•
Solve problems involving multiplication and division where large numbers are used by
decomposing them into factors
•
Solve addition and subtraction multi-step problems in contexts, deciding which operations and
methods to use and why; solve problems involving 3-decimal places and problems which
require knowledge of percentages and decimal equivalents
© Focus Education (UK) Ltd 2014
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Assessment: Exceeding Year 5 Expectations
Year 5 Exceeding Expectations: Number
• Have a concept of numbers well beyond 1,000,000 and their
relative association to distances to planets; historical data and
geographical aspects
• Divide whole numbers (up to 4 digits) by 2-digit numbers,
using preferred method
• Use rounding as a strategy for quickly assessing what
approximate answers ought to be before calculating
• Link working across zero for positive and negative numbers to
work time between BC and AD in history
• Recognise the symbol for square root (√) and work out square
roots for numbers up to 100
• Calculate number problems algebraically, e.g. 2x – 3 = 5
• Use knowledge of measurement to create plans of areas
around school, such as classroom , field, outside play area,
etc.
• Relate imperial measures still used regularly in our society to
their metric equivalents, eg, miles to Km and lbs to Kg
• Use a range of timetables to work out journey times on a fictional
journey around the world, eg, how long would it take to reach the
rainforests in the Amazon
• Collect own data on personal project and present information in
formats of their choosing, charts, graphs and tables
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 5 Parents’ Guide
Parents’ Guide
‘Must Dos’ by the end of Year 5
Number
•
•
•
•
•
•
•
•
Read, write and order numbers to
1,000,000
Count on and back in steps of
100,1,000, 10,000 up to 1,000,000
Round any number to the nearest 10,
100, 1,000, 10,000 or 100,000
Estimate and calculate additions
involving 2, 3-digit numbers (to
nearest 10)
Estimate and calculate subtractions
involving 2, 3-digit numbers (to
nearest 10)
Estimate and calculate
multiplications involving a 2-digit and
a 3-digit numbers (to nearest 10)
Estimate and calculate divisions of a
3-digit number by a 1-digit number
(to nearest 10)
Add 3, 5-digit numbers using column
addition
•
•
•
•
•
•
•
•
•
•
Subtract one 5-digit number from
another, using column subtraction
Rapid Recall: Mentally add a 2-digit
number to a 3-digit number
Rapid Recall: Mentally add a 1000s
number to a 5-digit number
Rapid Recall: Mentally subtract a 2digit number from a 3 or 4-digit
number
Rapid Recall: Mentally subtract a
1000s number from a 5-digit number
Know all factors that make up
numbers to 100
Recognise all prime numbers to 100
Multiply a 4-digit number by a 2-digit
number using formal methods
Divide a 4-digit number by a 1-digit
number (with remainders)
Multiply numbers by 10, 100 and 1,000
© Focus Education (UK) Ltd 2014
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Parents’ guide
‘Must Dos’ by the end of Year 5
Number
•
•
•
•
•
•
•
Number
Divide number by 10, 100 and 1,000
Recognise and use square
numbers and square roots
Know and use the symbols (²),(3)
and (√) accurately
Fractions: Compare and order
fractions whose denominators are
multiples of the same number
Convert mixed numbers to
improper fractions and visa versa
Add and subtract fractions with the
same denominator
Multiple proper fractions and mixed
fractions by whole numbers
•
•
•
•
•
•
Decimal Fractions: Read and write
decimal numbers as fractions (up
to hundredths)
Round decimals with two decimal
places to nearest whole number
and one decimal place
Read, write, order and compare
decimal numbers with up to three
decimal places
Percentages: Recognise the %
symbol
Understand that percentage is
measured as part of 100
Solve problems which require
knowing percentage and decimal
value of ½, ¼, ⅕, ⅖ and ⅘
© Focus Education (UK) Ltd 2014
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Parents’ Guide
‘Must Dos’ by the end of Year 5
Shape and measures
•
•
•
•
•
•
Shape and Measures
Measure angles in degrees
Draw a given angle accurately
Know and use reflex angles
Construct shapes from given
dimensions
Identify 3D shapes from 2D
representations
Identify, describe and represent the
position of a shape following
reflection and translation
•
•
•
•
Add, subtract, multiply and divide
units of measure (using decimal
notation)
Understand and use basic
equivalence between metric and
common imperial units
Calculate, estimate and compare
areas of squares and rectangles
using cm squared (cm²) and metre
squared (m²)
Recognise volume in practical
contexts
© Focus Education (UK) Ltd 2014
353
Focus on Mathematics
Year Group Objectives
Year 6
Year 6 Objectives: Number
NUMBER AND PLACE VALUE
Objective 1: Read, write, order and compare numbers to
10,000,000 and determine the value of each digit
Revise reading and writing numbers to: 1000 and then to 100,000
*1
Read and write numbers to 1,000,000
Read and write numbers to 10,000,000
*2
Recognise the value of each digit up to 10,000,000
Know and use terms: units; tens, hundreds, thousands, ten thousands,
hundred thousands, one million and ten million correctly
Partition any number up to 10,000,000 showing the value of each digit
Objective 2: Round any whole number to a required degree of
accuracy
Round any 7-digit number to the nearest million
*1
Round any 6-digit number to the nearest hundred thousand
Round any 5-digit number to the nearest ten thousand
*2
Round any 4-digit number to the nearest thousand
Round any number to the nearest degree of accuracy
© Focus Education (UK) Ltd 2014
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Year 6 Objectives: Number 2
NUMBER AND PLACE VALUE
Objective 3: Use negative numbers in
context , and calculate intervals across zero
Interpret temperatures at minus ⁰C on a
thermometer
*1
Calculate the interval from - 20 to + 100
Calculate the interval from + 30 to -30
*2
Objective 4: Solve number and practical
problems that involve all of the above
Calculate the answer to any given problem
involving the above
ADDITION, SUBTRACTION, MULTIPLICATION
AND DIVISION
Objective 5: Add and subtract negative
integers (Non Statutory)
Add any 2 negative numbers together
Know what happens when subtracting a
negative number form another negative
number
Objective 6: Multiply multi-digit numbers up
to 4-digits by a 2-digit whole number using
the formal written method of long
multiplication
Revise multiplication of HTU x U
*1
Revise multiplication of ThHTU x U
Multiply 4-digit numbers by a 2-digit number
using grid method or another conventional
method
© Focus Education (UK) Ltd 2014
*2
356
Year 6 Objectives : Number 3
ADDITION, SUBTRACTION, MULTIPLICATION
AND DIVISION
ADDITION, SUBTRACTION, MULTIPLICATION
AND DIVISION
Objective 7: Divide numbers up to 4-digits
by a 2-digit whole number using the formal
written method of long division, and interpret
remainders as whole number remainders,
fractions, or by rounding, as appropriate for
the context
Objective 8: Divide numbers up to 4-digits
by a 2-digit number using the formal written
method of short division where appropriate ,
interpreting remainders according to the
context
Revise division of numbers with up to 4-digits by
a single-digit number with and without
remainders
*1
Divide numbers with up to 4-digits by a 2-digit
number up to 20 without remainders
*2
Divide numbers with up to 4-digits by a 2-digit
number up to 20 with remainders
*3
Divide numbers with up to 4-digits by a 2-digit
number with remainders
Objective 9: Perform mental calculations,
including with mixed operations and large
numbers
Perform mental calculations with large numbers
Express remainder as a fractional value of the
number divided by
Perform mental calculations which require at
least two different operations, eg. addition and
multiplication
Divide numbers with up to 4-digits by any 2-digit
number with and without remainders
Use rounding up to express answers as a whole
number
Divide numbers with up to 4-digits by a 2-digit
number without remainders
*4
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Number 4
ADDITION, SUBTRACTION, MULTIPLICATION
AND DIVISION
Objective 10: Identify common
factors, common multiples and prime
numbers
Know the common factors of any 2 given numbers
Know the common multiples of any 2 given
numbers
Know all prime numbers
Objective 11: Use their knowledge of
the order of operations to carry out
calculations involving the four
operations
Objective 12: Solve addition and
subtraction multi-step problems in
contexts, deciding which operations
and methods to use and why
ADDITION, SUBTRACTION, MULTIPLICATION
AND DIVISION
Objective 13: Solve problems involving
addition, subtraction, multiplication and
division
Solve word problems involving addition with
numbers up to 10,000,000
*1
Solve word problems involving subtraction with
numbers up to 10,000,000
*2
Solve word problems involving multiplication
with numbers up to 10,000,000
*3
Solve word problems involving division with
numbers up to 10,000,000
Solve word problems with mixed operations
with numbers up to 10,000,000
*4
Objective 14: Use estimation to check
answers to calculations and determine, in
the context of a problem, an appropriate
degree of accuracy
Know when it is appropriate to represent an
answer to a given problem as a fractional value
rounded to the nearest whole number value
Estimate the answer to a problem before
working it out and use the estimation to check
on accuracy of problem solving
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Number 5
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
FRACTIONS INCLUDING DECIMALS AND
PERCENTAGES)
Objective 15: Use common factors to simplify
fractions; use common multiples to express
fractions in the same denomination
Objective 17: Divide proper fractions by
whole numbers
Find the greatest common factor to simplify
fractions
Divide a proper fraction by a whole number
and give answer in its simplest form
Know how to use common multiples to express
fractions in the same denomination
Objective 18: Associate a fraction with
division to calculate decimal fraction
equivalents, e.g. 0.375 for a simple fraction
⅜
Objective 16: Multiply simple unit fractions and
pairs of proper fractions, writing the answer in
its simplest form
Multiply a whole number with a fraction
*1
*2
Turn mixed fractions into an improper fraction
Multiply 2 mixed fractions and write answer in its
simplest form
Know that 1/10 can be represented as 0.1
*1
Know that ¼ can be represented as 0.25
Multiply a whole number with a fraction and give
answer in its simplest form
Multiply 2 simple fractions together and give
answer in its simplest form
Divide a proper fraction by a whole number
*3
Know that ¾ can be represented as 0.75
Know all the decimal fraction equivalents for
fractional values where the denominator is 3, 4,
5, 6, 8 or 10
© Focus Education (UK) Ltd 2014
359
Year 6 Objectives : Number 6
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
Objective 19: Add and subtract fractions with
different denominators and mixed numbers,
using the concept of equivalent fractions
Objective 21: Recall and use equivalences
between simple fractions, decimals and
percentages including in different contexts
Revise addition and subtraction of fractions with
the same denominator
*1
Work out common denominator for a pair of
fractions with different denominators, e.g. ⅔ and
⅗
Revise that ¼ can be represented as 0.25 and
use this to solve problems
Add 2 fractions with different denominators
*2
Add 2 mixed numbers where the fractional values
have different denominators
*3
Subtract 2 fractions with different denominators
Subtract 2 mixed numbers where the fractional
values have different denominators
Revise that 1/10 can be represented as 0.1 and
use this to solve problems
Revise that ¾ can be represented as 0.75 and
use this to solve problems
Revise all the decimal fraction equivalents for
fractional values where the denominator is 3, 4,
5, 6, 8 or 10 and use this to solve problems
*4
Objective 20: Multiply simple pairs of proper
fractions, writing the answer in its simplest form,
e.g. ¼ x ½ = 1/8
Multiply 2 simple fractions together and give the
answer in its simplest form
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Number 7
DECIMALS
DECIMALS
Objective 22: Identify the value of each digit in
numbers given to three decimal places and
multiply and divide numbers by 10, 100 and 1000
giving answers up to three decimal places
Objective 23: Multiply one-digit numbers
with up to two decimal places by whole
numbers
*1
Know the value of each digit in a decimal fraction
which has up to 3 decimal places
*1
Multiply a decimal fraction with up to 2 decimal
places by a single-digit number
*2
Know that when multiplying a decimal fraction by 10
the decimal point moves one place to the right, e.g.
3.457 x 10 = 34.57
*2
Multiply a decimal fraction with up to 2 decimal
places by a 2-digit number
Divide a decimal fraction with up to 2 decimal
places by a single-digit number
*3
Divide a decimal fraction with up to 2 decimal
places by a 2-digit number
*4
Know that when multiplying a decimal fraction by 100
the decimal point moves two places to the right, e.g.
3.457 x 100 = 345.7
Objective 24: Use written division
methods in cases where the answer
has up to two decimal places
Know that when multiplying a decimal fraction by
1000 the decimal point moves three places to the
right, e.g. 3.457 x 100 = 3457
Know that when dividing a decimal fraction by 10 the
decimal point moves one place to the left, e.g.
567.234 ÷ 10 = 56.7234
Know that when dividing a decimal fraction by 100
the decimal point moves two places to the left, e.g.
567.234 ÷ 100 = 5.67234
*3
Objective 25: Solve problems which
require answers to be rounded to
specified degrees of accuracy
Know that when dividing a decimal fraction by 1000
the decimal point moves three places to the left, e.g.
567.234 ÷ 1000 = 0.567234
© Focus Education (UK) Ltd 2014
361
Year 6 Objectives : Number 6
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
FRACTIONS (INCLUDING DECIMALS AND
PERCENTAGES)
Objective 19: Add and subtract fractions with
different denominators and mixed numbers,
using the concept of equivalent fractions
Objective 21: Recall and use equivalences
between simple fractions, decimals and
percentages including in different contexts
Revise addition and subtraction of fractions with
the same denominator
*1
Work out common denominator for a pair of
fractions with different denominators, e.g. ⅔ and
⅗
Revise that ¼ can be represented as 0.25 and
use this to solve problems
Add 2 fractions with different denominators
*2
Add 2 mixed numbers where the fractional values
have different denominators
*3
Subtract 2 fractions with different denominators
Subtract 2 mixed numbers where the fractional
values have different denominators
Revise that 1/10 can be represented as 0.1 and
use this to solve problems
Revise that ¾ can be represented as 0.75 and
use this to solve problems
Revise all the decimal fraction equivalents for
fractional values where the denominator is 3, 4,
5, 6, 8 or 10 and use this to solve problems
*4
Objective 20: Multiply simple pairs of proper
fractions, writing the answer in its simplest form,
e.g. ¼ x ½ = 1/8
Multiply 2 simple fractions together and give the
answer in its simplest form
© Focus Education (UK) Ltd 2014
362
Year 6 Objectives : Number 7
DECIMALS
DECIMALS
Objective 22: Identify the value of each digit in
numbers given to three decimal places and
multiply and divide numbers by 10, 100 and 1000
giving answers up to three decimal places
Objective 23: Multiply one-digit numbers
with up to two decimal places by whole
numbers
*1
Know the value of each digit in a decimal fraction
which has up to 3 decimal places
*1
Multiply a decimal fraction with up to 2 decimal
places by a single-digit number
*2
Know that when multiplying a decimal fraction by 10
the decimal point moves one place to the right, e.g.
3.457 x 10 = 34.57
*2
Multiply a decimal fraction with up to 2 decimal
places by a 2-digit number
Divide a decimal fraction with up to 2 decimal
places by a single-digit number
*3
Divide a decimal fraction with up to 2 decimal
places by a 2-digit number
*4
Know that when multiplying a decimal fraction by 100
the decimal point moves two places to the right, e.g.
3.457 x 100 = 345.7
Objective 24: Use written division
methods in cases where the answer
has up to two decimal places
Know that when multiplying a decimal fraction by
1000 the decimal point moves three places to the
right, e.g. 3.457 x 100 = 3457
Know that when dividing a decimal fraction by 10 the
decimal point moves one place to the left, e.g.
567.234 ÷ 10 = 56.7234
Know that when dividing a decimal fraction by 100
the decimal point moves two places to the left, e.g.
567.234 ÷ 100 = 5.67234
*3
Objective 25: Solve problems which
require answers to be rounded to
specified degrees of accuracy
Know that when dividing a decimal fraction by 1000
the decimal point moves three places to the left, e.g.
567.234 ÷ 1000 = 0.567234
© Focus Education (UK) Ltd 2014
363
Year 6 Objectives : Number 8
RATIO and PROPORTION
RATIO AND PROPORTION
Objective 26: Use percentages for
comparison and calculate percentages of
whole numbers or measures, .g. 15% of 360
Objective 27: Solve problems involving the relative sizes
of two quantities where missing values can be found by
using integer multiplication and division facts
*1
Recognise 50% as being a half of the original
value
Solve problems involving similar shapes where the
scale factor is known or can be found
Objective 28: Solve problems involving unequal sharing
and grouping using knowledge of fractions and
multiples.
Recognise 25% as being a quarter of the original
value
Recognise 75% as being three quarters of the
original value
Recognise 10% as being a tenth of the original
value
Know that to find 1% of a value you divide by
100
Find 25%, 50% and 75% of any given value
Find 10%, 20%, 30%, etc. of a given value
Find any percentage of a given value, eg, 18%
of 360
*2
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Number 9
ALGEBRA
Objective 29: Use simple formulae
Write rules algebraically for known relationships like p = 4s for finding out the
perimeter of a square
Objective 30: Generate and describe linear number sequences
Continue a linear number sequence involving positive and negative numbers
*1
Continue a linear number sequence involving fractions
*2
Continue a linear number sequence involving decimal fractions
*3
Objective 31: Express missing number problems algebraically
Write known rules algebraically, e.g. a + b = b + a
*1
Work out equations involving missing amount, e.g. If 2x -1 = 9, what is x?
Work out calculations when given value of 2 letters, e.g. What is 2a + 3b if a =2 and b
= 5?
*2
Objective 32: Find pairs of numbers that satisfy an equation with two
unknowns
Objective 33: Enumerate possibilities of combinations of two variables
© Focus Education (UK) Ltd 2014
365
Focus on Mathematics
Year 6 Pre-Learning Tasks
Number
Focus on Mathematics: Year 6
Name
Objective 1
Date
Number
Read, write, order and compare numbers to 10,000,000 and determine the
value of each digit
Can you write these numbers in
numerals?
Two hundred
thousand, four
hundred and
fourteen
*1
Can you write these numbers in words?
1,122,461
One million, thirteen
thousand, three
hundred and sixtyfour
5,123,879
Five million, two
hundred and four
thousand, one
hundred and sixteen
2,015,247
Six million, four
hundred thousand,
three hundred and
eighty- three
1,998,392
Five million, sixty
thousand, four
hundred and five
9,719,709
© Focus Education (UK) Ltd 2014
*2
367
Focus on Mathematics: Year 6
Name
Objective 2
Date
Number
Round any whole number to a required degree of accuracy
Can you round these numbers to the nearest 10, 100, 1000, 10,000 or 100,000?
2,391,385 to
the nearest
1,000,000
*1
2,134 to the
nearest 1,000
918,765 to
the nearest
100,000
*2
5,607 to the
nearest 100
357,385 to
the nearest
100,000
1145 to the
nearest 100
5607 to the
nearest 100
272 to the
nearest 10
159,887 to
the nearest
100,000
1167 to the
nearest 10
© Focus Education (UK) Ltd 2014
368
Focus on Mathematics: Year 6
Name
Objective 3
Date
Number
Use negative numbers in context , and calculate intervals across zero
Can you respond to these problems?
If Room A is -2⁰C and
Room B is -3⁰C, which is
warmer?
*1
What is the difference
between -3 and +6
If Room A is -5⁰C and
Room B is -7⁰C, which is
warmer?
What is the difference
between -13 and +62
If Room A is -10⁰C and
Room B is -7⁰C, which is
colder?
What is the difference
between -24 and +73
If Room A is -6⁰C; Room B is
-7⁰C and Room c is -3⁰C,
which is warmer?
What is the difference
between +28 and -28
If Room A is -8⁰C; Room B is
-9⁰C and Room c is -10⁰C,
which is warmer?
What is the difference
between +19 and -6
© Focus Education (UK) Ltd 2014
*2
369
Focus on Mathematics: Year 6
Name
Date
Objective 6
Number
Multiply multi-digit numbers up to 4-digits by a 2-digit whole number
using the formal written method of long multiplication
Can you multiply these accurately?
*1
902
x12
506
x26
607
x24
809
x32
230
3x
405
5x
670
4x
302
8x
317
9x
448
5x
752
6x
785
8x
1326
x25
8673
x45
8471
x26
5686
x34
5231
9x
5645
7x
7223
6x
9541
5x
3244
x34
7209
x24
8655
x45
6587
x34
6723
6x
5662
7x
9413
8x
5532
9x
© Focus Education (UK) Ltd 2014
*2
370
Focus on Mathematics: Year 6
Name
Date
Objective 7
Number
Divide numbers up to 4-digits by a 2-digit whole number using the formal
written method of long division, and interpret remainders as whole
number remainders, fractions, or by rounding, as appropriate for the
context
Can you divide these accurately?
285 ÷ 5
378 ÷ 6
252 ÷ 4
282 ÷ 3
*1
9150 ÷ 19
5720 ÷ 17
6076 ÷ 13
3360÷ 16
2640÷15
176÷11
6160÷14
*2
1452 ÷ 27
8987 ÷ 36
8114 ÷ 57
5655÷15
3424÷16
270÷18
3451÷17
3247 ÷ 13
7209 ÷ 35
8656 ÷ 33
8753÷15
5267÷19
239÷17
1987÷14
*3
*4
For *4 express remainder as a fraction or
round answer to nearest whole number.
© Focus Education (UK) Ltd 2014
371
Focus on Mathematics: Year 6
Name
Objective 13
Date
Number
Solve problems involving addition, subtraction, multiplication and
division (using numbers up to 10,000,000)
Can you respond to these problems?
Country A has a population of
1,234, 897; Country B a population
of 2,786,123 and Country C has a
population of 345,897. How many
people live in the 3 countries
altogether?
*1
Voyager spacecraft made three
journeys into space. The first journey
was 1,567,987Km; the second 3,456,
094Km and the third 3,675,912. How
far did Voyager travel altogether?
During a civil war in an unknown
country 1,267,894 people left to
seek asylum elsewhere. The country
originally had a population of
4,783,976. How many people were
left?
The total attendance at City’s
matches this season was 4,986,012
and the total attendance at
Rovers’ matches was 3,872,123.
How many more attended City’s
matches?
Can you respond to these problems?
At a factory 2,987,123 mints are
produced each week. How many
will be produced after 3 weeks?
*3
If 9,768,234 leaflets are produced
over 5 days at a printers, how many
are produced each day?
*2
A new style vehicle can travel for
3,985,123Km but has to change its
electrical system 5 times during the
journey. How far does it travel with
each electrical system?
*4
2,300,876 attended theatre
productions in London last year.
123,457 were male. How many
females attended? If each ticket
cost an average of £4, how much
money was taken altogether?
© Focus Education (UK) Ltd 2014
372
Focus on Mathematics: Year 6
Name
Objective 16
Date
Number
Multiply simple unit fractions and pairs of proper fractions, writing the
answer in its simplest form
Can you work out these fractions?
1
4
x 5
5
6
x 6
5
7
3
4
x 5
Turn these mixed fractions into improper
fractions:
*1
2 x 5
3
6
*2
x 3
4
5
2
7
4
1
5
x 8
6
1
4
4
5
x 10
8
3
8
6
5
x4 3
8
x
© Focus Education (UK) Ltd 2014
6
9
4
*3
*4
4
5
373
Focus on Mathematics: Year 6
Name
Date
Objective 18
Number
Associate a fraction with division to calculate decimal fraction equivalents,
e.g. 0.375 for a simple fraction ⅜
Can you write the following fractions as decimal fractions?
1/10
*1
5/6
3/10
1/6
1/4
5/8
3/4
7/10
3/5
9/10
1/5
2/5
1/8
3/8
7/8
1/2
© Focus Education (UK) Ltd 2014
374
Focus on Mathematics: Year 6
Name
Date
Objective 19
Number
Add and subtract fractions with different denominators and mixed
numbers, using the concept of equivalent fractions
Can you add these fractions?
Can you reorganise these fractions so
that they have the same denominator?
3
4
+
1
4
*1
8
5
6
+
9
5
6
+
4
5
*2
7
1
4
+
3
4
+
1
8
1
5
+
3
10
3
4
-
5
8
4
5
+
7
10
9
10
-
3
8
© Focus Education (UK) Ltd 2014
9
1
2
*3
7
8
*4
375
Focus on Mathematics: Year 6
Name
Date
Objective 22
Number
Identify the value of each digit in numbers given to three decimal places
and multiply and divide numbers by 10, 100 and 1000 giving answers up to
three decimal places
Can you show the decimal value of
each number?
U
t
h
th
*1
Can you divide these decimal fractions
by 10, 100 and 1000?
234.13÷10
5.389
239.1÷10
6.257
123.95÷100
Can you multiply these decimal
numbers by 10?
437.26÷100
23.85 x 10
1.457 x 10
*2
*3
2398.12÷1000
178.952÷1000
3.67 x 10
123.89 x 10
© Focus Education (UK) Ltd 2014
376
Focus on Mathematics: Year 6
Name
Objective 23
Date
Number
Multiply one-digit numbers with up to two decimal places by whole
numbers
Can you multiply or divide these decimal fractions?
23.85x 6
*1
28.67÷5
83.41x 8
82.54÷7
32.73x 9
63.23÷6
15.83x 7
76.34÷8
34.98x 13
*2
23.87÷12
93.25x 26
65.82÷19
92.82x 25
79.56÷17
72.85x 32
92.76÷21
© Focus Education (UK) Ltd 2014
*3
*4
377
Focus on Mathematics: Year 6
Name
Objective 26
Date
Number
Use percentages for comparison and calculate percentages of whole
numbers or measures, e.g. 15% of 360
Can you multiply or divide these decimal fractions?
50% of 268
*1
1% of 500
25% of 844
17% of 500
75% of 1500
23% of 600
50% of 238
95% of 1000
25% of 260
65% of 250
75% of 2375
80% of 2000
10% of 2580
70% of 3500
20% of 5160
95% of 2500
© Focus Education (UK) Ltd 2014
*2
378
Focus on Mathematics: Year 6
Name
Date
Objective 30
Number
Generate and describe linear number sequences
Can you work out what comes next in these sequences?
-4, -2, 0, +2, +4 …
*1
1.5, 1.25, 1.00, 0.75…
9, 7, 5, 3, 1, ….
7.5, 7.0, 6.5, 6.0, 5.5….
-10, -7, -4, -1, ….
0.11, 0.13, 0.15, 0.17…
15, 10, 5, 0, -5…
6.3, 5.9, 5.5, 5.1…..
1/8, ¼, 3/8, ½, ….
*2
-4, -10, -16, -22……
9/10, 4/5, 7/10, 3/5….
*3
-55, -35, -15……
0.2, 0.3, 0.4, 0.5….
17, 11, 5, ……
0.25, 0.29, 0.33, 0.37….
89, 64, 39, 14…..
© Focus Education (UK) Ltd 2014
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Focus on Mathematics: Year 6
Name
Date
Objective 31
Number
Express missing number problems algebraically
Can you work out the missing values?
2x – 4 = 8
*1
If a = 4 and b = 3 and c = 2
work out the following
5x + 4 = 24
2a + 3b =
6x – 6 = 18
7b – 4a =
7x + 3 = 24
2a + 5b + 6c
9x – 5 = 58
9c + 2b + 3a
10x – 6 = 54
2c x 2b
9x + 3 = 57
5c + 4b + 6a
8x + 7 = 39
10a + 10b + 10c
© Focus Education (UK) Ltd 2014
*2
380
Focus on Mathematics
Year 5 Group Objectives
Measurement, Geometry and
Statistics
Year 6 Objectives : Measurement
MEASUREMENT
Objective 1m: Solve problems involving the
calculation and conversion of units of
measure, using decimal notation up to three
decimal places where appropriate
MEASUREMENT
Objective 4m: Recognise that shapes with
the same areas can have different
perimeters and vice versa
Use decimal notation to three decimal places
to solve calculations with measures
Draw a number of rectangles with the same
perimeter
Use other compound units for speed such as
miles per hour and apply their knowledge in
science as appropriate
Objective 5m: Recognise when it is possible
to use formulae for area and volume of
shapes
Objective 2m: Use, read, write and convert
between standard units, converting
measurements of length, mass, volume and
time from a smaller unit of measure to a
larger unit, and vice versa, using decimal
notation to up to three decimal places
Use, add and subtract positive and negative
integers for measures such as temperature and
money
Know when to apply a given formula to find out
the area of a shape
Know when to apply a given formula to find out
the volume of a shape
Objective 6m: Calculate the area of
parallelograms and triangles
Know the formula associated with finding the area
of triangles
Convert large numbers of cm into metres; ml into l;
grams into Kg; and, minutes into hours
Know the formula associated with finding the area
of parallelograms
Objective 3m: Convert between miles and
kilometres
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Geometry
PROPERTIES OF SHAPES
Objective 3g: Compare and classify geometrical
shapes based on properties and sizes and find
unknown angles in any triangles, quadrilaterals,
and regular polygons
PROPERTIES OF SHAPES
Objective 1g: Draw 2-D shapes using given
dimensions and angles
Objective 2g: Recognise, describe and
build simple 3D shapes, including making
nets
Know what a net for a square looks like
Create a cube using knowledge of what the net
looks like
Know what a net for an oblong looks like
Classify triangles in terms of their properties
Know that an equilateral triangle has three angles of 60˚
and three equal sides
Know that an isosceles triangle has two sides which are
equal and two angles which are equal
Describe a right angled triangle according to properties
Describe a square and oblong in terms of their
properties
Know the properties of rectangles such as
parallelogram; trapezium; rhombus
Know that the total of the three angles of any triangle
adds up to 180˚
Use a protractor to measure individual angles of a
triangle
Draw a triangle given size of sides and angle sizes
Know that the four angles of any quadrilateral adds up
to 360˚
Work out the size of an angle in a quadrilateral by using
a protractor to measure it
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Geometry 2
PROPERTIES OF SHAPES
Objective 4g: Illustrate and name parts of
circles, including radius, diameter and
circumference and know that the diameter is
twice the radius
PROPERTIES OF SHAPES
(Non Statutory)
Objective 6g: Describe properties of common
3D shapes and identify parallel planes and
symmetry
Know that the line across the centre of a circle is
known as the diameter
Describe the properties of a cube, cuboid, sphere,
prism and pyramid
Know that the distance from the centre to the arc of
a circle is the radius
Point out the parallel planes associated with any 3d
shape
Know that the distance around the outside of a
circle is the circumference
Identify lines of symmetry in 3D shapes
Know that the diameter of a circle is twice its radius
Objective 5g: Recognise angles where
they meet at a point, are on a straight
line, or are vertically opposite, and find
missing angles
Objective 7g: Estimate size of angles
Recognise 90˚ as a corner angle and know that
there are many of them in the built environment
Recognise that 45˚ is half of a 90˚ and can estimate
if an angle is greater or smaller than 45˚
Given 2 angles of a triangle know what the value
of the third angle is
Given 3 angles of a quadrilateral know what the
value of the fourth angle is
Know missing angles in parallelogram; rhombus
and trapezium from working out diagonally
opposite angles, etc.
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Geometry 3
POSITION AND DIRECTION
Objective 8g: Describe positions on the full coordinate
grid (all four quadrants)
Identify each position on four quadrants of a grid using
numbers on the axes
Create shapes within a grid by following pairs of numbers on
the grid
Objective 9g: Draw and translate simple shapes on the
coordinate plane and reflect them in the axes
Use four quadrants of the grid to draw different shapes in
different quadrants
Reflect a given shape from one grid to another
Translate a given shape across different grids
© Focus Education (UK) Ltd 2014
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Year 6 Objectives : Statistics
STATISTICS
Objective 1s: Interpret and construct pie charts and line graphs and use these
to solve problems
Know how to interpret information from a pie chart to solve a problem
Know how to construct a pie chart from a set of given information
Know how to interpret information from a line graph to solve a problem
Know how to construct a line graph from a set of given information
Know how to apply scales on the axes of a line graph
Can read line graphs with scales
Can construct own line graph and make decisions about the scales for the axes
Objective 2s: Calculate and interpret the mean as average
Know the term ‘mean’ is the average
Find the average of a given set of numbers
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Step up to the Challenge
Year 6
Number
Year 6: Can you challenge yourself to meet the Objective?
Objective 1: Read, write, order and compare numbers to 10,000,000
and determine the value of each digit
Me
My
Teacher
Can you partition any number up to 10,000,000 showing the value of
each digit?
Do you know and use terms: units; tens, hundreds, thousands, ten
thousands, hundred thousands, one million and ten million correctly?
Can you recognise the value of each digit up to 10,000,000?
Can you read and write numbers to 10,000,000?
Can you read and write numbers to 1,000,000?
Can you remember how to read and write numbers to: 1000 and
then to 100,000?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 2: Round any whole number to a required degree of
accuracy
Me
My
Teacher
Me
My
Teacher
Can you round any 7-digit number to the nearest million?
Can you round any 6-digit number to the nearest hundred
thousand?
Can you round any 5-digit number to the nearest ten thousand?
Can you round any 4-digit number to the nearest thousand?
Can you round any number to the nearest degree of accuracy?
Objective 3: Use negative numbers in context , and calculate
intervals across zero
Can you calculate the interval from + 30 to -30?
Can you calculate the interval from - 20 to + 100?
Can you interpret temperatures at minus ⁰C on a thermometer?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 5: Add and subtract negative integers (non Statutory)
Me
My
Teacher
Me
My
Teacher
Do you know what happens when subtracting a negative number
form another negative number?
Can you add any 2 negative numbers together?
Objective 6: Multiply multi-digit numbers up to 4-digits by a 2-digit
whole number using the formal written method of long multiplication
Can you multiply 4-digit numbers by a 2-digit number using grid
method or another conventional method?
Can you remember how to multiply ThHTU x U?
Can you remember how to multiply HTU x U?
© Focus Education (UK) Ltd 2014
390
Year 6: Can you challenge yourself to meet the Objective?
Objective 7: Divide numbers up to 4-digits by a 2-digit whole number
using the formal written method of long division, and interpret
remainders as whole number remainders, fractions, or by rounding,
as appropriate for the context
Me
My
Teacher
Can you use rounding up to express answers as a whole number?
Can you divide numbers with up to 4-digits by any 2-digit number with
and without remainder?
Can you express remainder as a fractional value of the number
divided by?
Can you divide numbers with up to 4-digits by a 2-digit number up
to 20 with remainder?
Can you divide numbers with up to 4-digits by a 2-digit number up
to 20 without remainder?
Can you remember how to divide numbers with up to 4-digits by
a single-digit number with and without remainders?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 8: Divide numbers up to 4-digits by a 2-digit number using
the formal written method of short division where appropriate ,
interpreting remainders according to the context
Me
My
Teacher
Me
My
Teacher
Can you divide numbers with up to 4-digits by a 2-digit number with
remainder?
Can you divide numbers with up to 4-digits by a 2-digit number
without remainder?
Objective 10: Identify common factors, common multiples and prime
numbers
Do you know all the prime numbers?
Do you know the common multiples of any 2 given numbers?
Do you know the common factors of any 2 given numbers?
© Focus Education (UK) Ltd 2014
392
Year 6: Can you challenge yourself to meet the Objective?
Objective 13: Solve problems involving addition, subtraction,
multiplication and division
Me
My
Teacher
Can you solve word problems with mixed operations with numbers up
to 10,000,000?
Can you solve word problems involving division with numbers up to
10,000,000?
Can you solve word problems involving multiplication with numbers
up to 10,000,000?
Can you solve word problems involving subtraction with numbers
up to 10,000,000?
Can you solve word problems involving addition with numbers
up to 10,000,000?
© Focus Education (UK) Ltd 2014
393
Year 6: Can you challenge yourself to meet the Objective?
Objective 16: Multiply simple unit fractions and pairs of proper
fractions, writing the answer in its simplest form
Me
My
Teacher
Can you multiply 2 mixed fractions and write answer in its simplest
form?
Can you turn mixed fractions into an improper fraction?
Can you multiply 2 simple fractions together and give answer in its
simplest form?
Can you multiply a whole number with a fraction and give answer
in its simplest form?
Can you multiply a whole number with a fraction?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 18: Associate a fraction with division to calculate decimal
fraction equivalents, e.g. 0.375 for a simple fraction ⅜
Me
My
Teacher
Do you know all the decimal fraction equivalents for fractional
values where the denominator is 3, 4, 5, 6, 8 or 10?
Do you know that ¾ can be represented as 0.75?
Do you know that ¼ can be represented as 0.25?
Do you know that 1/10 can be represented as 0.1?
© Focus Education (UK) Ltd 2014
395
Year 6: Can you challenge yourself to meet the Objective?
Objective 19: Add and subtract fractions with different denominators
and mixed numbers, using the concept of equivalent fractions
Me
My
Teacher
Can you subtract 2 mixed numbers where the fractional values have
different denominators?
Can you subtract 2 fractions with different denominators?
Can you add 2 mixed numbers where the fractional values have
different denominators?
Can you add 2 fractions with different denominators?
Can you work out the common denominator for a pair of
fractions with different denominators, e.g. ⅔ and ⅗ ?
Can you remember how to complete addition and subtraction
of fractions with the same denominator?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 21: Recall and use equivalences between simple fractions,
decimals and percentages including in different contexts
Me
My
Teacher
Do you remember all the decimal fraction equivalents for fractional
values where the denominator is 3, 4, 5, 6, 8 or 10 and use this to solve
problem?
Do you remember that ¾ can be represented as 0.75 and use this to
solve problems?
Do you remember that ¼ can be represented as 0.25 and use this to
solve problems?
Do you remember that 1/10 can be represented as 0.1 and use this
to solve problems?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 22: Identify the value of each digit in numbers given to
three decimal places and multiply and divide numbers by 10, 100
and 1000 giving answers up to three decimal places
Me
My
Teacher
Do you know that when dividing a decimal fraction by 1000 the decimal point
moves three places to the left, e.g. 567.234 ÷ 1000 = 0.567234?
Do you know that when dividing a decimal fraction by 100 the decimal
point moves two places to the left, e.g. 567.234 ÷ 100 = 5.67234?
Do you know that when dividing a decimal fraction by 10 the decimal
point moves one place to the left, e.g. 567.234 ÷ 10 = 56.7234?
Do you know that when multiplying a decimal fraction by 1000 the
decimal point moves three places to the right, e.g. 3.457 x 100 = 3457?
Do you know that when multiplying a decimal fraction by 100 the
decimal point moves two places to the right, e.g. 3.457 x 100 = 345.7?
Do you know that when multiplying a decimal fraction by 10 the
decimal point moves one place to the right, e.g. 3.457 x 10 = 34.57?
Do you know the value of each digit in a decimal fraction
which has up to 3 decimal places?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 23: Multiply one-digit numbers with up to two decimal
places by whole numbers
Me
My
Teacher
Can you divide a decimal fraction with up to 2 decimal places by a
2-digit number?
Can you divide a decimal fraction with up to 2 decimal places by
a single-digit number?
Can you multiply a decimal fraction with up to 2 decimal places
by a 2-digit number?
Can you multiply a decimal fraction with up to 2 decimal places
by a single-digit number?
© Focus Education (UK) Ltd 2014
399
Year 6: Can you challenge yourself to meet the Objective?
Objective 26: Use percentages for comparison and calculate
percentages of whole numbers or measures, e.g. 15% of 360
Me
My
Teacher
Can you find any percentage of a given value, e.g. 18% of 360
Can you find 10%, 20%, 30%, etc. of a given value?
Can you find 25%, 50% and 75% of any given value?
Do you know that to find 1% of a value you divide by 100?
Do you recognise 10% as being a tenth of the original value?
Do you recognise 75% as being three quarters of the original
value?
Do you recognise 25% as being a quarter of the original value?
Do you recognise 50% as being a half of the original value?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 27: Use ratio to show the relative sizes of two quantities
(non Statutory)
Me
My
Teacher
Me
My
Teacher
Can you use ratio in defining the sizes of various shapes?
Do you know what is meant by the term ‘ratio of 1:2’?
Do you recognise that the symbol associated with ratio is ‘:’?
Do you understand the term ratio?
Objective 30: Generate and describe linear number sequences
Can you continue a linear number sequence involving decimal
fractions?
Can you continue a linear number sequence involving fractions?
Can you continue a linear number sequence involving positive
and negative numbers?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 31: Express missing number problems algebraically
Me
My
Teacher
Can you work out calculations when given value of 2 letters, e.g.
What is 2a + 3b if a =2 and b = 5?
Can you work out equations involving missing amount, e.g. If 2x -1
= 9, what is x?
Can you write known rules algebraically, e.g. a + b = b + a?
© Focus Education (UK) Ltd 2014
402
Making Mathematics Work
Step up to the Challenge
Year 6
Measurement, Geometry and Statistics
Year 6: Can you challenge yourself to meet the Objective?
Objective 1m: Solve problems involving the calculation and
conversion of units of measure, using decimal notation up to three
decimal places where appropriate
Me
My
Teacher
Me
My
Teacher
Can you use other compound units for speed such as miles per hour and
apply your knowledge in science as appropriate?
Can you use decimal notation to three decimal places to solve
calculations with measures?
Objective 2g: Recognise, describe and build simple 3D shapes,
including making nets
Do you know what a net for an oblong looks like?
Can you create a cube using knowledge of what the net looks like?
Do you know what a net for a square looks like?
© Focus Education (UK) Ltd 2014
404
Year 6: Can you challenge yourself to meet the Objective?
Objective 3g: Compare and classify geometrical shapes based on
properties and sizes and find unknown angles in any triangles,
quadrilaterals, and regular polygons
Me
My
Teacher
Can you work out the size of an angle in a quadrilateral by using a protractor to
measure it?
Do you know that the four angles of any quadrilateral adds up to 360˚?
Can you draw a triangle given size of sides and angle sizes?
Can you use a protractor to measure individual angles of a triangle?
Do you know that the total of the three angles of any triangle adds up to
180˚?
Do you know the properties of rectangles such as parallelogram;
trapezium; rhombus?
Can you describe a square and oblong in terms of their properties?
Can you describe a right angled triangle according to
properties?
Do you know that an isosceles triangle has two sides
which are equal and two angles which are equal?
Do you know that an equilateral triangle has three
angles of 60˚ and three equal sides?
Can you classify triangles in terms of their
properties?
© Focus Education (UK) Ltd 2014
405
Year 6: Can you challenge yourself to meet the Objective?
Objective 4g: Illustrate and name parts of circles, including radius,
diameter and circumference and know that the diameter is twice
the radius
Me
My
Teacher
Do you know that the diameter of a circle is twice its radius?
Do you know that the distance around the outside of a circle is the
circumference?
Do you know that the distance from the centre to the arc of a circle is
the radius?
Do you know that the line across the centre of a circle is known as the
diameter?
© Focus Education (UK) Ltd 2014
406
Year 6: Can you challenge yourself to meet the Objective?
Objective 5g: Recognise angles where they meet at a point, are on a
straight line, or are vertically opposite, and find missing angles
Me
My
Teacher
Me
My
Teacher
Can you work out the missing angles in parallelogram; rhombus
and trapezium from working out diagonally opposite angles, etc.?
Given 3 angles of a quadrilateral can you work out what the
value of the fourth angle is?
Given 2 angles of a triangle can you work out what the value of
the third angle is?
Objective 6g: Describe properties of common 3D shapes and identify
parallel planes and symmetry
Can you identify lines of symmetry in 3D shapes?
Can you point out the parallel planes associated with any 3d
shape?
Can you describe the properties of a cube, cuboid, sphere,
prism and pyramid?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 8g: Describe positions on the full coordinate grid (all four
quadrants)
Me
My
Teacher
Me
My
Teacher
Can you create shapes within a grid by following pairs of numbers
on the grid?
Can you identify each position on four quadrants of a grid using
numbers on the axes?
Objective 9g: Draw and translate simple shapes on the coordinate
plane and reflect them in the axes
Can you use four quadrants of the grid to draw different shapes in
different quadrants?
Can you reflect a given shape from one grid to another?
Can you use four quadrants of the grid to draw different shapes
in different quadrants?
© Focus Education (UK) Ltd 2014
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Year 6: Can you challenge yourself to meet the Objective?
Objective 1s: Interpret and construct pie charts and line graphs and
use these to solve problems
Me
My
Teacher
Me
My
Teacher
Can you construct own line graph and make decisions about the scales for
the axes?
Can you read line graphs with scales?
Do you know how to apply scales on the axes of a line graph?
Do you know how to construct a line graph from a set of given
information?
Do you know how to interpret information from a line graph?
Do you know how to construct a pie chart from a set of given
information?
Do you know how to interpret information from a pie chart?
Objective 2s: Calculate and interpret the mean as average
Can you find the average of a given set of numbers?
Do you know the term ‘mean’ is the average?
© Focus Education (UK) Ltd 2014
409
Focus on Mathematics
Non-Negotiables
Year 6 Possible Planning Outline
Year 6 Mathematics Non-Negotiables
• The following areas of learning are known as the non-negotiables. They have a specific
role in helping pupils meet the year group expectations. In a nutshell we are suggesting
that if pupils are not confident in these areas then they will find the rest of the curriculum
difficult to access.
•
The non-negotiables are designed to:
1.
Identify the essential components that pupils need to become confident with, i.e. be
able to demonstrate in independent tasks and be able to apply in other contexts.
2.
Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at
the expense of progress.
3.
Unlock learning and progress.
•
The non-negotiables are not designed to imply that the rest of the curriculum is an
irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what
the right curriculum is for their pupils.
© Focus Education (UK) Ltd 2014
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Year 6 Mathematics Non-Negotiables
• Compare and order numbers up to 10,000,000.
• Identify common factors, common multiples and prime numbers.
• Round any whole number to a required degree of accuracy.
• Multiply:
o 4-digit by 2-digit
• Divide:
o 4-digit by 2-digit
•
•
•
•
Add and subtract fractions with different denominators and mixed numbers.
Multiply simple pairs of proper fractions, writing the answer in the simplest form.
Divide proper fractions by whole numbers.
Calculate percentage of a whole number.
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the non-negotiables
The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should be
some element of teaching of these each day.
Autumn Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back from a given number in steps of 10/100/1000/10000
up to at least 1,000,000
Count on/back in whole numbers, fraction and decimal sequences
through zero to include negative numbers (e.g. 2.5 or 1 ¼)
Find 0.01, 0.1, 1, 10 and powers of 10 more or less than a given
number
Read, write, partition, order and compare numbers to at least
1,000,000
Round any number to 1,000,000 to the nearest 10, 100, 1000, 10,000
and 100,000 (e.g. round 5 digit number to the nearest 10.000)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up to
3dp
Round decimals with 1 and 2dp to the nearest whole number and to
1dp
Multiply and divide mentally drawing upon known facts and/or
using place value
Multiply and divide any whole and decimal number by 10, 100 and
1000 giving answers up to 2dp
Mentally add and subtract tenths and one-digit whole numbers and
tenths
Add/subtract mentally a 5-digit number and 4- digit numbers (e.g.
15,345 + 2300 and 12,462 – 2300 )
Count on/back with positive and negative numbers, including
through zero
Count on/back in fraction and decimal sequences
Find factors and factor pairs of each number to 100
Find complements to 100. 1000 ,10,000 and to £1.00, £5.00 and
£10.00
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back from a given number in steps of 10/100/1000/10000
to 1,000,000 and beyond
Count on/back in whole numbers, fraction and decimal sequences
through zero to include negative numbers? (e.g. 2.5 or 1 ¼)
Find 0.01, 0.1, 1, 10 and powers of 10 more or less than a given
number
Read, write, partition, order and compare numbers to 1,000,000
and beyond?
Round any number to 1,000,000 to the nearest 10, 100, 1000, 10,000
and 100,000 (e.g. round 5 digit number to the nearest 10.000; 6 digit
number to the nearest 100,000)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up to
3dp
Round decimals with 3dp to the nearest whole number or to one or
two decimal places
Multiply and divide drawing upon known facts and/or using place
value
Multiply and divide any whole and decimal number by 10, 100 and
1000 giving answers up to 2dp
Mentally add and subtract tenths and one-digit whole numbers and
tenths
Add/subtract mentally a 5-digit number and 4- digit numbers (e.g.
15,345 + 2300 and 12,462 – 2300 )
Continue a linear number sequence with positive and negative
numbers, decimal and proper fractions including through zero
Find factors and factor pairs of each number to 100
Convert units of measurement (km and m; cm and m; cm and mm;
gram and km, ml and l and time)
Find complements to 100, 1000 ,10,000 and to £5.00, £10.00 and
£20.00
© Focus Education (UK) Ltd 2014
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Planning to meet the requirement of the non-negotiables
Spring Term
Ist Half Term
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
2nd Half Term
Count on/back from a given number in steps of 10/100/1000/10000
to 1,000,000 and beyond
Count on/back in whole numbers, fraction and decimal sequences
through zero to include negative numbers (e.g. 2.5 or 1 ¼
Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given
number
Read, write, partition, order and compare numbers to 5,000,000
Round any number to 5,000,000 and beyond to the nearest 10, 100,
1000, 10,000 and 100,000 (e.g. round any 6 digit number to the
nearest hundred thousand and 7-digit number to the nearest
million)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up to
3dp
Round decimals with 3dp to the nearest whole number or to one or
two decimal places
Multiply and divide drawing upon known facts and/or using place
value
Multiply and divide any whole and decimal number by 10, 100 and
1000 giving answers up to 3dp
Add/subtract mentally a 5-digit number and 4-digit numbers (e.g.
15,345 + 2300 and 12,462 – 2300 )
Mentally add and subtract tenths and 1-digit whole numbers and
tenths
Perform mental calculations with larger numbers and mental
calculations which include at least 2 different operations (e.g.
addition and multiplication)
Continue a linear number sequence with positive and negative
numbers, decimal and proper fractions including through zero
Find factors and factor pairs of each number to 100
Convert units of measurement (km and m; cm and m; cm and mm;
gram and km, ml and L and time)
Find complements to 100. 1000 ,10,000 and to £5.00, £10.00 and
£20.00
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Count on/back from a given number in steps of 10/100/1000/10000
to 1,000,000 and beyond
Count on/back in whole numbers, fraction and decimal sequences
through zero to include negative numbers (e.g. 2.5 or 1 ¼)
Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given
number
Read, write, partition, order and compare numbers to 5,000,000 and
beyond
Round any number to 5,000,000 and beyond to the nearest 10, 100,
1000, 10,000 and 100,000 (e.g. round any 6 digit number to the
nearest hundred thousand and 7-digit number to the nearest
million)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up to
3dp
Round decimals with 3dp to the nearest whole number or to one or
two decimal places
Multiply and divide drawing upon known facts and/or using place
value
Multiply and divide any whole and decimal number by 10, 100 and
1000 giving answers up to 3dp
Perform mental calculations with larger numbers and mental
calculations which include at least 2 different operations (e.g.
addition and multiplication)
Continue a linear number sequence with positive and negative
numbers, decimal and proper fractions including through zero
Find factors and factor pairs of each number to 100
Convert units of measurement using decimal notation up to 3dp (km
and m; cm and m; cm and mm; gram and km, ml and l and time)
Find complements to 1000, 10,000 and to £10.00, £20.00 and £50
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Planning to meet the requirement of the non-negotiables
Summer Term
Ist Half Term
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2nd Half Term
Count on/back from a given number in steps of 10/100/1000/10000
to 1,000,000 and beyond
Count on/back in whole numbers, fraction and decimal sequences
through zero to include negative numbers (e.g. 2.5 or
1¼
Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a
given number
Read, write, partition, order and compare numbers to 10,000,000
Round any 6 digit number to the nearest hundred thousand and 7digit number to the nearest million.
Round any number to 10,000,000 to the nearest 10, 100, 1000,
10,000 and 100,000 (e.g. round any 6 digit number to the nearest
hundred thousand and 7-digit number to the nearest million)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up to
3dp
Round decimals with 3dp to the nearest whole number or to one or
two decimal places
Multiply and divide any whole and decimal number by 10, 100 and
1000 giving answers up to 3dp
Perform mental calculations with larger numbers and mental
calculations which include at least 2 different operations (e.g.
addition and multiplication)
Continue a linear number sequence with positive and negative
numbers, decimal and proper fractions including through zero
Find factors and factor pairs of each number to 100
Convert units of measurement using decimal notation up to 3dp
(km and m; cm and m; cm and mm; gram and km, ml and L and
time)
Find complements to 1000, 10,000 and to £10.00, £20.00 £50 and
£100
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Count on/back from a given number in steps of
10/100/1000/10000 to 1,000,000 and beyond
Count on/back in whole numbers, fraction and decimal
sequences through zero to include negative numbers (e.g. 2.5
or 1 ¼)
Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a
given number
Read, write, partition, order and compare numbers to
10,000,000
Round any number to 10,000,000 to the nearest 10, 100, 1000,
10,000 and 100,000 (e.g. round any 6 digit number to the nearest
hundred thousand and 7-digit number to the nearest million)
Order and compare numbers including integers, decimals and
negative numbers
Read, write, order, partition and compare decimal numbers up
to 3dp
Round decimals with 3dp to the nearest whole number or to
one or two decimal places
Multiply and divide any whole and decimal number by 10, 100
and 1000 giving answers up to 3dp
Perform mental calculations with larger numbers and mental
calculations which include at least 2 different operations (e.g.
addition and multiplication)
Continue a linear number sequence with positive and negative
numbers, decimal and proper fractions including through zero
Find factors and factor pairs of numbers to 100
Convert units of measurement using decimal notation up to 3dp
(km and m; cm and m; cm and mm; gram and km, ml and l
and time)
Find complements to 1000, 10,000 and to £10.00, £20.00 £50 and
£100
© Focus Education (UK) Ltd 2014
415
Focus on Mathematics
Year 6 Assessment
Assessment: Meeting Year 6 Expectations
The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 6 expectations. The Year 6 expectations
for number are set out below on this page. To meet the Year 6 expectations a pupil must be able to meet all of the statements outlined in
the table, plus the ones for measurement and geometry, shown later.
If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an
assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is
exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper
analysis, if required.
Year 6 Expectations: Number
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Use negative numbers in context, and calculate intervals across zero
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Round any whole number to a required degree of accuracy and solve problems which require answers to be rounded to a specific
degree of accuracy
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Solve problems involving the relative sizes of two quantities where the missing values can be found by using integer multiplication and
division facts
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Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
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Solve problems involving the calculation of percentages, (e.g. of measures) such as 20% of 440 and the use of percentages for
comparison
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Multiply 1-digit numbers with up to two decimal places by whole numbers
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Perform mental calculations, including with mixed operations with large numbers
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Divide numbers up to 4-digits by a 2-digit whole number using formal written methods of long division and interpret remainder in
various ways
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Use knowledge of order of operations to carry out calculations involving all four operations
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Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
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Multiply simple pairs of proper fractions, writing the answer in its simplest form
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Divide proper fractions by whole numbers (⅛ ÷ 2 = 1/16)
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Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375 for ⅜)
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Express missing number problems algebraically
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Find pairs of numbers that satisfy an equation with two unknowns
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 6 Expectations
The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 5 expectations. The Year 5 expectations
for number are set out below on this page. To meet the Year 5 expectations a pupil must be able to meet all of the statements outlined in
the table, plus the ones for measurement and geometry, shown later.
If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an
assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is
exceeding the expectations or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper
analysis, if required.
Year 5 Expectations: Number
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Count forwards and backwards in steps of power 10 for any given number up to 1,000,000
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Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents
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Recognise mixed numbers and improper fractions and convert from one to the other
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Read and write decimal numbers as fractions, e.g. 0.47 = 47/100
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Recognise the per cent symbol (%) and understand per cent relates to number of parts per hundred
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Write percentages as a fraction with denominator hundred, and as a decimal number
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Compare and add fractions whose denominators are all multiples of the same number
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Multiply and divide numbers mentally drawing upon known facts up to 12 x 12
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Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
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Round decimals with 2dp to the nearest whole number and to 1decimal place
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Recognise and use square numbers and cube numbers and the notation for squared (²) and cubed (³)
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Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
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Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including long multiplication for 2-digit numbers
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Divide numbers up to 4-digits by 1-digit numbers
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Solve problems involving multiplication and division where large numbers are used by decomposing them into factors
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Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why; solve
problems involving 3 decimal places and problems which require knowledge of percentages and decimal equivalents
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 6 Expectations
The 3 or 9-point scale
Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as
having met the expectations; emerging towards the expectations or exceeding the
expectations.
However, for many schools, this may not give them enough information when tracking
pupils through the school. So, if schools desire, the following 9-point system is outlined for
them to use.
Assessed
position
Emerging
Stage C
Emerging
Stage B
Emerging
Stage A
Meeting
Stage C
Meeting
Stage B
Meeting
Stage A
Exceeding
Stage C
Exceeding
Stage B
Exceeding
Stage A
Points
allocation
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2
3
4
5
6
7
8
9
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As is illustrated, Point 4 is the point that indicates that a pupil has met the
expectations. If we are to take account of the new Assessment arrangements then it
is hoped that 85% of pupils will be at least at this stage by the end of the year.
Points 1 to 3 are the ‘emerging’ stages;
Points 4 to 6 are the ‘meeting’ expectations stages; and
Points 7 to 9 are the ‘exceeding’ stages.
The following page sets out what each point actually means and provides clarity
about the allocation of the points.
© Focus Education (UK) Ltd 2014
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Assessment: Meeting Year 6 Expectations
Year 6 Expectations: Number
Year 6 Expectations:
Measurement, Geometry and
Statistics
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Use negative numbers in context, and calculate intervals across zero
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Round any whole number to a required degree of accuracy and solve problems
which require answers to be rounded to a specific degree of accuracy
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Recognise, describe and build simple 3D
shapes, including making nets
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Solve problems involving the relative sizes of two quantities where the missing values
can be found by using integer multiplication and division facts
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Use common factors to simplify fractions; use common multiples to express fractions
in the same denomination
Compare and classify geometric shapes
based on their properties and sizes and find
unknown angles in any triangle,
quadrilateral and regular polygons
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Solve problems involving the calculation of percentages, (e.g. of measures) such as
20% of 440 and the use of percentages for comparison
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Multiply 1-digit numbers with up to two decimal places by whole numbers
Illustrate and name parts of circles,
including radius, diameter and
circumference and know that the radius is
half the diameter
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Perform mental calculations, including with mixed operations with large numbers
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Divide numbers up to 4-digits by a 2-digit whole number using formal written methods
of long division and interpret remainder in various ways
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Use knowledge of order of operations to carry out calculations involving all four
operations
Use, read, write and convert between
standard units, converting measurements of
length, mass, volume and time from a
smaller unit of measure to a larger unit, and
visa versa, using decimal notation to up to 3
decimal places
Add and subtract fractions with different denominators and mixed numbers, using the
concept of equivalent fractions
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Multiply simple pairs of proper fractions, writing the answer in its simplest form
Calculate the area of a parallelogram and
triangles and calculate, estimate and
compare volume of cubes and cuboids
using standard units
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Divide proper fractions by whole numbers (⅛ ÷ 2 = 1/16
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Interpret and construct pie charts and line
graphs and use these to solve problems
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Associate a fraction with division and calculate decimal fraction equivalents (eg,
0.375 for ⅜)
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Express missing number problems algebraically
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Find pairs of numbers that satisfy an equation with two unknowns
© Focus Education (UK) Ltd 2014
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Assessment: Exceeding Year 6 Expectations
Year 6 Exceeding Expectations: Number
• Compare, order and convert between fractions, decimals and percentages in
contexts related to science, history or geography learning
• Move beyond squared and cubed numbers to calculate problems such as X x 10n
where n is positive
• Use =, ≠, <, >, ≤, ≥ correctly
• Multiply all integers, (using efficient written methods) including mixed numbers and
negative numbers
• Recognise an arithmetic progression, and find the nth term
• Use formula for measuring area of shape, such as cuboid and triangle to work out
area of irregular shape in the school environment
• Use four operations with mass, length, time, money and other measures, including
with decimal quantities
• Create a scaled model of a historical or geographical structure showing an
acceptable degree of accuracy using known measurements
• Calculate costs and time involved to visit a destination in another part of the world relating
to on-going learning in history or geography
• Collect own data on personal project and present information in formats of their choosing,
charts, graphs and tables and answer specific questions related to their research
© Focus Education (UK) Ltd 2014
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Focus on Mathematics
Year 6 Parents’ Guide
Parents’ Guide
‘Must Dos’ by the end of Year 6
Number
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Number
Read, write and order numbers to
10,000,000
Round any number to any degree of
accuracy
Add and subtract negative numbers
Multiply a 4-digit number by a 2-digit
number
Divide a 4-digit number by a 2-digit
number, expressing remainder as a
fraction, decimal fraction or by rounding
to whole numbers
Mental Agility: Calculations involving
large numbers
Mental Agility: Calculations involving two
operations
Use estimation to check answers
Carry out problem solving calculations
involving all 4 operations
Add and subtract mixed numbers with
fractions of different denominations
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Fractions: Multiply simple fractions, writing
answers in their simplest forms
Divide proper fractions by whole numbers
Identify value of each digit in a 3 decimal
place number
Multiply decimal fraction with 3 decimal
places by 10, 100 and 1000
Multiply and divide a number with 2
decimal places by 1-digit and 2-digit
numbers
Percentages: Use percentages for
comparisons
Calculate percentage of whole numbers
Recall and use equivalences between
fractions, decimal fractions and
percentages
Ratio: Use ratio to show relative sizes of 2
quantities
Algebra: Solve linear missing numbers
Continue a linear number sequence
involving positive and negative numbers
© Focus Education (UK) Ltd 2014
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Parents’ Guide
‘Must Dos’ by the end of Year 6
Shape and Measures
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Shape and Measures
Compare and classify geometrical
shapes based on properties and size
Find unknown angles in a triangle,
quadrilateral and regular polygon
Illustrate and name parts of a circle,
including radius, diameter and
circumference
Recognise, describe and build 3D
shapes
Create a cuboid from a net
Describe properties of 3D shapes and
identify parallel planes and symmetry
Estimate size of angles
Describe position on the full coordinate
grid
Draw, translate and reflect shapes
Read, write and convert between
standard units
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Calculate area of parallelograms and
triangles
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Data: Draw, read and interpret graphs
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Use and interpret mean as an average
© Focus Education (UK) Ltd 2014
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