Transcript to access presentation - North Rigton Primary School

Maths evening 12th October
2015
• Welcome
• Changes in teaching and expectations
since introduction of New Curriculum 2014
• Calculating and efficient written methods
• Assessment For Learning
• Launching ‘Launch Pad’ maths.
• Have a look around and see how we do it.
Example of
Changes to the
Maths Curriculum

Year 5


Read, write, order and compare numbers to at least
1 000 000 and determine the value of each digit

Count forwards or backwards in steps of powers of 10 for any given
number up to 1 000 000
Round any number up to 1 000 000 to the nearest 10, 100,
1000, 10 000 and 100 000





Read Roman numerals to 1000 (M) and recognise years written in Roman
numerals.Divide using the efficient written method of short division.
Recognise and use square numbers and cube numbers, and the notation for
squared (2) and cubed (3)
add and subtract fractions with the same denominator and related
fractions; write mathematical statements >1 as a mixed number (e.g. 2/ 5 +
4

/ 5 = 6/ 5 = 11/ 5 )
multiply proper fractions and mixed numbers by whole numbers, supported by
materials and diagrams
Recognise and estimate volume (e.g. using 1 cm3 blocks to build cubes
and cuboids) and capacity (e.g. using water)
Solve problems involving converting between units of time

Draw shapes using given dimensions and angles


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
Year 6
Read, write, order and compare numbers up to 10 000 000 and determine
the value of each digit

Multiply multi-digit numbers up to 4 digits by a two-digit whole number
using the efficient written method of long multiplication
Divide numbers up to 4 digits by a two-digit whole number using the efficient
written method of long division, and interpret remainders as whole number
remainders, fractions, or by rounding, as appropriate for the context
Add and subtract fractions with different denominators and mixed
numbers, using the concept of equivalent fractions
Multiply simple pairs of proper fractions, writing the answer in its simplest
form (e.g. 1/ 4 × 1/ 2 = 1/ 8 )
Divide proper fractions by whole numbers (e.g. 1/ 3 ÷ 2 = 1/ 6 ).
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 three
decimal places
Calculate the area of parallelograms and triangles







Recognise when it is necessary to use the formulae for area and volume of
shapes
North Rigton Church of England
Primary
Calculations
Addition
Subtraction
Multiplication
Division
Assessment
Early addition
5+4 =
Addition method 1
In our school to work out addition
problems we use the partitioning method.
37 + 24 = 61
How did you work it out?
30 + 20 = 50
7 + 4 = 11
50 + 11 = 61
Addition progression
The partitioning method is now used for
increasingly large numbers e.g.
2471 + 3524 = 6001
2000 + 3000 = 5000
400 + 500 = 900
70 + 20 = 90
7+
4=
11
This is then extended to include larger numbers and numbers
with more decimal places.
Addition progression
Again we use the partitioning method, but
this is extended to include decimals.
7.6 + 5.8 = 13.4
7 +
5 = 12
0.6 + 0.8 = 1.4
Adding (transition)
To progress with addition using efficient written
methods we begin to encourage the children to use
more traditional column methods.
123
The children need a secure knowledge of
+74
place value.
1 1
197
123
+89
212
Early Subtraction
5-4 =
Subtraction method 1
Children are encouraged to begin by
using the empty number line method.
This method is quick and efficient and
develops children's mental calculation
skills.
Children are encouraged to always count
forwards along the number line.
The Number Line:
96 – 32 =
8
50
6
32_______________________________96
40
90
This is extended to include more difficult numbers and decimals.
In later years this may also become jottings.
Subtraction Method 2
Introducing the column method.
96
-32
64
Progression: Decomposition
Other wise known as borrowing.
2 1
326
-95
231
Early Multiplication
• Groups of/ lots of/arrays
Multiplication method 1
We begin multiplying using the partitioning
method.
23 x 3 = 69
20 x 3 = 60
3x3= 9
60 + 9 = 69
Multiplication method 2
In year four the children continue to use
partitioning but the grid method is introduced.
23 x 3 = 69
x
20
3
3
60
9
Multiplication progression
We now use the grid method for larger
numbers and decimals.
X 20
10 200
7
20 = 270
X
40 40
8
1.2
5
35 = 135
5
1
0.15 = 6.15
100
27 x 15 = 405
1
5
0.2
0.03
= 49.2
1.23 x 45 =55.35
Multiplication method 3
Long multiplication
27
X15
1
270
+ 135
405
Division
We teach division as the opposite of
multiplication e.g.
4 x 5 = 20
20 / 5 = 4
This is taught as a KIRF alongside the
teaching of times tables.
By the end of year 4 children should know
this up to 12x12!
Early division
9/3=
Division method 1
To solve division problems we use the
chunking method.
We reinforce the idea that division is repeated addition
and encourage the use of an empty number line.
How many groups of 8 do we need to make 24?
24 / 8 = 3
1x8
1x8
1x8
0_________________________________________24
8
16
3 groups of 8 make 24
Division progression 2
As children begin dividing larger numbers they add together groups of
numbers.
176 / 8 = 22
10 x 8
10 x 8
2x8
0________________________________176
80
160
Children are encouraged to make informal jottings to help with their
calculation.
10 x 8 = 80
20 x 8 = 160
5 x 8 = 40
2 x 8 = 16
4 x 8 = 32
Children use knowledge of doubles and halves to help.
Children are then taught to solve problems including remainders and
larger numbers.
Division
Progression 3
At this point we
turn the layout of
the chunking
around in
preparation for
long division.
176/8
176
80
96
80
16
16
00
10x8
10x8
2x8
22
Division
method 2
In preparation for
transition, we now
come to long
division (the more
traditional method)
022
8 176
0
17
16
016
016
000
Division
method 3
And finally once all
the understanding is
secured, we move onto
short division.
22
8 11716
Assessing maths
AFL and SPIDERS
AFL
Assessment for learning
Promotes awareness, independence
and self motivation.
Spiders are a tool used by the
children and the teacher to set
targets
Astronaut selection
Recites numbers in order to 10
Recognises numerals 1 to 5
Counts up to three or four objects by
saying one number name for each of
them
Counts out up to six objects from a
larger group
Selects the correct number to
represent 1 to 5
Selects the correct number to
represent 1 to 10
Counts objects to 10
Count beyond 10
Parent
Peer Teacher
Saturn
Count from any number in
steps of 6
Count from any number in
steps of 7
Count from any number in
steps of 9
Count from zero in steps of
25
Count from zero in steps of
1000
Know by heart all
multiplication facts for 11, up
to 11 x 12
Know by heart all division
facts for 11 up to 11 x 12
Know by heart all
multiplication facts for 12, up
to 12 x 12
Know by heart all division
facts, for 12, up to 12 x 12
Pare
nt
Peer
Teache
r
Uranus
Use knowledge of time facts to write
equivalent times to multiples of 1/4
of a unit e.g. 180 seconds = 3
minutes, 5 ¼ hours = 5 hours 15
mins
Use knowledge of mass and weight
facts to write equivalent measures
e.g. 3.75kg = 3750g, 5678g =
5.678kg
Use knowledge of volume and
capacity facts to write equivalent
measures e.g. 7.45l = 7450ml,
3278ml = 3.278l
Use knowledge of length facts to
write equivalent measures e.g.
5.2km = 5200m, 22mm = 2.2cm
Count up and down in tenths from
any given number
Know by heart 1 tenth more of any
given number
Know by heart 1 tenth less than any
given number
Parent
Peer
Teacher
The Milky Way
Identify pairs of factors for all 2 digit
whole numbers
Know by heart all the squares of
numbers up to 12 x 12
Know by heart all the cubes
numbers up to 12³
Recognise and recall factors of
numbers up to 100 and
corresponding multiples of 100
Use knowledge of place value and x
facts to 12 x 12 to derive related
multiplication and division facts
involving decimals… 0.8 x 7 = 5.6
Know by heart tests of divisibility for
multiples of 2, 3, 4, 5, 6, 9 and 10
Parent
Peer
Teacher
Key Instant Recall Facts
Autumn 1a
This half term your child is working towards achieving their individual KIRF target, indicated below.
The ultimate aim is for your child to be able to recall these facts instantly!
Say the number
names in order
to 5
Know all the
number bonds
to 5 (then
moving to 10)
Example of number bonds to 5:
All number bonds to 10:
Five teddies are sitting on a shelf, 1 fell off,
how many are left?
Well done, that was quick!
Know all the
number bonds to
20
Four are left!
Know all the
number bonds for
each number to 20
0 +
1 +
2 +
3 +
4 +
5 +
6 +
7 +
8 +
9 +
10 +
10 = 10
9 = 10
8 = 10
7 = 10
6 = 10
5 = 10
4 = 10
3 = 10
2 = 10
1 = 10
0 = 10
Building confidence in mathematics is crucial so be pleased with their efforts and always encourage with praise. Make
sure these practice sessions are enjoyable - if your child is really not in the mood it is the wrong time to be practising!
Developed by the North Yorkshire Primary Maths Consultants
Autumn 1a
Helpful hints for parents
 Use objects to consider the bonds in a practical way.
 Look at the patterns with both objects and numbers e.g. as one number increases the other one decreases.
 Practise with the numbers in order and chosen randomly - remember the aim is for the child to be able to respond
immediately.
Key vocabulary
Add, Total, How many more to make?, Altogether
Make it real!
There are 5 ladybirds on the leaf. Two fly away,
how many are left?
3 ladybirds!
How do you know?
Well, 2 add 3 make 5.
I have 7p in my purse. How much more do I need to make 10p?
3p!
Why?
Because 3p and 7p totals
10p
I have 18 cm of ribbon, I cut off 14 cm. How much ribbon is left?
Make it fun!
Call out!
Play number ping pong!
Start of saying 'ping', child replies with 'pong'.
Repeat and then convert to numbers i.e. say '2' and they reply '8'
(number bonds to 10)
What's hidden?
There are 5 beans on this plate, I hide some under a beaker how many have I hidden?
Playing cards:
Take out the picture cards from the deck of cards. Include
the jokers as 'zero'.
1) Play snap by matching the number bonds.
2) Play the 'memory game' to find matching number bonds.
Dominoes:
Connect two dominoes to make the bond.
Songs and rhymes
e.g. 5 speckled frogs, 10 in a bed, 10 green bottles
4 centimetres.
Are you sure?
Yes, because I know that 4 and 14 make 18 altogether.
Timed Games:
How well are you doing? How many questions can you answer in
2 minutes. Can you beat your own record?
Developed by the North Yorkshire Primary Maths Consultants
Key Instant Recall Facts
Autumn 1b
This half term your child is working towards achieving their individual KIRF target, indicated below.
The ultimate aim is for your child to be able to recall these facts instantly!
Example of number bonds to 100:
I have a metre of string. I use 67cm to wrap my parcel.
How much string is left?
33cm are left!
Well done, that was
quick!
All decimal bonds to 1:
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
+
+
+
+
+
+
+
+
+
+
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
=
=
=
=
=
=
=
=
=
=
1
1
1
1
1
1
1
1
1
1
Example of decimal bonds to 10:
6.2 + 3.8 = 10; 6.2 + 3.8 = 10
so
10 - 6.2 = 3.8; 10 - 3.8 = 6.2
4.9 + 5.1 = 10; 5.1 + 4.9 = 10
so
10 - 4.9 = 5.1; 10 - 5.1 = 4.9
Building confidence in mathematics is crucial so be pleased with their efforts and always encourage with praise. Make
sure these practice sessions are enjoyable - if your child is really not in the mood it is the wrong time to be practising!
Developed by the North Yorkshire Primary Maths Consultants
Helpful hints for parents
Autumn 1b
 Create regular, short opportunities for rapid fire questions where an instant correct answer is required
 Use objects to consider the bonds in a practical way
 Look at the patterns with both objects and numbers e.g. as one number increases the other one decreases
 Practise with the numbers in order and chosen randomly - remember the aim is for the child to be able to respond
immediately
Key vocabulary
How many more to make?
altogether, make, sum, total, how much more is…than…, …difference between
Make it real!
Jack has £1, he spends 30p. How much change does
he get?
70p!
Are you sure?
Yes, the sum of 70p and 30p is 100p that's £1
A bag of sugar contains 1 kg. If I use 340g how much will I have
left?
660 grams!
How do you know?
The difference between 1000 grams and 660g is 340g.
A litre jug is filled with 0.25l of juice. How
much more is needed to make a litre?
0.75 of a litre!
How did you work that out?
Because a quarter of a litre plus three quarters of
a litre equals 1 whole litre.
Remember - a great place to think about capacity
is in the bath!
Make it fun!
Call out!
Play number ping pong!
Start of saying 'ping', child replies with 'pong'.
Repeat and then convert to numbers i.e. say '0.3' and they reply '0.7'
(decimal bonds to 1)
What's hidden?
There are 17 beans on this plate, I hide some under a beaker - how
many have I hidden? (bonds for each number to 20)
Playing cards:
Remove picture cards and the 10s. Play snap treating each card as
tenths. When you have a pair which total 1, shout snap and explain
why e.g. 0.2 + 0.8 = 1
Dice:
Roll two die treat them as the first as the tens digit and the
second as the ones - ask how many more to make 100.
Dominoes:
Pick a domino from a set facing down. Choose one side to
represent the whole number and the other side to be the tenth.
Ask how much more to make 10.
e.g. picture shows 5.2, so 4.8 more makes 10.
Timed Games:
How well are you doing? How many questions can you answer in
2 minutes. Can you beat your own record?
Developed by the North Yorkshire Primary Maths Consultants
Assessing
Weekly Times table tests (timed as they improve)
Weekly mental maths tests (see tests on tables)
Launchpad tests