Transcript End Of Year Objective

Maths Evening
November 2015
Aims
 To help you support your children at home by
encouraging the use of methods promoted in school
 To consider the progression of addition, subtraction,
multiplication and division
 To introduce resources used to support children in
their mathematical development
Early Learning Goals

Mathematics involves providing children with the opportunities to:





Count reliably with numbers 1-20
Place numbers in order
Say which number is one more or less than a given number
Use quantities and objects
Add and subtract two single digit numbers and count on and back
to find the answer
Solve problems, including doubling, halving and sharing
Use everyday language to talk about size, weight, capacity,
position distance, time and money to compare quantities and
objects and to solve problems
Recognise, create and describe patterns
Explore characteristics of everyday objects and shapes and use
mathematical language to describe them




Aims of the National Curriculum
 The national curriculum for mathematics aims to ensure that all pupils:
 become fluent in the fundamentals of mathematics, including through
varied and frequent practice with increasingly complex problems over time,
so that pupils develop conceptual understanding and the ability to recall and
apply knowledge rapidly and accurately.
 reason mathematically by following a line of enquiry, conjecturing
relationships and generalisations, and developing an argument, justification
or proof using mathematical language
 can solve problems by applying their mathematics to a variety of routine
and non-routine problems with increasing sophistication, including breaking
down problems into a series of simpler steps and persevering in seeking
solutions.
Our Vision
 Excellence and enjoyment for all
 Progressive and Challenging
 Embedded across the curriculum
 Inclusive and collaborative
Addition
(Stage 1)
In the early stages of Reception children will learn the foundations of
number, developing their number recognition skills through lots of fun
games and activities.
Children will then begin to understand addition as the combination of two
groups.
Children will be encouraged to develop a mental picture of the number
system in their heads and develop pictorial representations to record their
calculations;
Bead strings will be used to demonstrate addition to children;
8+2=10
End of Year Objective – Using quantities and objects, children add 2 single-digit numbers
and count on to find the answer.
Year 1
(Stage 2)
Children will continue to use pictures to represent addition
calculations.
Children will then begin to use readymade number lines to support their own calculations
by using a number line or bead string to count on in ones.
8 + 5 = 13
Children move on to using Base 10 equipment to support their developing understanding
of addition.
11 + 5 = 16
11 cubes are lined up (1 ten and 1 unit/one).
5 cubes are added to the line of 11 giving a total of 16
End of Year Objective – add one and two-digit numbers to 20,
including zero.
Year 2
(Stage 2)
Children continue to use the Base 10 equipment, cubes, art straws and Numicon to
support their calculations including exchanging 10 units/ones for 1 ten when the total
of the units/ones is 10 or more.
They will record their own drawings of the Base 10 equipment, using lines for 10 rods
and dots for the unit blocks.
34 + 23 = ?
The units/ones are added first 4 + 3 = 7
The tens are added next
30 + 20 = 50
answers are put together 50 + 7 = 57
28 + 36 = ?
The units/ones are added first
8 + 6 = 14 with ten units/ones exchanged for 1 ten.
A ring is put around the units/ones not exchanged – this is the units part of the
answer. The tens are then added, including the exchanged ten, to complete the
sum.
End of Year Objective – add numbers using concrete objects, pictorial representations,
and mentally, including: a two-digit number and ones; a two-digit numbers and tens; two
two-digit numbers; adding three one-digit numbers.
Year 3

(Stage 4)
Continue to use Base 10 for practical work and recording.
65 + 27
End of Year Objective – Add numbers with up to three digits
using formal written methods of column addition.
Year 4,5,6 (Stage 4)
This is the final stage of the method, and should be continued to be used for all
written addition calculations.
The example would be ‘said’ as follows:
5 + 8 = 13, put 3 down and carry the 10
20 + 40 + 10 that was carried over = 70 (7 written in the tens column)
600 + 0 = 600 (6 written in the hundreds column)
Chil
Year 4,5,6 (Stage 4)
Children will be expected to use this method for adding numbers with more than 3
digits, numbers involving decimals and adding any number of amounts together.
End of Year Objective Y4 – Add numbers with up to
4-digits and decimals with one decimal place using formal written method of column
addition.
End of Year Objective Y5 – Add whole numbers with more than 4-digits and decimals
with two decimal places using formal written method of column addition.
End of Year Objective Y6– Add whole numbers and decimals using formal written
method of column addition.
Vocabulary
Subtraction (Stage 1)
In Reception children will subtract two numbers by taking one away from the
other and counting how many are left.
Touch counting and dragging.
7–3=4
They begin to recognise and use Numicon equipment to help ‘take away’.
When ready, they begin to record subtraction number sentences such as 8 – 5 = 3.
End Of Year Objective - Using quantities and objects, children subtract two single-
digit numbers and count on or back to find the answer.
Year 1 (Stage 2)
Children move on to using Base 10 and Numicon equipment alongside a number
track to support their developing understanding of subtraction. They will also
continue to use cubes and counters.
13 - 4 = ?
13 cubes are lined up.
4 cubes are removed from the end of the line leaving 9 left.
It is important that children keep track of how many have been removed.
Touch count and remove the number to be taken away.
Touch count to find the number that remains.
End of Year Objective – Subtract one-digit and two-digit numbers to 20, including zero.
Year 2 (Stage 3)
Children continue to use the Base 10 equipment to support their calculations.
Eg 54 – 23
which leaves
They will record their own drawings of the Base 10 equipment, using lines for 10 rods
and dots for the unit blocks.
39 - 17 = ?
39 is drawn
17 is crossed out
A ring is drawn around
what is left to give the answer giving 22
Children will begin to use empty number lines
End of Year Objective - Subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones; a two-digit number and tens; two two-digit numbers.
-3
-20
47-23=
24 25 26 27
37
47
End of Year Objective - Subtract numbers using concrete objects, pictorial
representations, and mentally, including: a two-digit number and ones; a two-digit
number and tens; two two-digit numbers.
Year 3 (Stage 4a)
Children move from using the Base 10 method to expanded vertical method, using base
10 notation and arrow cards.
89-57
Arrow cards help with partitioning
Children learn to subtract the least significant digits first (start with the numbers on
the right and work from right to left).
The answer to each individual subtraction is written underneath before these answers
are recombined.
Year 3 (Stage 4b)

Exchange needed
71-46
It is clear that there are not enough units to subtract 6 from 1, so one of the tens from
the 70 is exchanged for 10 ones.
The initial number 71 is rearranged as 60 and 11 to make the calculation easier
This would be recorded by the children as:
End of Year Objective - Subtract numbers with up to three digits, using formal written
method of columnar subtraction.
Year 4 (Stage 5)
Move from subtraction through partitioning
to decomposition
End of Year Objective - Subtract numbers with up to 4 digits and decimals with
one decimal place using the formal written method of columnar subtraction where
appropriate.
Year 5 (Stage 5)
Using decomposition
2
6
13
6
7
-
3
3
(4-digits)
3
10
7
12
2
2
6
8
4
6
-
1
1
.
4
12
.
7
6
.
6
6
(decimals to two places)
End of Year Objective - Subtract whole numbers with more than 4 digits and decimals
with two decimal places, including formal written methods (columnar subtraction).
Year 6 (Stage 5)
When subtracting decimals with different numbers of decimal places, children should
be taught and encouraged to make them the same through identification that 2 tenths
is the same as 20 hundredths, therefore, 0.2 is the same value as 0.20
3
6
4
11
3
3
8
11
7
.
2
4
.
7
2
.
4
10
1
9
End of Year Objective - Subtract whole numbers and decimals using formal written
methods (columnar subtraction).
Vocabulary
Multiplication
(Introduction to Stage 1)
Children are encouraged to develop a mental image of the size of numbers.
They learn to think about equal groups or sets of objects in practical, real life situations.
They begin to record these situations using pictures.
A child’s jotting showing fingers on each
hand as a double.
A child’s jotting showing double three as
three cookies on each plate.
Introduction to arrays using practical activities such as placing
items in an egg box.
End of Year Objective - Children solve problems, including doubling.
Year 1
(Stage 1)
Children will use practical equipment and jottings.
They may use the equipment to make groups of objects.
Children should see everyday versions of arrays, e.g. egg boxes, baking
trays, ice cube trays, wrapping paper etc.
End of Year Objective - Solve one-step problems involving multiplication by
calculating the answer using concrete objects, pictorial representations
and arrays with the support of the teacher.
Year 2
(Stage 2)
Children understand that multiplication is repeated addition and that it can
be done by counting in equal steps/groups using practical apparatus.
Children can then be introduced to
images of rectangular arrays; and use
these to show that counting up in
equal groups can be a quicker way of
finding a total. Numicon can be used
for exploring arrays.
Children also understand that
3 x 5 is the same as 5 x 3
End of Year Objectives - Calculate mathematical statements for multiplication
(using repeated addition)
and write them using the multiplication (x) and equals (=) signs.
Year 3
(Stage 3)
Children continue to use arrays and create their own to represent multiplication
calculations. Use of numicon to explore arrays.
(Stage 4)
Children will continue to use arrays to lead into the grid method of multiplication.
14 x 6
End of Year Objective - Write and calculate mathematical statements for
multiplication using the multiplication tables that they know, including for two-digit
numbers times one-digit numbers, progressing to formal written methods.
Year 3 and Year 4
(Stage 5)
In this stage, the array is removed and children use the grid method. This
is an important step in retaining children’s understanding of multiplication.
Y3: 2-digit numbers x by 1-digit numbers;
Y4: Solve problems involving money and measures.
End of Year Objectives – Multiply two-digit and three-digit numbers
by a one-digit number using formal written layout.
Year 5
(Stage 6)
x
20
2000
600
90
3
40000
12000
1800
60
40000
+
4
8000
2400
360
12
+
+
+
+
+
+
8000
12000
2400
1800
360
60
12
64632
End of Year Objectives - Multiply numbers up to 4 digits by a one- or two-digit
number using a formal written method, including long multiplication for
two-digit numbers.
Year 5
(Stage 6 contd)
Introduce formal ‘expanded vertical method’ from grid method
(Stage 7)
The expanded method can then be taken into the compact vertical method.
.
Year 5
(stage 8)
When ready the children can be introduced to long multiplication.
Year 6
TU.t h
TU.t h
4.9 2
x
3
4.9 2
x
3
0.0 6
(0.02 x 3)
2.7 0
(0.9 x 3)
+12.0 0
14.7 6
(4 x 3)
14.76
End of Year Objectives - Multiply multi-digit numbers up to 4 digits by a two-
digit whole number using the formal written method of long multiplication.
Multiply one-digit numbers with up to two decimal places by whole
numbers.
Vocabulary
DIVISION
(Stage 1)
Children are encouraged to develop a mental image of the number system
in their heads to use for calculation. They should experience practical
calculation opportunities involving equal groups and equal sharing.
Use pictures and jottings. A child’s
jotting showing halving six spots
between two sides of a ladybird.
A child’s jotting showing how
they shared the apples at snack
time between two groups.
End of Year Objective – Children solve problems, including halving and
sharing.
Year 1
(Stage 2)
Practical contexts for sharing and grouping
Sharing
Grouping
Equal sharing (6 shared equally between 2) Equal grouping (How many groups of 2 are
there in 6?)
6 football stickers are shared
equally between 2 people, how
many do they each get? Children
may solve this by using a ‘one for
you, one for me’ strategy until all of
the stickers have been given out.
There are 6 football stickers, how
many people can have 2 stickers
each?
End of Year Objective - Solve one-step problems involving division by
calculating the answer using concrete objects, pictorial representations
and arrays with the support of the teacher.
Year 2
(Stage 3)
Children continue to use practical equipment including numicon to represent
division calculations as grouping (repeated subtraction) and use jottings to
support their calculation.
12 ÷ 3 = ? Children begin to read this calculation as,
‘How many groups of 3 are there in 12?’
Introduction to remainders
13 ÷ 4 = 3 remainder 1
End of Year Objective - Calculate mathematical statements for division
within the multiplication tables and write them using the division (÷) and
equals (=) signs.
Year 3
(Stage 4)
Division by grouping continued.
Children learn if a remainder should be rounded up or down e.g. 62 ÷ 8 = 7
remainder 6
I have 62p. Sweets are 8p each. How many can I buy?
Answer: 7 (the remaining 6p is not enough for another sweet)
Apples are packed into boxes of 8. There are 62 apples. How many boxes
do I need?
Answer: 8 (the remaining 6 apples still need to be placed into a box)
(Stage 5)
Use repeated subtraction on a number
line.
Begin to use vertical number line to
show repeated subtraction.
Subtract ‘chunks’ of the divisor.
End of Year Objectives Y3 - Write and calculate mathematical
statements for division using the multiplication tables that they know,
including for two-digit numbers divided by one-digit numbers,
progressing to formal written methods
Year 4
(Stage 6)
The 'chunking' method, following on from repeated subtraction.
End of Year Objectives - Divide numbers up to 3 digits by a one-digit
number using the formal written method of short division and interpret
remainders appropriately for the context.
Year 5
(Stage 6 contd)
Continue with more efficient methods of chunking the divisor.
End of Year Objective - Divide numbers up to 4 digits by a one-digit number
using the formal written method of short division and interpret remainders
appropriately for the context. Solve money and measures problems.
Year 6
(Stage 6 contd)
End of Year Objective - Divide numbers up to 4 digits by a two-digit number
using the formal written method of short division where appropriate,
interpreting remainders according to the context.
Show the remainder as a fraction and a decimal.
Year 6 contd
Stage 7 – Introduce short division quick method
4) 752
Vocabulary