Mawsley Primary School Calculation Policy

Addition and Subtraction

5 7

Models for addition

Adding on to a set (augmentation)

Counting on with a bead bar/number line

Combining two sets of objects (aggregation)

12

Issue:Tend to count one set, count the other and then count all.

5 6 7 8 9101112

Issue:Requires fluency with counting from any number.

12 5 0

+ 7 Issues:Bead bar is a useful bridge from cardinal to ordinal.Number line helps to stop counting all

Also:Bead bar and number line (showing 10s) encourages use of number bonds and place value for added efficiency.

10 +2+52

Commutative Laws

The "Commutative Laws" say you can swap numbers over and still get the same answer ...

... when you add:

a + b  =  b + a

Models and images

Associative Laws

• The "Associative Laws" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ...

... when you add:

(a + b) + c  =  a + (b + c)

Vocabulary

Foundation stage

• Recognise numbers 0 to 20, including Numicon.• Count beyond 10 everyday objects. • Find one more than a number• Count in ones and tens• Begin to relate addition to combining 2 groups• Count along a number line to add numbers

together• Begin to use + and = to record mental

calculations in a number sentence• Be able to calculate doubles

Level 1

• Know by heart all pairs of numbers with a total of 10 and 20

• Know that addition can be done in any order

• Using a number line adding by counting up to the next ten then counting in ones.

• Draw own number lines to add

• Begin to partition numbers in order to add

Level 2

• Add 2 single digits that bridge 10• Use base 10 apparatus to add two 2-digit

numbers together up to =100, exchanging ten units for a ten.

• add a number up to =50 on a number line, in jumps of 1, 5 or 10

• Adding two 2-digit numbers first without and then with bridging 10’s boundary

• Start to use partititioning

Level 3

• Expanded method of addition

• Column method, first without and then with carrying

• Column addition to add money without carrying

Level 4

• Continue with the strategies to add numbers up to 2 decimal places, including numbers which do not have the same number of decimal places

Overview

Number line

Partitioning

Expanded method

Standard written method

12

Models for subtraction

Removing items from a set (reduction or take-away)

- 1- 2- 3- 4- 5 = 7Issue:Relies on ‘counting all’, again.

Comparing two sets (comparison or difference)Issue:Useful when two numbers are ‘close together’, where ‘take-away’ image can be cumbersome

Seeing one set as partitioned

Seeing 12 as made up of 5 and 7

Issue:Helps to see the related calculations; 5+7=12, 7+5=12, 12-7 = 5 and 12-5=7 as all in the same diagram

N.B.When this is done on a bead bar, there are links with both counting back and difference on a number line

13

Models for subtractionCounting back on a number line

Finding the difference on a number line

12 0

- 5

7

Issue:Number line helps to stop ‘counting all’.

Also:Knowledge of place value and number bonds can support more efficient calculating

12 0 5

7 Issue:Useful when two numbers are ‘close together’, use of number bonds and place value can help.

5 2 10

10 -2-3

14

Subtraction key vocabulary

Foundation stage

• Begin to count backwards in familiar contexts

• Continue the count back in ones from any given number

• Find one less than a number

• Count back in tens

Level 1

• Draw on a number line to count back in ones

• Draw own number line to take away• Find the difference between 2 numbers

less than 20• Subtract single digit numbers bridging

through 10• Begin to find the difference by counting up

from the smallest.

Level 2

• Know by heart subtraction facts for 10 and 20

• Subtract a single digit from a 2 digit number

• Begin to use partitioning

Level 3

• Decide whether to count on or back

• Compensation method

• Take too much and add back

84 – 56

8424 28

(84 – 60) +4 = 28

-60

+4

• Partitioning when there is an exchange:

57 – 28

50 & 7 40 & 17 50 & 7

- 20 & 8 - 20 & 8 - 20 & 8

20 & 9 20 & 9

•

• Expanded method

500 + 30 40 + 10 + 3 - 100 + 20 + 7

400 + 10 + 6

Level 4

• Formal column method

• Continue with the strategies to subtract numbers up to 2 decimal places, including numbers which do not have the same number of decimal places.

Overview

Number line

Partitioning

Expanded method

Standard written method