1. Mawsley Primary School Calculation Policy Addition and Subtraction

2. 57 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+5 2

3. Commutative Laws The "Commutative Laws" say you can swap numbers over and still get the same answer...... when you add: a + b = b + a

4. Models and images

5. 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)

6. Vocabulary

7. 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

8. 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

9. 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

10. Level 3 Expanded method of addition Column method, first without and then with carrying Column addition to add money without carrying

11. 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

12. Overview Number line Partitioning Expanded method Standard written method

13. 12 Models for subtraction Removing items from a set (reduction or take-away) - 1- 2- 3- 4- 5= 7 Issue: 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

14. Models for subtraction Counting 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. 52 10 -2-3 14

15. Subtraction key vocabulary

16. 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

17. 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.

18. Level 2 Know by heart subtraction facts for 10 and 20 Subtract a single digit from a 2 digit number Begin to use partitioning

19. Level 3 Decide whether to count on or back Compensation method

20. Partitioning when there is an exchange: 57 – 28 50 & 7 40 & 17 50 & 7 - 20 & 8 - 20 & 8 - 20 & 8 20 & 9 20 & 9

21. Expanded method 500 + 30 40 + 10 + 3 - 100 + 20 + 7 400 + 10 + 6

22. 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.

23. Overview Number line Partitioning Expanded method Standard written method