1. Maths the Modern Way!! Addition and Subtraction
St Teresa’s Primary School
with
Essex County Council

2. The Primary National Strategy
Basis of teaching since 1999 – based on extensive research and proven success
Daily entitlement to maths lesson
Key features
Progression carefully set out
Interactivity – use of models, images, games, practical activities
Focus on mental skills as well as written
Vocabulary, problem solving, communication, explanation and reasoning

3. There is no “right way” to work!!
Children exposed to a range of methods.
Methods selected will depend upon the situation and the numbers involved, including when to use calculators.
Children make decisions about methods and draw on a range of strategies and approaches when applying Maths in context.
Children in same class could be using different methods to others depending on their ability, confidence and stage of mathematical development.

4. Addition Foundation Stage (Reception) Counting and recognising numbers
Counting on using number lines or apparatus
Recall of facts and number bonds
Numbers to 10, then beyond.

5. Key Stage 1
Year 1
Introduce + and = signs to record calculations done mentally
Securing bridge over 10s boundary
Mental recall of facts
Numbers extend to 30, 40…
Recognise patterns in 100 square (+10, +1)
Splitting numbers and recombining

6. The Importance of Place Value
Place Value Runaround!

7. Key Stage 1 Year 2 Extension of Year 1 Introduction of partitioning
Adding significant digits first

8. How to Partition
= 100
= 7
= 107

9. Try these by partitioning!!
45+67
154+78
This can work with any size of number – is it
efficient to use this method for this?

10. Key Stage 2 The Numberline!! 67 77 87 97 99

11. Expanded Addition (Introduced Year 3)
43+25 43
+ 25
Try this method with these!! 60 8 68

12. Standard Method
63+39
6 3
+ 3 9
1 2
9 0
1 0 2
6 3
+ 3 9 2 1
6 3
+ 3 9
1 0 2 1

13. You may like to try these problems
using some of the methods that we
have used so far.
623+12

14. The Roundabouts of Harlow

15. FINISH 1 1 2 4 11 8 5 9 2 3 5 12 7 6 1 10
START

16. Subtraction Foundation Stage (Reception)
Counting and recognising numbers
Counting back using numberlines or apparatus
Recall of facts and number bonds
Numbers to 10, then beyond.

17. Key Stage 1
Year 1
Introduce - and = signs to record calculations done mentally
Mental recall of facts
Subtracting 10 from “teens” number
Recognise patterns in 100 square (-10, -1)
Splitting numbers and recombining

18. Key Stage 1 Year 2 Extension of Year 1
Crossing 10s boundary with numbers to 20,30…. (crossing 100s boundary in Y3)
May use splitting of numbers/partitioning to assist in calculation (e.g. 27–15 = 27–5–2–8)

19. Key Stage 2 The Numberline!! -2
-10
-10
-10 35 37 47 67 57
ANSWER!!!

20. OR…. 32 42 52 67 62
+10 +5
= 35
+10
+10 +7 +8 32 40 50 60 67
= 35

21. Complementary Addition32 40 50 67 60 +8
+10 +7
= 35
6 7
- 3 2
8 to 4 0
2 0 to 6 0
7 to 6 7
3 5

22. The Standard Method - Decomposition
Introduced from Year 3
Linked initially with use of images and practical apparatus to secure understanding of how place value is being used in the calculation
Lots of stages where children can make errors
Not always the most efficient method to use
If children can obtain an answer using another method, that is OK.

23.
Which written method is most appropriate to use for these numbers?
Shall I use a written method?
Can I do this mentally?

24.
3 3
- 1 7

25.
3 3
- 1 7
I’m going to partition the numbers.

26.
3 3
- 1 7
30 + 3 =

27.
3 3
- 1 7
30 + 3 =

28.
3 3
- 1 7
30 + 3
I start with the units, so I need to take away 7 small cubes.
But I only have 3 of them.
I’ll break up one of the 10s into 10 units. =

29.
3 3
- 1 7
30 + 3 = =
I’ve now got 2 lots of 10, so that’s 20, as well as 13 units, so let’s write it down to show what I am doing.

30.
3 3
- 1 7
30 + 3 = =
Now I can take away 7!

31.
3 3
- 1 7
30 + 3 6 = =

32.
3 3
- 1 7
30 + 3 6 = =
Now I can take away 10!

33.
3 3
- 1 7
30 + 3 = =

34.
3 3
- 1 7
30 + 3 = =
= 1 6

35. Have a Go! There is some base 10 apparatus in the
tables if you would like to run through using
this to be clear about the process involved.
42 – –

36. There will be examples like this…
75 – 32
where no exchange is needed, but partitioning is still useful as children are more successful at working with tens and units separately. - =
= 2 3

37. Next stages will involve increasing the number of digits in the numbers (HTU, the ThHTU), working with apparatus, then without, to ensure children are secure with place value before moving on to the final stage. Often this would be taught side by side with the more expanded method so that children can see how they relate.

38.
= =
= 1 1 3 - 6 1 6 1 6 1 6 1 - - - - -

39. Why the additional steps?

40. Why the additional steps?2 1 - -

41. Why the additional steps?2 1 - - - -

42. Maths the Modern Way!! Addition and Subtraction
St Teresa’s Primary School
with
Essex County Council