This document outlines the new curriculum expectations for math in the UK, including substantially more content taught at earlier ages. It discusses strategies and methods for teaching key math concepts like addition, subtraction, multiplication and division. Visual models and understanding of place value are emphasized. Memorizing number facts and using doubling/halving strategies are also presented as important foundations for math learning.

1. Aston Rowant
C of E Primary School.
New Curriculum
2014
Maths Workshop
Calculation Strategies

2. New Curriculum 2014
• The new curriculum represents a substantial increase
in both the amount of Maths being taught and the
expectations of children at each age range. In
general, much of what was traditionally taught in
Y5/Y6 (3-digit multiplication using formal written
methods, formal column addition and subtraction of
4-digit numbers as well as amounts of money, time
intervals involving 24 hour clock, two-place decimals
...) now has to be completed and may be assessed
by the end of Y4.

3. Year 6
• By the end of Y6, the children may be
assessed on addition/subtraction of fractions
including mixed numbers, multiplication and
division of fractions by integers, formal
algorithms for multiplication and division of
four-digit by two-digit numbers, as well as
more advanced calculations involving
decimals and percentages, for example using
the fact that 3/8 is 0.375.

4. Calculation Strategies
Aims
To develop an understanding of the expanded and formal
(traditional) methods we teach at Aston Rowant School for
addition, subtraction, multiplication and division.
We want pupils at Aston Rowant School:
• To develop efficient methods of calculation with all four operations.
• To be able to choose an appropriate method for calculation
e.g mental, mental with jottings, expanded written, formal written, calculator.
• To develop a mathematical understanding, a feel for the value of number
rather than just learning a mechanical method that can be prone to error.
To develop learners for life

5. 4 Pillars of Calculation
At Aston Rowant School we want the children to
have:
• Good understanding of Place Value
• To use images and models
• To use memorised number facts
• To Double/Halve

6. 1. Place Value
Common errors:
• Write 101 in figures (1001)
• 3.4 x 10 (3.40)
• Write one pound and 5p as a decimal (1.5)
• 0.2 x 0.2 (0.4)
It is so important that children at KS1 have
sound understanding of place value to be able
to use written calculation methods at KS2
(examples on next slides)

7. Addition
Partitioning:
47 + 35=
40 30 70
7 5 12
82

8. Addition
Partitioning:
374 + 248=
300 70 4
200 40 8
500 110 12
600 20 2
622

9. Addition
Partitioning:
£48.56 + £23.70 =
40.00 8.00 0.50 0.06
20.00 3.00 0.70 0.00
£60.00 £11.00 £1.20 £0.06
£70.00 £2.00 £0.20 £0.06
£72.26

10. Addition
Expanded Vertical Method:
374 + 248=
374
248
12
110
500
+
+
622

11. Addition
Expanded Vertical Method:
£48.56 + £23.70=
£48.56
£23.70
0.06
1.20
11.00
60.00
+
+
£72.26

12. Addition
Compact Vertical Method:
374 + 248 = 374
248
+
6
2
1
2
1

13. Addition
Compact Vertical Method:
£48.56 + £23.70= £48.56
+
£23.70
£7 .26
2
1
1

14. Subtraction
Partitioning:
This method links to counting back on a number line.
74 - 27 =
74 - 20 = 54
54 - 7 = 47

15. Subtraction
Expanded Method – No adjustment or decomposition needed:
563 - 241=
500 + 60 + 3
200 + 40 + 1
_
300 + 20+ 2 = 322

16. Subtraction
Expanded Method – Adjustment from the tens to the units:
563 - 246=
50 13
500 + 60 + 3
200 + 40 + 6
_
300 + 10+ 7 = 317

17. Subtraction
Compact Method – Adjustment from the tens to the units:
563 + 246=
51
563
-246
317

18. Multiplication
Compact Grid Method
47 x 36 =
X 40 7
30 1200 210 1410
6 240 42 282
1692

19. Multiplication
Expanded Vertical Method
237 x 4= 237
x 4
28
120
800
948

20. Multiplication
Compact Vertical Method
237 x 4= 237
x 4
4
8
2
9
1

21. Multiplication
Compact Vertical Method
256 x 18= 256
x 18
2560
204
8
4 4
460
8
1

22. Division
Grouping Expanded (The Bus Stop Method)
196 ÷ 6 = 32 R 4
6 ) 196
(6 x 10)
(6 x 10)
(6 x 10)
(6 x 2)
-60
136
-60
76
-60
16
-12
4

23. Division
Grouping Efficiently (The Bus Stop Method)
346 ÷ 8 = 43 R 2
8 ) 346
(8 x 40)
(8 x 3)
-320
26
-24
2

24. 2. Use of Images and Models
Addition
Pictures and Symbols:
I buy 2 cakes and my friend buys 3 cakes. How many cakes did we
buy altogether?
May be recorded as: 2 + 3 = 5

25. Addition
Pictures and Symbols:
18 + 5 = 23

26. Addition
Number Line:
18 + 5 =
+1 +1
+1 +1 +1
18 20 23
19 21 22

27. Addition
Number Line - Efficient Jumps:
47 + 35 =
+30 +3 +2
47 77 80 82

28. Addition
Number Line - Efficient Jumps:
374 + 248 =
+200 +40 +8
374 574 614 622

29. Addition
Number Line - Efficient Jumps:
£48.56 + £23.70 =
+£20 +£3 +70p
£48.56 £68.56 £71.56 £72.26

30. Subtraction
Pictures and Symbols:
I have five cakes I eat two of them. How many do I have left?
May be recorded as: 5 - 2 = 3
XX

31. Subtraction
Stage 1
Pictures and Symbols:
13 - 5 = 8

32. Subtraction
Stage 2
Number Line - Counting Back:
13 - 5 =
-1 -1
-1 -1 -1
8 10 13
9 11 12

33. Subtraction
Number Line – Counting Back Efficient Jumps:
74 - 27 =
-3 -4
-20
47 50
54 74

34. Subtraction
Number Line – Counting On Efficient Jumps:
74 - 27 =
+3 +40 +4
27 30 70 74
40 + 4 + 3 = 47

35. Multiplication
Pictures and Symbols:
There are three sweets in one bag.
How many sweets are there in five bags?

36. Multiplication
Number Line – Repeated Addition:
5 x 3 or 3 x 5
0 3 6 9 12 15
0 5 10 15

37. Multiplication
Arrays
5 x 3 or 3 x 5

38. Multiplication
Expanded Grid Method
13 x 4 =
X 10 3
4
10 x 4 = 40 3 x 4 = 12
40 + 12 = 52

39. Multiplication
Compact Grid Method
13 x 4 =
X 10 3
4 40 12
40 + 12 = 52

40. Division
Pictures and Symbols:
How many apples in each bowl if I share 12 apples between 3
bowls?

41. Division
Number Line:
15 ÷ 3 = 5
0
+3 +3 +3 +3 +3
3 6 9 12 15
15
-3 -3 -3 -3 -3
0 3 6 9 12

42. Division
Number Line: Chunking.
96 ÷ 6 = 16
10 x 6 = 60 6 x 6 = 36
0 60 96

43. Division
Number Line: Counting Back by Chunking.
200 ÷ 6 = 33 R 2
3 x 6 = 18 30 x 6 = 180
2 20 200
0

44. 3. Memorised Number Facts
• Fewer children come to school knowing
rhymes/numbers etc.
• Memorisation is the grounds on which we
build maths. 78+5= by year 3 children should
not be counting on in ones but know that 2
more is 80 plus another 3.
• If children don’t know their number facts,
they can’t do maths.

45. 4. Double and Halve
• Why is doubling and halving important?
• It is the simplest maths function we teach. We
do this and then it is reversed.
• 1 million divide by 8 How would you do it?
Halve, Halve, Halve it
• 13 divided by 5 How? Divide by 10 and double
it.

46. Thank you.
• Please feel free to visit the classrooms. We
have some of the resources on display for you
to have a look at.
• The teachers will be there to answer any
questions.