1. Howe Dell School Maths Calculation Policy

2. Why do we have a calculation policy?
Clarity
Progression
Children’s “Tool Box”
Consistency
Vocabulary

3. Addition
Year 1 use marked number lines or beads to “count on” – recognising when they “go through 10.”
They use number lines and practical resources to support calculation and teachers demonstrate the use of the number line.
Bead strings or bead bars can be used to illustrate addition including bridging through ten by counting on 2 then counting on 3.
Children then begin to use numbered lines to support their own calculations using a numbered line to count on in ones.

4. Addition
Year 2 continues to build on the methods used in Year 1 but with larger numbers. Children begin to use ‘empty number lines’ themselves, starting with the larger number, and 100 squares
First counting on in tens and ones.
Then helping children to become more efficient by adding the units in one jump
Followed by adding the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.

5. Addition
Year 3 continues to use empty number lines with increasingly large numbers, up to 3 digits, including compensation where appropriate.
Count on from the largest number irrespective of the order of the calculation
Compensation
Under the new curriculum, once children are secure with place value they can begin to have a vertical method modelled alongside a number line; at first this could be an expanded method:

6. Addition
Year 4 children should build on their use of the formal written method of columnar addition with numbers up to four digits.
From this children begin to CARRY BELOW the line, making it a clearer visual link.

7. Addition
Year 5 concentrates on reinforcing the use of an efficient written method for column addition involving whole numbers with more than four digits.
Using similar methods, children will:
add several numbers with different numbers of digits;
begin to add two or more decimal fractions with up to three digits and the same number of decimal places;
know that decimal points should line up under each other, and that the decimal point should have its own space, particularly when adding or subtracting mixed amounts, e.g. 3.2 m – 280 cm.

8. Addition
Year 6 extends the carrying method to a number with any amount of digits.
Using similar methods, children will:
add several numbers with different numbers of digits;
begin to add two or more decimal fractions with up to four digits and either one or two decimal places;
know that decimal points should line up under each other, and that the decimal point should have its own space, particularly when adding or subtracting mixed amounts, e.g

9. Subtraction
Year 1 , as with addition, use marked number lines or beads to “count back” – recognising when they “go through 10.”
Bead strings or bead bars can be used to illustrate subtraction including bridging through ten by counting back 3 then counting back 2.
13-5=8
Children then begin to use numbered lines to support their own calculations - using a numbered line to count back in ones.
The number track should be used to show that means the ‘difference between 13 and 5’ or ‘5 and 13’. This needs to be done alongside practical methods such as lining up groups of objects and can be demonstrated on the number line.
They are shown how to find a difference by counting up from the smaller to the larger number.

10. Subtraction
Year 2 continues to build on the methods used in Year 1 but with larger numbers. 100 squares can be used to subtract multiples of 10
First counting back in tens and ones.
Then children becoming more efficient by subtracting the units in one jump
Followed by subtracting the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.

11. Subtraction
Year 2 counting on can also be introduced as a way of addressing different learning styles:
Counting on:
It is helpful for the children to understand that this method is another way of finding the difference (as addition is the inverse of subtraction) .
Use the number line to count up from 47 to 82 in jumps of 10 and jumps of 1.
(The number line should still show 0 so children can cross out the section from 0 to the smallest number. They then associate this method with ‘taking away’.)

12. Subtraction
Year 3 continues to use empty number lines with increasingly large numbers, gradually introducing jottings to record and explain mental methods, including counting-on.
Partitioning
and
Decomposition
Once secure a column method is introduced:

13. Subtraction
Year 4 reinforces the use of formal columnar subtraction introduced in Year 3 involving numbers up to four digits.

14. Subtraction
Year 5 concentrates on establishing an efficient written method based on decomposition, using increasingly larger numbers beyond four digits.
Children should:
be able to subtract numbers with different amounts of digits;
begin to find the difference between two decimal fractions with up to three digits and the same number of decimal places;
know that decimal points should line up under each other and that the decimal point has its own space.
Children should only be using a number line for quicker mental methods, especially where the numbers involved in the calculation are close together or near to multiples of 10, 100 etc.

15. Subtraction
Year 6 secures the work in Year 5 with the condensed vertical method using the decomposition process being the preferred method.
Children should:
be able to subtract numbers with different amounts of digits;
be able to subtract two or more decimal fractions with up to three digits and either one or two decimal places;
know that decimal points should line up under each other and that the decimal point has its own space.
Some children may still need to use a number line or an expanded method.

16. Multiplication
Year 1 children will learn to multiply by using groups of objects and pictorial representations
They will count in 2s, 5s and 10s
They will work on practical problem solving activities involving equal sets or groups.
3 x 4:
is the same as 3 lots of same ( )
which means 3 groups of 4
so, 3 x 4 = 12

17. Multiplication
Year 2 develops the children’s understanding, introducing jottings, reinforcing repeated addition and introducing complimentary calculations and arrays. Children should also be able to recall multiplication facts for the 2, 5 and 10 times tables.
Repeated addition
3 times 5 is = or 3 lots of 5 or 3 x 5
Repeated addition can be shown easily on a number line:
Complimentary Calculations
Children should know that 3 x 5 has the same answer as 5 x 3.
This can also be shown on the number line:

18. Multiplication
Year 3 continues to develop times table knowledge (including the 3, 4 and 8 times tables) with a view to progression onto a written method (such as the Grid Method).
Children should be able to write and calculate mathematical statements using the times tables they know (including two-digit by one-digit multiplication).
They should also develop methods using commutativity:
4 x 12 x 5 is the same as (=) 4 x 5 x 12 which is the same as (=) 20 x 12

19. Multiplication
Year 3 children will be introduced to written methods with the Grid Method of multiplication, before moving onto more formal written methods.
Grid method:
TU x U
(Short multiplication – multiplication by a single digit)
23 x 8
Children should begin to approximate first
23 x 8 is approximately 25 x 8 = 200
then add the products:
= 184

20. Multiplication 24 (6 x 4) 24 x 6 starts off as: 24 x 6 120 (6 x 20)
Year 4 children will use a formal written method to multiply two-digit and three-digit numbers by one-digit numbers. They should also know all multiplication facts for tables up to 12 x 12.
24 x 6 starts off as: 24
x 6
24 (6 x 4)
120 (6 x 20)
144

21. Multiplication
Year 5 develops the use of the formal written method to include multiplying up to four-digit numbers by one or two-digit numbers
Using similar methods, they will be able to multiply decimals with one decimal place by a single digit number, approximating first. They should know that the decimal points line up under each other.

22. Multiplication
Year 6 further develops the knowledge of the formal written method (using long multiplication) from Year 5 to incorporate larger numbers and single digit numbers with up to two decimal places
Using similar methods, they will be able to multiply decimals with up to two decimal places by a single digit number, understanding that the decimal point has its own space.
4.92 x 3 is approximately 5 x 3 = 15

23. Division
Year 1 children will learn to divide by using equal groups and sharing
They will count in 2s, 5s and 10s and will be introduced to doubling and halving.
They will work on practical problem solving activities.
12 ÷ 4 = 3
Share 12 between 3 people
12 split into groups of 4

24. Division
Year 2 develops the children’s understanding, reinforcing sharing and grouping, introducing jottings, and using repeated subtraction.
Sharing equally
6 sweets shared between 2 people, how many do they each get?
Repeated Subtraction
12 ÷ 3 = 4
this means place 12 into groups of 3 – how many groups will there be?
or continue to subtract groups of 3 from 12:

25. Division
Year 3 ensures that the emphasis is on grouping not sharing. Associated division facts are used more and a reliable written method is introduced.
Children should use associativity to derive corresponding division facts
30 x 2 = ÷ 2 = 30 2 = 60 ÷ 30
The Chunking Method
Children also move onto using symbols to stand for unknown numbers to complete equations using inverse operations
26 ÷ 2 =  24 ÷  = 12  ÷ 10 = 8

26. Division
Year 4 develops the use of the written method introduced in Year 3
Children can start to subtract larger multiples of the divisor, e.g. 30x
Remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.
Children need to be able to decide what to do after division and round up or down accordingly. They should make sensible decisions about rounding up or down after division.

27. Division
Year 5 introduces the idea of using a formal written method to divide numbers with up to four digits by a one-digit number.

28. Division
Year 6 reinforces the use of written methods and introduces long division, dividing by two-digit numbers

29. Things to remember Maths questions are CALCULATIONS NOT SUMS
+ means “add, sum, plus, total, altogether”
- means “subtract, minus, take away, difference”
x means “multiply, times, lots of, product”
÷ means “divide, group, share”
Numbers are made up of digits
HTU can be EXCHANGED for each other
INVERSE means the opposite calculation
Number bonds are important
Times tables are important
Mathletics – please use it!

30. The Calculation Policy
Whilst the policy is set out by Year Group this is only an indication.
By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved.
Children should not be made to go onto the next stage if they are not ready or they are not confident.
Children should be encouraged to approximate their answers before calculating.
Children should be encouraged to consider if a mental calculation would be appropriate before using written methods.

31. What does the new curriculum expect of our children?
The new curriculum is broadly presented in three sections: Key Stage 1, Lower Key Stage 2 and Upper Key Stage 2. It requires of children:
Fluency
Reasoning
Problem Solving

32. What does the new curriculum expect of our children?
Under the new curriculum it is expected that children within a year group will move through the programmes of study at the same rate, with more able children being challenged more deeply.

33. What does the new curriculum expect of our children?
Key Stage 1:
“The principal focus … is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value.”

34. What does the new curriculum expect of our children?
Lower Key Stage 2:
“The principal focus … is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value.”

35. What does the new curriculum expect of our children?
Upper Key Stage 2:
“The principal focus … is to ensure that pupils extend their understanding of the number system and place value to include larger integers.”

36. What does the new curriculum expect of our children?
Upper Key Stage 2:
“The principal focus … is to ensure that pupils extend their understanding of the number system and place value to include larger integers.”

37. What does the new curriculum expect of our children?
Key Stage 1:
By the end of Year 2 children should:
Know all number bonds to 20 and derive related facts to 100
Recognise the place value in a two-digit number
Read, write, compare and order numbers to 100
Know the 2, 5 and 10 multiplication tables

38. What does the new curriculum expect of our children?
Lower Key Stage 2:
By the end of Year 4 children should:
Have efficient written and mental calculation methods
Know all multiplication tables up to 12 x 12
Recognise place value in a four-digit number
Order and compare numbers beyond 1000

39. What does the new curriculum expect of our children?
Upper Key Stage 2:
By the end of Year 6 children should:
Have a fluent formal written for all operations (including with fractions, decimals and percentages)
Read, write, order and compare numbers to
Use simple formula with algebra