# Calculation Policy ## Progression in Written Calculations

This shows the progression towards pupils achieving compact written calculations. Mental skills need to be developed across the primary and secondary phases. Use the methods with decimals

(eg. money and measures). Teachers also need to refer to ‘Teaching children how to calculate mentally’. Stages are progressive and can correlate to year groups. A child can be on different stages across and within different operations.

1

Represent and use number bonds and

Represent and use number bonds and related subtraction facts within 20

Add 1-digit and 2-digit numbers to 20, including zero related addition facts within 20

Subtract 1-digit and 2-digit numbers to 20, including zero

Using pictorial recording , manipulatives, use

Using pictorial recording , manipulatives - Show number sequences alongside practical

Use number tracks and simple number lines

1 2 3 4 5 6 7 8 9 10 number tracks and simple number lines.

Show number sequences alongside practical

Teach number sequences alongside practical

Use number tracks and simple number lines.

2

Read, write and interpret mathematical statements involving addition (+) and equals (=) signs

Adding 2-digit numbers and ones, 2-digit numbers and tens, two 2-digit numbers and adding three 1-digit numbers using concrete objects, pictorial representations, and mentally.

Steps in addition can be recorded on a number line. The steps often bridge through a multiple of 10.

48 + 36 = 84

Read, write and interpret mathematical statements involving subtraction (-) and equals (=) signs

Understand subtraction as take away and as difference

Subtracting 2-digit numbers and ones, 2-digit numbers and tens, two 2-digit numbers using concrete objects, pictorial representations, and mentally.

Using number line first with horizontal recordings and then vertical recordings:

+30 + 6

48 78 84

Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

3 + 40 + 4 = 47

Children need to spend time partitioning

Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot

# Multiplication

Oral counting in twos; e.g. pairs of gloves, socks

….

Make a bead necklace, 2 red, 2 blue, 2 red, 2 blue …

Count in repeated groups of the same size

Count in 2s, 5s and 10s

Recall and use doubles of all numbers to 10 and corresponding halves

Practical work to show links between 2 lots of 4 and 4 lots of 2 etc

Practical work recorded as repeated addition

(See models and images charts for multiplication and division)

Show number sequences alongside practical

Calculate mathematical statements within the multiplication tables and write them using the multiplication (x) and equals (=) signs

Number line, number track, 100 square as a visual support, manipulatives

Understand multiplication as the inverse of division.

# Division

Practical work recorded as repeated subtraction

Share objects into equal groups and count how many in each group e.g. fruit for a snack, cup for every person

Sharing numbers equally using 2, 5 and 10 groups.

E.g. I have 8 wheels, how many bikes can I make? Get into groups of 4 for PE

(See models and images charts for multiplication and division)

Show number sequences alongside practical

Calculate mathematical statements for division within the multiplication tables that they know and write using the division (÷ ) and equals (=) signs

Understand division as sharing and grouping

Sharing equally:

12 ÷ 3 =

*   *   *

* * *

Grouping equally:

12 ÷ 3 = * * * * * *

*

* *

* * * * * *

Understand division as the inverse of multiplication.

*

1

3

4

5

Record steps in addition up to 3 digit numbers formal written methods of columnar addition

Using partitioning:

147 + 276

= 100 + 200 + 40 + 70 + 7 + 6

= 300 + 110 + 13 = 423

Partitioned numbers are then written under one another:

147 = 100 40 7

+ 276 200 70 6  Possible support

300 110 13

Add fractions with same denominators with 1 whole using diagrams

5/7 + 1/7 = 6/7

Record steps in subtraction up to 3 digit numbers using formal written methods of columnar subtraction

Partitioned numbers are written under one another (Note support to mirror the teaching of addition):

Example: 741 − 367

600 130 11 6 13 11

700 40 1 700 40 1 7 4 1

-

300 60 7

-

300 60 7

-

3 6 7

300 70 4 3 7 4

Subtract fractions with same denominations with 1 whole using diagrams

5/7 + 1/7 = 4/7

1234

+ 2341

3575

Addition with up to 4 digit numbers using the formal written methods of columnar addition.

Add numbers with decimals to one decimal place using formal methods of columnar addition

Add fractions with the same denominator using diagrams

Add whole numbers with more than 4 digits, including formal written methods (columnar addition)

Add numbers with two decimal places using formal written methods of columnar addition where appropriate

Add fractions with the same denominator and multiples of the same number using diagrams

Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number

2/5 + 4/5 = 6/5 or 1 1/5

9876

- 4321

5555

Subtraction with up to 4 digit numbers using the formal written methods of columnar addition.

Subtraction of numbers with decimals to one decimal place using formal methods of columnar subtraction

Subtract fractions with the same denominator using diagrams

Subtract whole numbers with more than 4 digits, including formal written methods

Subtract numbers with two decimal places places using formal written methods of columnar subtraction where appropriate

Subtract fractions with the same denominator and multiples of the same number using diagrams

Recognise mixed numbers and improper fractions and convert from one form to the other.

Write mathematical statements > 1 as a mixed number

8/5 - 4/5 = 4/5

1 3/5 – 4/5 = 4/5

Write and calculate mathematical statements for multiplication using multiplication tables that they know, including for 2-digit numbers times 1-digit numbers, using mental and progressing to formal written methods

Understand multiplication as describing an array

 5 x 3 = 3 x 5

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Informal recording might be:

οοοοο

43

40 3

X6

240 18 = 258

Multiplying 2-digit and 3-digit numbers by a 1digit number using formal written layouts

38 × 7 = (30 × 7) + (8 × 7) = 210 + 56 = 266 to use of grid method

Write and calculate mathematical statements for division using the multiplication tables that they know, including for 2-digit numbers times 1-digit numbers, using mental and progressing to formal written methods

Mental division using partitioning:

Informal recording for 84 ÷ 7 might be:

84

70 14

÷7

10 2 = 12

Divide numbers up to 3-digits by 1-digit number using formal written layout

Example: Short division method:

81 ÷ 3 =

2 7

3 8 1

Multiply numbers up to 4-digits by 1digit or 2digit numbers using a formal written method, including long multiplication for 2-digit numbers

56 56 x 27 x 27

42 7x 6 = 42 1120 56 x 20

350 7 x 50 = 350 392 56 x 7

120 50 x 6 = 120 1512

1000 20 x 50 = 1000 1

1512

1

Multiplying proper fractions and mixed numbers by whole numbers, supported by manipulatives and diagrams

Divide numbers up to 4-digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context

2

6

Add whole numbers and decimals using formal written methods

Add fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Subract whole numbers and decimals using formal written methods

Subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Multiply multi-digit numbers up to 4 digits by a 2digit whole number using the formal written method of long multiplication

Multiplying simple pairs of proper fractions, writing the answer in its simplest form using diagrams

¼ x ½ = 1/8

Continue to divide numbers up to 4-digits by a 2digit whole number using the formal written method of short division where appropriate for the context

Divide numbers up to 4-digits by a 2-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

Use written division methods in cases where the answer has up to two decimal

Long division method:

806 ÷ 13 =

6 2

13 ) 7 8 1 0 6

7 8

2 6

0

3