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
7 beads 3 beads
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
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.
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
(columnar addition)
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 οοοοο
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