1. ADDITION + + = 3 + 2 = 5 STAGE 1 STAGE 2 STAGE 3 STAGE 4 STAGE 5 1 2 3
Counting everyday objects as often as possible. Counters, pasta pieces or anything else you can find, e.g
Then jumps on a number line, e.g = 5 + =
3 + 2 = 5 +1 +1 1 2 3 4 5 6 7 8 9 10
Jumps on a number line by partitioning a 2 digit number,
e.g = 35
Adding 9 or 11 using jumps on a number line, then adjusting
e.g = 44
When children are secure with place value, expanded column method
e.g = 44
Moving on to adding 2 digit numbers, e.g = 58
STAGE 2
+10 +2 23 33 35
+10 35 44 4 5 -1 3 + 6 9
STAGE 3
Expanded column method: 3 6 7 + 1 8 5 2 4
= 125
= 552
STAGE 4
Compact column method for whole numbers.
Expanded column method for decimals. 7 2 . 8 + 5 4 6 1
= 821
= 127.4 3 5 6 + 4 8 2 1
STAGE 5
Compact column method. See STAGE 4 guidance for whole numbers. Compact method used with decimals of increasing difficulty, e.g
= 127.4 =
then… 7 2 . 8 + 5 4 6 1 1 3 . 8 6 + 9 4 2

2. SUBTRACTION - - = 3 - 2 = 1 STAGE 1 STAGE 2 STAGE 3 STAGE 4 STAGE 5
Taking away everyday objects as often as possible. Counters, pasta pieces or anything else you can find, e.g
Using a number line to find the difference, e.g I have saved 5p the socks I want cost 11p. How much more money do I need: - =
3 - 2 = 1 11 1 2 3 4 5 6 7 8 9 10 +1
= 6p
Using a number line to find a small difference, e.g 42 – 39 = 3
Use a number line and partition numbers to subtract, counting backwards, e.g 32 – 17 = 15 or find the difference by counting up
STAGE 2
+ 1
+ 2 39 40 42 32 22 20 15
-10 -2 -5 32 30 20 17
+10 +2 +3
STAGE 3
As STAGE 2 but using larger numbers, e.g 754 – 86 = Children find the difference by counting up. Use find the difference for decimals (see L4 example). At 3b children start to use column method for whole numbers only using models to support concept of exchange. 9 5 2 3 7 - 1 4 86
700
100
754
+14
+600
+54
= 54 = 668 8 7 4 5 2 3 - 1
then…
Columnar for whole numbers. Find the difference for decimals (including numbers with a mixed number of decimal places).
STAGE 4
6.1 – 2.4 = 3.7
6.1
2.4
+0.6
3.0
6.0
+3.0
+0.1 9 3 2 4 5 7 - 1 8
932 – 457 = 475
0.5 – 0.31 = 0.19
+0.09
0.31
0.4
0.5
+0.1
Columnar for whole numbers & decimals.
STAGE 5 3 2 5 1 6 8 - 7
2325 – 1568 = 757

3. DIVISION ÷ STAGE 1 STAGE 2 STAGE 3 STAGE 4 STAGE 5
Sharing. 6 sweets are shared between two people. How many do they each have?
Grouping. Children sort objects into 2s, 3s, 4s, etc. For example, how many pairs of socks are there?
STAGE 2
Grouping / chunking using a number line, e.g 6 ÷ 2 = 3
Then grouping / chunking using multiplication facts (x10, x5, x2) with & without remainders.
74 ÷ 4 = 18 r2
2 X 1 2
2 X 1 4 6
4 X 10 40
4 x 5
4 x 2 60 68
41 x 1 72 74 r2
Vertical chunking.
222 ÷ 6 = 37
Number facts:
6 x 20 = 120
6 x 10 = 60
6 x 5 = 30
6 x 2 = 12
STAGE 3 - 1 2
6 x 20
6 x 10 6 4 3
6 x 5
6 x 2
When children are secure with the concept of division through chunking, introduce short division. Children should master 1 digit and 2 digit divisors, e.g 496 ÷ 11 (see L5 example). Continue to use chunking for decimal division.
STAGE 4
98 ÷ 7 = 14
432 ÷ 5 = 86 r2
28.8 ÷ 1.6 = 18 9 8 7 2 1 4 5 4 3 8 2 6 r2
10 x 1.6 16
5 x 1.6
2 x 1.6 24
27.2
1 x 1.6
28.8
STAGE 5
When children are secure with short division using a 2 digit divisor (see example below), move to long division. Continue to use chunking for decimal division (see STAGE 4 example).
496 ÷ 11 = 45 r1
965 ÷ 5 = 193
432 ÷ 15 = 28 r12 5 9 6 1 3 - 15 4 3 2 8 1 -
r12 11 4 9 5 6 r1

4. MULTIPLICATION X STAGE 1 STAGE 2 STAGE 3 STAGE 4 STAGE 5
Counting groups of the same size.
Columns:
2 multiplied by 3
2 x 3 = 6
Grouping. Children sort objects into 2s, 3s, 4s, etc. For example, how many pairs of socks are there?
There are 3 sweets in one bag. How many sweets are there in 5 bags? 3 x 5 = 15
Rows:
3 + 3
3 multiplied by 2
3 x 2
Children use arrays and repeated addition:
STAGE 2
Then move on to the grid method multiplying a 2 digit number, e.g 1 5 x 2 = 3 0
Rows:
4 + 4 = 8
4 x 2 = 8 10 5 x 2 20
= 30
Columns
= 8 or
2 x 4 = 8
STAGE 3
Grid method multiplying by a 2 digit number, e.g 72 x 38 = When working out 30 x 70 encourage children to think in patterns, i.e 3 x 7 = 21, 3 x 70 = 210, 30 x 70 = 2100 70 2 x 30
2100 60 8
560 16
Then column method for addition:
2100
560 60 16
2736
When children are secure with the grid method, short multiplication (i.e multiplying by a single digit) for whole numbers. Continue to use grid method for decimals.
Encourage pattern spotting with your child, e.g 6 x 3 = 18 so 6 x 0.3 = 1.8
STAGE 4
24 x 6 = 144
342 x 7 = 2394
7.3 x 6 = 43.8 2 4 6 x 1 4 2 7 x 9 3 1 7
0.3 x 6 42
1.8
Long multiplication (i.e multiplying by more than 1 digit) for whole numbers and decimals.
STAGE 5 2 4 x 1 6 8 7 3
124 x 26 = 3244