Year 1
Addition
KEY OBJECTIVES
Understand the operation of subtraction and use related vocabulary.
Use mental strategies to solve simple problems using counting, addition, subtraction, doubling and
halving, explain methods and reasoning orally
Practical work, songs and rhymes using numbers to 10
then 20.
Use knowledge of number bonds for 10, 6 + 4 = 10
When adding more than 2 numbers, put the largest
number first, then add on the smallest.
Practical work, songs and rhymes using numbers to 10 and then 20.
15 + 3 = Put 15 in head and count on 3 using fingers.
Find 15 on a number line and count on 3 jumps
Count out 15 beads on a bead frame and count
on 3 more
Use knowledge of number bonds for 10, 10 - 6 = 4
15 – 3 = Put 15 in your head and count back 3 using
fingers
Find 15 on a number line and count back 3.
Count out 15 beads and take away 3 beads
KEY OBJECTIVES
Know by heart all addition facts for each number to at least 10.
Use knowledge that addition can be done in any order to do mental calculations more
efficiently.
KEY OBJECTIVES
Know by heart all subtraction facts for numbers to at least 10
Understand that subtraction is the inverse of addition. State the subtraction corresponding to a
given addition and vice versa
Consolidate and refine methods used in Year 1.
Use knowledge of number bonds for 10 and 20, doubles
Consolidate and refine methods used in Year 1
Use related subtraction facts of number bonds for 10,20 and
halves.
45 – 23 = Partition smallest into tens and ones
45 + 23 =
Year 2
Subtraction
KEY OBJECTIVES
Understand the operation of addition and use related vocabulary.
Use mental strategies to solve simple problems using counting, addition, subtraction,
doubling and halving, explain methods and reasoning orally
Partition smallest number into tens and ones.
Using a 100sq add tens
45
55
Then add ones 65, 66, 67, 68
Count on 23 using an ENL
+10
+10
+3
___________________________
45
55
65
68
ENL = empty number line
Using a 100sq
22, 23, 24, 25 Count back ones
35
45 Count back tens
Count back 23 using an ENL
-3
-10
-10
_________________________
22
25
35
45
Count on from 23 using an ENL
+10
+10
+2
_________________________
23
33
43
45
Year 3
Addition
KEY OBJECTIVES
Know by heart all addition facts for each number to at least 10.
Add and subtract mentally a ‘near multiple of ten’ to or from a two-digit number
Consolidate and refine the use of ENL to count on by
using more efficient jumps.
42 + 23 =
+20
+3
__________________
42
62
65
Introduce partitioning of both numbers.
Consolidate and refine the use of ENL to count on by using more
efficient jumps.
42-21
-1
-20
____________________
Count back
21
22
42
42 + 23 =
40 + 20 = 6 0
2 + 3 = 5+
65
ENL = empty number line
+20
+1
Count on
_____________________
21
41
42
Partition smallest number into tens and ones.
42 – 20 = 22
22 – 1 = 21
KEY OBJECTIVES
Use known facts and place value to add or subtract mentally, including any pair of twodigit whole numbers.
Carry out column addition and subtraction of two integers less than 1000, and column
addition of more than two such integers.
KEY OBJECTIVES
Use known facts and place value to add or subtract mentally, including any pair of two-digit whole
numbers.
Carry out column addition and subtraction of two integers less than 1000, and column addition of
more than two such integers.
Consolidate and refine ENL and partitioning
Consolidate ENL
Refine partitioning using two then three digit numbers
Introduce Column Method
Year 4
Subtraction
KEY OBJECTIVES
Know by heart all addition facts for each number to at least 10.
Add and subtract mentally a ‘near multiple of ten’ to or from a two-digit number
45
+34
9 (5+4)
7 0 (40+30)
79
86 – 54
324
+165
9 (4+5)
8 0 (20+60)
4 0 0 (300+100)
489
754 – 286
80
6
-5 0
4
3 0 + 2 = 32
745 – 200 = 554
554 – 80 = 474
474 – 6 = 468
Year 6
Year 5
Addition
Subtraction
KEY OBJECTIVES
Calculate mentally a difference such as 8006 – 2993
Carry out addition and subtraction of positive integers less than 10, 000
KEY OBJECTIVES
Calculate mentally a difference such as 8006 – 2993
Carry out addition and subtraction of positive integers less than 10, 000
Consolidate Year 4 methods using H,T,U and TH,H,T,U
587 + 475 =
500 + 400 = 900
80 + 70 = 150
7 + 5 =
12 +
1062
Consolidate Year 4 Methods using H,T,U and Th, H, T, U
Expanded Column
587
+ 475
12 (7+5)
150 (80+70)
900 (500 +400)
1062
Column
587
+ 475
1062
754 – 286
600
200
400 +
140
4
80
6
60 + 8 = 468
754
-286
468
KEY OBJECTIVES
Carry out column addition and subtraction of numbers involving decimals.
KEY OBJECTIVES
Carry out column addition and subtraction of numbers involving decimals.
Continue to use ENL and column methods to include
decimals
14  82 + 16  01 =
Continue to use ENL and column methods to include decimals.
+10
+4
+0.8
+0.02
_____________________________________
1601
2601
3001
3081
3083
14  82
+ 16  01
30  83
9  60 – 4 70 =
+0.30
+4.0
+0.60
_____________________________________
4 70
500
900
960
9  60
- 4  70
4  90
Division
KEY OBJECTIVES
To understand the operation of multiplication as repeated addition or as describing an array.
Know by heart the multiplication facts for 2, 5 and 10 times tables. Derive doubles and
halves quickly.
KEY OBJECTIVES
To understand the operation of division as grouping (repeated subtraction) or sharing.
Derive quickly division facts corresponding to the 2, 5 and 10 times tables. Derive doubles and
halves quickly.
Counting on in twos, fives and tens.
Practical work developing to pictorial representation.
Counting on in twos, fives and tens
Practical work developing to pictorial representation.
Year 1
Multiplication
Year 2
3 lots of 2
=00
6
00
Repeated addition
2 +
2
Leading to
3x2 =6
Arrays
0
0
0
0
+
00
=6
62
2
=6
Share equally between 2 sets
Count on in twos
Inverse of multiplication
000
0
0
Halving
000
3x2
Recall of 2, 5 and 10 times tables
Doubles of numbers up to 20
2, 4, 6
2x3
000
3 lots of 2
000
Year 3
Multiplication
Division
KEY OBJECTIVES
To extend understanding that multiplication can be done in any order.
To know by heart the multiplication facts for 3, 4 and 6 times tables.
KEY OBJECTIVES
Recognise that division is the inverse of multiplication. Begin to find reminders after simple
division. Derive quickly division facts corresponding to the 3, 4 and 6 times tables
Consolidate and refine methods used in Year 2 extending to
the 3, 4 and 6 times tables.
Count on 4 lots of 3’s
3, 6, 9, 12
4 lots of 3 =
4x3=
Repeated addition on an ENL
4x3
+3
+3
+3
+3
______________________________
0
3
6
9
12
Consolidate and refine methods used in Year 2.
Sharing equally between groups.
How many groups of 3 in 12?
Repeated subtraction on an ENL
12  3 =
-3
-3
-3
-3
_________________________
0
3
6
9
12
Year 4
Recall of multiplication facts
KEY OBJECTIVES
To extend understanding of the operation of multiplication and division and their relationship
to each other.
KEY OBJECTIVES
To extend understanding of the operation of multiplication and division and their relationship
to each other.
Consolidate and refine methods used in Year 3 extending to 7,
8, 9 times tables.
Introduce Grid Method
Consolidate and refine methods used in Year 4.
Chunking, counting on.
72  5 =
4x5
4x5
4x5
4x5
______________________________
0
20
40
60
70
Chunking:
72
- 2 0(4x5)
52
- 2 0(4x5)
32
- 2 0(4x5)
1 2
1 0(2x5)
4 + 4 + 4 + 2 =14r2
2
X 20 3
8 160 24
Introduce Column Method
20 + 3
x 8
2 4 (8x3)
1 6 0 (8x20)
1 8 4
= 184
2 3
x
8
184
72
Multiplication
KEY OBJECTIVES
To understand and use the relationship between the addition, subtraction, multiplication and
division. To extend use of written methods.
Consolidate and refine the use of the grid method.
Consolidate and refine the use of ENL, counting on and
chunking.
256  7 =
256
256
7 0 (10x7)
- 2 1 0 (30x7)
7 0 (10x7)
46
116
4 2 (6x7)
7 0 (10x7)
4 36r4
46
4 2 (6x7)
4 36r4
Introduce bus stop method
3 6 r4
7 256
Year 5
72 x 38 =
X
30
8
70
2100
560
Introduction of long multiplication
2
60 = 2160
16 = 576 +
2736
72
x38
1 6 (8x2 )
5 6 0 (8x70)
6 0 (30x2)
2 1 0 0 (30x70)
2736
KEY OBJECTIVES
To understand and use the relationship between the addition, subtraction, multiplication and
division. To extend use of written methods.
KEY OBJECTIVES
To understand and use the relationship between the addition, subtraction, multiplication and
division. To extend use of written methods.
Consolidate and refine Year 5 methods.
Consolidate and refine year 5 methods.
372 x 24 =
Year 6
Division
KEY OBJECTIVES
To understand and use the relationship between the addition, subtraction, multiplication and
division. To extend use of written methods.
X 300
70 2
20 6000 1400 40 = 7440
4 1200 280 8 = 1488+
8928
372
x 24
8 (4x2)
2 8 0 (4x70)
1 2 0 0 (4x300)
4 0 (20x2)
1 4 0 0 (20x70)
6 0 0 0 (20x300)
8928
977  36 =
Bus stop
36 x 10 = 360
36 x 20 = 720
36 x 25 = 900
36 x 27 = 972
2 7r5
36 9 7 7
27r5
Foundation
Key Objectives
To count reliably up to 10 objects and recognise numbers up to 10
To use language such as more or less, greater or smaller, to compare two numbers.
In practical activities and discussion, begin to use the vocabulary involved in adding and subtracting.
To find one more or one less than a number from 1 to 10.
To begin to relate addition to combining two groups of objects, and subtraction to ‘taking away’.
Make your child aware of numbers in their environment. eg. ages, house numbers, car registrations, telephone numbers.
Count as part of your everyday life. eg. stairs as you go up to bed, apples in the fruit bowl, cakes on a plate, spoons on the table.
Practical one to one counting activities. eg. count the red Smarties, children around a table, birds in the picture.
Recognise digits from 1 to 10 and match to a set of objects.
Count out 4 objects. What is one more/one less?
Development of addition and subtraction through practical activities.
5+3=
Count out 5 counters and 3 counters. Then count how many altogether using one to one counting.
OOOOO + OOO = OOOOOOOO
12345
123
12345678
Count out 5 counters and 3 counters. Then count on from 5.
OOOOO +
OOO = 8
678
5–3=
Count out 5 counters and take away 3, leaves 2 left.
OOOOO
12345
Count out 5 counters and count back 3, leaves 2
OOOOO = 2
345