© Harcourt 2007
Progression of models and images – towards using the empty number line
Year 1 / Primary 2
Year 2 / Primary 3
Spring
Autumn
Summer
Autumn
+4
1
2
3
4
6
5
7
8
9
10
11
12
Counting, addition and subtraction
+5
40
50
46
100-bead bar
100-bead string
20-bead bar
0
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number line marked in ones
5
5p
Penny number line
0
5
60
55 56
20
10
30
40
50
70
60
80
90
+10
100
10
10p
0
20
10
30
40
60
70
80
90
Number line marked and labelled in 10s
15
15p
20
20p
+3
30
20
10
0
10
20
30
40
50
60
40 – 17 = 23
Using a number line to illustrate a word problem
70
80
90
+10 +1
40
+10
40
+10
40
Vertical number lines in context
30
+10
50 60
100
61
Empty number lines supporting mental calculation
+10
+10
20
+10
50
+1
60 61
Segments of a number line supporting mental
calculation
100
Number line marked and labelled in 10s
15
10
5
100
0
Reading a scale as a number line in context
0
50
100
J10
T10 and J10 on a number line
20
0
Beaded number line labelled in 5s
0
25
50
75
0
Children sketch their own number lines
0–100 beaded number line labelled in 10s
20-bead string
0
T10
–1
50
46
60
55
+10
40
0p
Summer
13 14 15 16 17 18 19 20
Washing line to 20
0 1
Spring
10
25
50
75
100
Number line marked and labelled every 25
15
20
Number line marked and labelled in 5s
0
5
10
Number facts
Fractions, multiplication and division
1
15
20
Double 3 = 6
Half of 6 = 3
Counting in 2s on a counting stick
2
Two groups of 5
Grouping objects
2
4
Doubles and halves using objects
2
1
4
6
3
9
5
8
7
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Multiples of 2
17
2
Odd and even numbers
8
14
5x4=20
Double 6 = 12
Half of 12 = 6
Doubles and halves on a 20-bead bar
5
5
Doubles and halves on a bead bar
Counting in fives using hands
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quarters
quarters
15
Half
7
9
11
13
18 stickers
3
4
5
6
7
5
8
9
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
2
2
Commutativity of multiplication using arrays
2
18 =
+
+ 9
2
0
4
5x2=10
5 stickers each
1 left over
Sharing with remainders
4
2
0
Half of 18 is 9
11 stickers
10
6
8
10
2x5=10
2
2
2
2
2
Multiplication
as hops
on a number line
18 = 9
10
11
2
2
5
0
6
8
grouping
Interpreting division as grouping or sharing
10
2x5=10
5
5
Sharing without remainders
2
10
5x2=10
sharing
Not half
Halves and not halves of shapes
3
5
0
5
5
10
Identifying multiples using a 100-square
1
� �
� �
12
6
Arrays
Multiples of 5
4
1
Halves of shapes
4x5=20
5x2=10
2x5=10
15
11
Doubles and halves on dominoes
Five groups of 2
1
3+3=6
5
5
5
0
10
15
20 ÷ 5 =
0
5
5
5
10
5
15
20…
Multiplication and division on an empty number line
Grouping as hops on a number line
10 + 10 + 10 + 10 = 40
Colouring patterns of multiples on a 100-square
10 ≠ 4 = 40
Multiplication as repeated addition
1 0
Halves of strips of pictures
Coat hanger pairs to 10
not quarters
Quarters and not quarters of shapes
1
Thirteen
25 rabbits
0 can be2fed
3 0
Grouping
1 0
1
1 0
1
2 0
2
2 0
2
3 0
3
3 0
3
4 0
4
5 0
5
�
�
34
54
Interpreting division involving remainders
Forty
five
56
Missing numbers on a 100-square
2 04
Twenty-four
Place value cards
133 134 135 One hundred and thirty-four
143 144 145
Missing numbers above 100 on a 101–200 grid
135 – 100
4
�
123 124 125
4
Jigsaw pairs to 10
�
They can
sell 5 packs
36
45
Thirteen
2 0
2 0
�
Fraction chart
3
Place value chart
Place value chart
�
5 packs
4 left over
2 04
Twenty-four
1 0 30 5
1 0 0
3
5
3-digit numbers with place value cards
Give every child the green light for success. Web: www.harcourt.co.uk/gomaths Tel: 01865 888020
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