Multiplication
and Division
Calculating efficiently
and accurately
Progression for multiplication and division
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Counting
Doubling and halving
context
Multiplication as repeated addition, describing an array and
scaling
Division as grouping and sharing
Understand that multiplication and division are inverses
Recall of multiplication and division facts
Multiply two / three-digit numbers by 10 / 100
Dice race game
Counting in context

How many 10p coins are here?
How much money is that?

How many toes are there on 2 feet?

How many gloves in 3 pairs?

If Sarah counts in 2s and Nigel counts in 5s, when will they
reach the same number?

How many lengths of 10m can you cut from 80m of rope?
Doubling and halving in context

There are 8 raisins. Take half of them.
How many have you taken?

One snake is 20cm long.
Another snake is double that length.
How long is the longer snake?

I double a number and then double the answer.
I now have the number 32.
What number did I start with?
94 65 48 30 71
28 36 56 97 32
12 24 51 82 19
77 63 44 53 28
60 96 75 17 43
2 x 3 or 3 x 2
Multiplication
3 plates, 2 cakes on each plate
pictures
(Children could draw a picture to help them work out the answer)
2 x 3 or 3 x 2
3 plates, 2 cakes on each plate
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines
(modelled using bead strings)
2 x 3 or 3 x 2
[two, three times] or [three groups of two]
0
2
4
6
Arrays
5 x 3 or 3 x 5
14 x 2 = 28
x
2
10
20
4
8
Array creator
13 x 4 = 52
X
10
3
4
Answer = 52
X
10
3
4
40
12
43 x 6
X
40
3
40 x 6 = 240
6
240
18
3 x 6 = 18
43
x 6
258
1
27 x 34
27 x 34
Approximation:
Answer lies between 600 (20 x 30) and 1200 (30 x 40)
or 30 x 30 = 900
27
x 34
108 (27 x 4)
810 (27 x 30)
918
Extend to HTU x U, U.t x U and HTU x TU
Multiplication
grid ITP
6÷2
Division
6 cakes shared between 2
pictures
6 cakes put into groups of 2
(Children could draw a picture to help them work out the answer)
6÷2
6 cakes shared between 2
6 cakes put into groups of 2
symbols
(Children could use dots or tally marks to represent objects – quicker than drawing a picture)
Number tracks and number lines - grouping
(modelled using bead strings)
8÷2=4
6÷2=3
0
2
4
6
Number lines / Arrays
15 ÷ 5 = 3
0
5
10
15
Grouping
ITP
67 ÷ 4 = 16 r 3
67 ÷ 4
4 x 10 = 40
4 x 6 = 24
[64]
Number dial ITP
97 ÷ 9 = 10 r 7
Efficient methods . . . .
754 ÷ 6
Approximation:
Answer lies between 100 (600 ÷ 6) and
150 (900 ÷ 6)
Answer = 125 r 4
754
- 600
154
- 120
34
- 30
4
(6 x 100)
(6 x 20)
(6 x
Extend to U.t ÷ U and HTU ÷ TU
5)
Efficient methods . . . .
Short division
291 ÷ 3 = 97
Estimation: 270 ÷ 3 = 90
97
3
291
2
43.4 ÷ 7 = 6.2
6.2
Estimation: 42 ÷ 7 = 6
7
43.4
1
A Challenge for you!
Domino Magic

Imagine a domino

Add the two numbers together

Multiply by five

Double

Add the larger of the two numbers.
What is your number?