multiplication and division calculating efficiently and accurately

Multiplication and Division

Calculating efficiently and accurately

• Counting• Doubling and halving

• 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

Progression for multiplication and division

context

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 23 plates, 2 cakes on each plate

(Children could draw a picture to help them work out the answer)

2 x 3 or 3 x 23 plates, 2 cakes on each plate

(Children could use dots or tally marks to represent objects – quicker than drawing a picture)

Multiplication

pictures

symbols

Number tracks and number lines(modelled using bead strings)

2 x 3 or 3 x 2

4 620

[two, three times] or [three groups of two]

Arrays

5 x 3 or 3 x 5

14 x 2 = 28

x 10 42 20 8

Array creator

XX 10 3

4

X 10 3

4 40 12Answer = 52

13 x 4 = 52

43x 6

2581

40 x 6 = 240

3 x 6 = 18

X 40 3

6 240 18

43 x 6

27 x 34

Multiplication grid ITP

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

27 x 34

6 ÷ 2 6 cakes shared between 2

6 cakes put into groups of 2

(Children could draw a picture to help them work out the answer)

pictures

Division

6 ÷ 2

6 cakes shared between 2

6 cakes put into groups of 2

(Children could use dots or tally marks to represent objects – quicker than drawing a picture)

symbols

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

Number dial ITP

67 ÷ 4 = 16 r 3

67 ÷ 4

4 x 10 = 40

4 x 6 = 24 [64]

97 ÷ 9 = 10 r 7

Efficient methods . . . .

Answer = 125 r 4

Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6)

754

- 600 (6 x 100)

154

- 120 (6 x 20)

34

- 30 (6 x 5)

4

Extend to U.t ÷ U and HTU ÷ TU

754 ÷ 6

Efficient methods . . . . Short division

291 ÷ 3 = 97

Estimation: 270 ÷ 3 = 90 3 291

972

7 43.4

6.21

43.4 ÷ 7 = 6.2

Estimation: 42 ÷ 7 = 6

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?