Multiplication and Division

Multiplication Multiplication and Divisionand Division

Calculating efficiently

and accurately

Objectives

To explore the knowledge, skills and understanding required for children to multiply / divide efficiently and accurately

To explore the progression in recording and (some of) the teaching approaches used

Self-esteem

The Four RulesUnderstandinUnderstandin

gg

Mental Mental calculationcalculation

ss

Rapid Rapid recallrecall

Efficient Efficient written written

methodsmethods

Models, images & concrete materials

Stories / rhymesProblem solving and role play

Use of ICT

• Counting• Doubles / halves / near doubles• Multiplication as repeated addition, describing an

array and scaling• Division as grouping and sharing• Recall of multiplication / division facts for 2, 3, 4, 5,

10 times tables and beyond• Multiply two / three-digit numbers by 10 / 100• Understand that multiplication and division are

inverses

Progression in knowledge and understanding for x / ÷

Counting and estimation

There are 5 principles of counting:1. The stable order principle - understanding that

the number names must be used in that particular order when counting

2. The one-to-one principle - understanding and ensuring that the next item in a count corresponds to the next number

3. The cardinal principle - knowing that the final number represents the size of the set

4. The abstraction principle - knowing that counting can be applied to any collection, real or imagined

5. The order irrelevance principle - knowing that the order in which the items are counted is not relevant to the total value

Counting in context How many 10p coins are here? How many 10p coins are here?

How much money is that?How much money is that?

How many toes are there on 2 feet?

How many gloves in 3 pairs?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 How many lengths of 10m can you cut from 80m of rope?80m of rope?

Mr Noah

Doubling and halving in context

There are 8 raisins. Take half of them.There are 8 raisins. Take half of them.How many have you taken?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 I double a number and then double the answer. answer. I now have the number 32. I now have the number 32. What number did I start with?What number did I start with?

Doubling machineChip the chopper

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

12 63 28 20 32

24 80 56 27 40

30 8 42 18 1648 70 15 45 3572 54 10 90 6

2 3 4 5 6 7 8 9 10

Three in a Three in a rowrow

Choose two numbers from the row of numbers above the grid.

Multiply them together.

If the answer is on the grid, cover that number with a counter.

4 30 6 12

20 9 5 25

7 2 15 10

3 60 50 8

1 2 3 4 5 10 15 18 20 24 30 60 100

Three in a row

Choose two numbers from the row of numbers above the grid.

Divide the larger number by the smaller number.

If the answer is on the grid, cover that number with a counter.

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 / 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 4

2 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

( 3 x 6) 18(40 x 6) 240 258

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

28 ( 7 x 4)

80 (20 x 4) 210 ( 7 x 30) 600 (20 x 30) 918

27 x 34

108 (27 x 4)

810 (27 x 30)

918Extend 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 / number lines - grouping(modelled using bead strings)

8 ÷ 2 = 4

6 ÷ 2 = 3

0 2 4 6

Number lines / Arrays15 ÷ 5 = 3

0 5 10 15 Groupin

g ITP

0 60 96

(6 x 10)

(6 x 6)Starting from 0

Number dial ITP

96 ÷ 6 = 16

96 96 ÷ 6 ÷ 6

6 x 10 = 606 x 10 = 60

6 x 6 = 366 x 6 = 36

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 = 97Estimate: 270 ÷ 3 = 90 3 291

972

7 43.4

6.21

43.4 ÷ 7 = 6.2Estimate: 42 ÷ 7 = 6