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# St John's First School Calculation Policy Multiplication and Division

By Beth Freeman,2014-11-17 00:21
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St John's First School Calculation Policy Multiplication and DivisionSt,S,ST,and,first,First,John

MULTIPLICATION

Mental strategies for multiplication include counting on in steps of a constant size,

doubling, using commutativity and multiplying by partitioning a number, multiplying each

part and then putting it back together again, e.g. double 34 by doubling 30 and doubling 4. The ‘grid’ written method builds on this partitioning of numbers, performing the multiplication on each part and then adding the result.

These notes show the stages in building up to using an efficient method for two-

digit by one-digit multiplication by the end of Year 4, two-digit by two-digit

multiplication by the end of Year 5, and three-digit by two-digit multiplication

by the end of Year 6 FOR AVERAGE MATHEMATICIANS.

To multiply successfully, children need to be able to:

; count on in steps, e.g. work out 10 × 3 by counting on in 10s

; understand commutativity, e.g. work out 5 × 7 by recalling seven 5s if they don’t

yet know their seven times table

; recall all multiplication facts to 10 × 10 by the end of Year 4

; partition number into multiples of one hundred, ten and one;

; work out products such as 70 × 5, 70 × 50, 700 × 5 or 700 × 50 using the related

fact 7 × 5 and their knowledge of place value;

; add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the

related addition fact, 6 + 7, and their knowledge of place value;

Foundation Stage

Children will experience equal groups of objects.

Children will experience doubling numbers to 5. They will count in 1s, 2s, 5s and 10s

They will work on practical problem solving activities involving equal sets or groups.

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St John’s First School Calculation Policy April 2013

Year 1

Double single-digit numbers to 10 Count on in steps Double 5 1 2 3 4 5 6 7 8 9 10

2, 4, 6, 8, 10…

2, 4, 6, 8, 10…

Double 6, two groups of 6 10 + 10 + 10

10, 20, 30, 40, 50…

Year 2

Count on in repeated steps

Find five 3s, six 5s, five 10s

Use commutativity

Know that 5 × 3 can be worked out

as three 5s or five 3s

Double 23 is double 20 plus double 3, 40 + 6 = 46 3 × 5

=

5 × 3

Double two-digit numbers

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St John’s First School Calculation Policy April 2013

Year 3

Year 4

Main Focus Grid method Double two-digit numbers -Double 46

46

Multiply any two-digit numbers by single- 40 6

digit numbers 80 12

92

93 x 8 = 744

Multiply teens numbers by single-digit x 90 3

numbers

8 720 24 =744 17 × 3 = 10 x 3 =30 and 7 x 3 = 21 30+21=51

x 10 7

3 30 21 =51

Extend to: Year 5

Multiply three-digit numbers by single-digit numbers and two-digit numbers two-

digit numbers

256 x 3 = 768

x 200 50 6

3 600 150 18 =768

26 x 32 = 832

6 x 20

600

30 600 180 180

40 2 40 12

12

832

3 St John’s First School Calculation Policy April 2013

DIVISION

Children consider division as sharing (halving and quartering) and division as grouping

(how many groups in…?). The written method used for division is based on the ‘grouping’

method of division and is known as ‘chunking’.

These notes show the stages in building up to using an efficient method for two-

digit by one-digit division by the end of Year 4, three-digit by one-digit division by

the end of Year 5, and three-digit by two-digit division by the end of Year 6 FOR

AVERAGE MATHEMATICIANS.

To divide successfully, children need to be able to:

; count on in steps, e.g. work out 18 ? 3 by counting on in 3s

understand and use multiplication and division as inverse operations; ;

; partition two-digit and three-digit numbers in different ways, e.g. partition 42 into

30 and 12 when dividing by 3 (dividing 30 by 3 and 12 by 3);

; recall multiplication and division facts to 10 × 10, recognise multiples of one-digit

numbers and multiply multiples of 10 or 100 by a single-digit number using their

knowledge of multiplication facts and place value;

; understand that division can leave a remainder;

; understand that division by grouping and sharing (halving/quartering) give the same

answer and choose which is most efficient for a given calculation ; use multiplication facts and place value to estimate how many times one number

divides into another for example, how many sixes there are in 147, or how many

23s there are in 472;

Foundation Stage

Children will understand equal groups and share items out in play and

problem solving. They will count in 1s, 2s and 10s.

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St John’s First School Calculation Policy April 2013

Year 1

Halving by Sharing

Find half of 8, by sharing 8 cubes between two people or folding a strip of 8 objects in

half.

Begin to find a quarter by halving and halving again, e.g. find a quarter of 8.

Year 2

Halving and quartering

Find half and a quarter of 20.

Grouping

18 ? 3, how many groups of 3 are in 18?

7 8 9 10 11 12 13 14 15 16 17 18 0 1 2 3 4 5 6

188 Use multiplication facts to help, e.g. 60 ? 10: how many 10s are in 60? 20 ? 5: how many 5s are in 20?

Realise that division can sometimes leave some ’left over’

16 ? 3

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St John’s First School Calculation Policy April 2013

Year 3 Year 4

Chunking

Taking off a chunk of the divisor using a Horizontal chunking on an empty number

multiple of 10: 67 ? 3, 100 ? 6 line

Key Facts:

2 x 6 = 12, 5 x 6 = 30 and 10 x 6 = 60 Introduce the key:

2 x 100 6

5 x

100 10 x

- 60 (X10) Dividing giving answers just over 10 40 42 ? 3: x10 x4 - 36 (X6)

4

= 16

Extend to: Year 5 Chunking

Key Facts

× 10 = 60 2 x 6 =12 × 20 = 120 5 x 6 = 30 × 30 = 180

× 40 = 240

The answer is between 30 and 40, so I’ll

subtract 30 lots of 6, leaving 16.

196 6

196

- 180 (X30)

16

- 12 (X2)

4

= 32

196 6 = 32 r 4

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St John’s First School Calculation Policy April 2013

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