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PROGRESSION THROUGH CALCULATIONS FOR MULTIPLICATION

MENTAL CALCULATIONS

(ongoing)

These are a selection of mental calculation strategies:

Doubling and halving

Applying the knowledge of doubles and halves to known facts.

e.g. 8 x 4 is double 4 x 4

Children should also be taught that the 4 x tables can be calculated from knowing the 2 x

tables and that the 6 x tables can be calculated from knowing the 3x tables.

Using multiplication facts

Tables should be taught regularly from Y2 onwards, either as part of the mental oral starter or other times as appropriate within the day.

Year 2 2 times table

5 times table

10 times table

Year 3 2 times table

3 times table

4 times table

5 times table

8 times table

10 times table

Year 4 Derive and recall all multiplication facts up to 12 x 12

Years 5 & 6 Derive and recall quickly all multiplication facts up to 12 x 12 and beyond

Using and applying division facts

Children should be able to utilise their tables knowledge to derive other facts.

e.g. If I know 3 x 7 = 21, what else do I know?

3 x 70 = 210, 30 x 7 = 210, 300 x 7 = 2100, 3000 x 7 = 21 000, 0.3 x 7 = 2.1 etc

Use closely related facts already known

13 x 11 = (13 x 10) + (13 x 1)

= 130 + 13

= 143

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Multiplying by 10 or 100

Knowing that the effect of multiplying by 10 is a shift in the digits one place to the left.

Knowing that the effect of multiplying by 100 is a shift in the digits two places to the left.

Partitioning

23 x 4 = (20 x 4) + (3 x 4)

= 80 + 12

= 92

Use of factors

8 x 12 = 8 x 4 x 3

MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE USED. THEY ARE NOT REPLACED BY WRITTEN METHODS.

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THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF

CHILDREN TO ACHIEVE.

Y1

Children will experience equal groups of objects and will count in 2s and 10s and begin to

count in 5s. They will work on practical problem solving activities involving equal sets or

groups.

Y2

Children will develop their understanding of multiplication and use jottings to support

calculation:

Repeated addition

5 x 3 is 5 + 5 + 5 = 15 or 3 lots of 5 or “Get 5 and keep getting it 3 times” (the 5

tells you what you count in; the 3 tells you how many times)

Repeated addition can be shown easily on a number line and can be shown using practical

materials:

5 x 3 = 5 + 5 + 5

and on a bead bar:

5 x 3 = 5 + 5 + 5

Commutativity

Children should use the language made familiar to them through “Maths Makes Sense”

(MMS) as and when appropriate. For instance, with the law of commutativity: “Same

Value, different appearance.”

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

5 5 5

5 5 5

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Children should know that 3 x 5 has the same answer as 5 x 3. This is spoken as:

a) 3 x 5 = 3 multiplied 5 times/5 lots of 3

b) 5 x 3 = 5 multiplied 3 times/ 3 lots of 5

This can also be shown on the number line.

Arrays

Children should be able to model a multiplication calculation using an array. This knowledge

will support with the development of the grid method.

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

5 5 5

3 3 3 3 3

3 x 5 = 15 (3 multiplied 5 times)

5 x 3 = 15 (5 multiplied 3 times)

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Y3

Children will continue to use:

Repeated addition

6 multiplied by 4 is 6 + 6 + 6 + 6 = 24 or 4 lots of 6 or 6 x 4

Children should use number lines or bead bars to support their understanding.

0 6 12 18 24

Arrays

Children should be able to model a multiplication calculation using an array. This knowledge

will support with the development of the grid method.

Children will also develop an understanding of

Scaling

e.g. Find a ribbon that is 4 times as long as the blue ribbon

5 cm 20 cm

Using symbols to stand for unknown numbers to complete equations using inverse

operations

x 5 = 20 3 x = 18 x = 32

6 6 6

6 6 6 6

6

4 x 9 = 36

9 x 4 = 36

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Correspondence

Correspondence type questions (i.e. balanced equations) need to be explicitly taught,

whereby children can understand that the left hand side of an equation corresponds (is

equal to) the right hand side of an equation.

Example:

5 = 3 + ?

2 x 5 = 13 - ?

Partitioning

38 x 5 = (30 x 5) + (8 x 5)

= 150 + 40

= 190

Children will continue to use arrays where appropriate, leading into the grid method of

multiplication.

x 6

4

10

(10 x 6) + (4 x 6)

60 + 24

84

60

24 Placing the digits to be

partitioned along the side makes the step towards vertical addition of the

products in the grid method more logical (see example

below)

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Grid method

Children need to estimate their answers prior to solving them, by rounding to the

nearest multiple of 10.

E.g 23 x 8

Estimate = 20 x 10 = 200

TU x U

(Short multiplication – multiplication by a single digit)

23 x 8

8

20

3

160

+ 24

184

160

24

Placing the digits to be partitioned along the side makes the step towards vertical addition of the products more logical

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Y4 Expanded Standard Format

Children need to estimate their answers prior to solving them, by rounding to the

nearest multiple of 10.

e.g. 45 x 18

Estimate = 50 x 20 = 1000

The grid method then leads into an expanded standard format for TU x U and HTU x U

TU

23

X 8

24 (8 x 3)

160 (8 x 20)

184

This then progresses to the compact formal method:

23

X 8

1284

The digits that are carried over into the next column need to be written above and to the

left of that column. Once the carried-over digit has been added, it then needs to be

crossed out.

HTU x U

234 x 8

234

X 8 1 28 37 2

When multiplying using the formal

method, each calculation can be

treated as being a single digit by a

single digit. However, it is important

to verbally explain what numbers are

being multiplied. For example, 8 x 3

is 24. The calculation being done is 8

x 3 tens which is 24 tens or 240.

Three tens are then added, so there are

27 tens, which is 270

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Yr 5

Expanded Standard format – long multiplication TU x TU

23

X 28

24 (8 x 3)

160 (8 x 20)

60 (20 x 3)

400 (20 x 20)

644 1

Compact method – long multiplication TU x TU

2 3

X 2 8

1 8 24

4 6 0

6 4 4

1

Using similar methods, they will be able to multiply decimals with one decimal place by a

single digit number, approximating first. They should know that the decimal points line up

under each other.

Children are also shown that the product will contain decimal places corresponding to the

number of decimal places in the calculation. For example, the calculation 4.9 x 3.4 has a

total of 2 digits after the decimal places; the calculation will therefore produce an answer

with 2 decimal places. This principle works as, in the above example, there are two values

in the tenths column and tenths x tenths = hundredths

When multiplying TU x TU, children

are shown that a zero is added prior to

the calculation of the tens number on

the second row. It is explained to

them that it is added as a place holder

as we are multiplying by 10 and not

units so the units column is zero.

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(Note – some calculations, while producing an answer with the corresponding decimal places, will need to be rounded to 2dp as the final digit will be a zero. Example: 15 x 12.548. The calculation using the compact method will give 188.220 but the answer would be written as 188.22)

E.g. 4.9 x 3.4

Children will approximate first

4.9 x 3.4 is approximately 5 x 3 = 15

(Estimating will help the children to establish where the decimal point will go in the product.)

4 . 9

X 3 . 4

1 3 9 6

1 2 4 7 0

1 6. 6 6

1

Y6 In year 6, children consolidate their understanding of the methods used in year 5 and

progress onto larger calculations up to ThHTU x TU

+ - + - + - + - + - + - +

By the end of year 6, children will have a range of calculation methods, mental and

written. Selection will depend upon the numbers involved.

Children should not go onto the next stage if:

1) They are not ready.

2) They are not confident.

Children should be encouraged to approximate their answers before calculating.

Children should be encouraged to consider if a mental calculation would be appropriate

before using written methods.