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SSchoolchoolCCalculationalculation P Policyolicy

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Multiplication

Addition Subtraction

Division

*Only click when prompted to ensure all steps are seen.

Select an operation to become a

maths wizard!

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Select a stage!Select a stage!

⋆ Addition - Stage 1




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Pre-Written Methods

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⋆ Subtraction - Stage 1




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Pre-Written Methods

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⋆ Multiplication - Stage 1




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Pre-Written Methods

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Select a stage!Select a stage!⋆ Division - Stage 1

⋆ Division - Stage 2



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!

Pre-Written Methods

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Begin by drawing a number line starting with the biggest number

++ AdditionAddition ~~ Watch and Watch and

Learn!Learn! ++ Stage 1 ~ 1

22 + 33 =

______________________________

Next

33

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22 + 33 =

______________________________

Next

33

+10 +10

43 53

Add 2 tens first

T

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22 + 33 =

______________________________33

+10 +10 +1 +1

43 555453

Then add 2 unitsU

So 22 + 33 is 55

55

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stage.

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36 + 43 = Start by partitioning the tens and the units.

TU TU

30 + 40

6 + 3

Next

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36 + 43 =

30 + 40 = 70 6 + 3 = 9

Add the tens together and then the units.



70 + 9 = 79

So 36 + 43 is 79

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stage.

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47 + 76 =

Next



Write the numbers so that the Tens and the Units are in line.

T U

47

+ 76

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47

+ 76

Start by adding the the units.

7 + 6 =

U

13

Next

Stage 3 ~ 2


Learn!Learn! ++

47 + 76 =

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47

+ 76

Next

Stage 3 ~ 3


Learn!Learn! ++

110

Then add the tens.

40 + 70 =

T

13

47 + 76 =

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110

47

+ 76

Stage 3 ~ 4


Learn!Learn! ++

13

123

Now add these together

110 + 13 = +

So 47 + 76 is 123

47 + 76 =

HTU + HTU

Select a

stage.

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Learn!Learn! ++ HTU + HTU

247 + 176 =

110

247

+ 176

13

423

Set out as before. Add the units and tens as before and record.

The extra step, add the hundreds together

200 + 100 = 300

Then add the numbers.

+300

So 247 + 176 is 423

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stage.

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47 + 76 =

Next


Learn!Learn! ++

Stage 4 ~ 1

47

+ 76Write the numbers so that the Tens and the Units are in line.

T U

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47 + 36 =


Learn!Learn! ++

Stage 4 ~ 2

47

+ 36

Now add the units

7 + 6 = 13U

3 units go in the units column33 units go in the units column

1

7 + 6 = 13

Next

Exchange 10 units for 1 ten. This goes under in the tens column

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47 + 36 =


Learn!Learn! ++

Stage 4 ~ 3

3

1

Now add the tens

40 + 30 = 70T

Remember there is one ten here to add too. 7 tens + 1 ten = 8 tens

You need to put the ten digit in the tens column

8

47

+ 36

So 47 + 36 is 83

Select a

stage.

See HTU + HTU

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147 + 186 =


Learn!Learn! ++

HTU + HTU

1

3

147

+ 186

So 147 + 186 is 333

Select a

stage.

Carry any units over 9,

any tens over 90.

Remember to add the carry!

7 + 6 = 13 carry the ten

40 + 80 + 10 = 130 carry the hundred

100 + 100 + 100 = 300

133

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-- SubtractionSubtraction ~~ Watch and Learn!Watch and Learn!

--Stage 1 ~ 1

______________________________-10

473727

47 - 23 =

-10

So 47 – 23 = 24

Take away in steps of 10 first as this is easier. 23 = 2 tens.

-1-1-1

262524

Then take away in jumps of 1. 3 units equal 3 jumps.

Place the largest number at the end of the line.

24

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stage.

See HTU-HTU

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--HTU-HTU

______________________________-100

347247227

347 - 123 =

-20

So 347 – 123 = 224

Take away in steps of 100 first as this is easier. 123 = 100.

-3

224

Then take away the tens. Then the units.

Place the largest number at the end of the line.

224

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stage.

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--Stage 2 ~ 1 taking away by counting up

74 - 35 =

Write the numbers so that the Tens and the Units are in line.

T U

74

- 35

Start at 35 add 5 to make 40. Then add suitable numbers to reach 74.

+5 (40)

+30 (70)

+4 (74)Add the numbers together.

39

So 74 - 35 is 39

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stage.

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563 - 241 =

Next


--Stage 3 ~ 1

500 + 60 + 3- 200 + 40 + 1

Repeat with 241

Partition 563 into hundreds, tens and units.

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- 200 + 40 + 1300

Next, subtract the tens

60 – 40 = 20

563 - 241 =

Next


--Stage 3 ~ 2

500 + 60 + 3- 200 + 40 + 1

Start with the units

3 – 1 = 2

2

UH T

20Next, subtract the hundreds

500 – 200 = 300

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--Stage 3 ~ 3

Add the answers together

300 + 20 + 2 = 322- 200 + 40 + 2300

563 - 241 =

500 + 60 + 3- 200 + 40 + 1

220 = 322

So 563 - 241 = 322Select

a stage.

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Next


--Stage 4 ~ 1 Decomposition 137 - 85 =

Write the numbers so that they are in place value position.

137

- 85

H T U

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Next


--Stage 4 ~ 2

137 - 85 = 1 3 7

- 8 5

Subtract the units first. 7 – 5 =

And write under the units.

2

The tens can’t be subtracted as 30 – 80 = - 50

Borrow 1 hundred from the hundred column.

01

Cross out the hundred and leave a 0 above. The 100 is put in the tens as a 1.

The tens column now has 130 in it and the hundred has 0.

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--Stage 4 ~ 3

So 137 - 85 = 52

Now solve 130 – 80 and write the answer.

There are 0 hundreds to subtract.

1 3 7

- 8 5

2

01

5

137 - 85 =

Select a

stage.

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xx MultiplicationMultiplication ~~ Watch and Watch and

Learn!Learn! xxStage 1 ~ 1

= 4 x 5

= 10 x 5

14 x 5 =

Next

Partition the 14 into 2 parts, tens and units.

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So 14 x 5 = 70

4 x 5

10 x 5

14 x 5 =

= 50

= 20

Now add 50 + 20 and write the answer.

Select a

stage.

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Draw a box two across and one down because you are multiplying a 2 digit number by a 1 digit number.


Learn!Learn! xx

Stage 2 ~ 1

16 x 4 =

Next

10 6

4

Partition 16 into 1 ten and 6 units

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The answer to 10 x 4 goes here.


Learn!Learn! xx

Stage 2 ~ 216 x 4 =

10 6

4


x

40 24

Now add these answers together. 40 + 24 =

So 16 x 4 = 64

See TU x TU See HTU x U

Select a

stage.

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Partition 56 into 5 tens and 6 units


Learn!Learn! xx TU x TU ~ 1

56 x 27 =

Next

20 7

6

50

Partition 27 into 2 tens and 7 units

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56 x 27 = 20 7

6

50


1000

350

The answer to 6 x 7 goes here

Next

x

120 42

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56 x 27 = 20 7

6

50 Add these four numbers together.

1000 + 350 + 120 + 42 =

Children can use the addition methods to help them add.

1000

350

x

120 42

So 56 x 27 = 1512

See HTU x U

Select a

stage.

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Learn!Learn! xx HTU x U ~ 1126 x 4 =

Next

100 20

4

Partition 126 into 1 hundred,

2 tens and 6 units

6

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Next

100 20

4

Partition 126 into 100,

20 and 6

6

400 80 24The answer to 4 x 100 goes here.

The answer to 20 x 4 goes here


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100 20

4

6

400 80 24

Add 400 + 80 + 24

So 126 x 4 = 504

See TU x TU

Select a

stage.

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38 x 7 =



38

x 7Set the sum out like this so that the numbers are in the correct columns.

T U

Next

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38 x 7 =

Next



38

x 7

56

210

Multiply the tens by 7

7 x 30 = 210

Multiply the units by 7

7 x 8 = 56

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38 x 7 =



38

x 7

56210266

Now add these two answers together. 56 + 210.

So 38 x 7 = 266

See TU x TU

Select a

stage.

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15 x 24 =


Learn!Learn! xxTU x TU ~ 1

15


T U

Next

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15 x 24 =

Next



X 24

20

40

Multiply by the units

4 x 5 = 20 and

4 x 10 = 40

15

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15 x 24 =

Next



X 24

2040

Multiply by tens

20 x 5 = 100 and

20 x 10 = 200

15

100200

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15 x 24 =



Now add these numbers together.

So 15 x 24 = 360

X 24

2040

15

100200360

Select a

stage.

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38 x 7 =

Next



38


T U

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38 x 7 =

Next



38

x 7

Now multiply 7 x 8 = 56 and write the units and carry the tens underneath.

6

5

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38 x 7 =

Next



38

x 7

Now multiply 7 x 30= 210 and add the 5 tens to the 10 and write this and carry the hundreds underneath.

6

5

6

2

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38 x 7 =



38

x 7

Now put the hundreds into the answer

6

5

6

2

2

So 38 x 7 = 266Select

a stage.

See TUxTU

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38 x 27 =


Learn!Learn! xxTU x TU – Magic 0

38

x 27

65

6

0

2

Set out as shown.

First multiply 7 x 8 = 56.

Carry the 5 tens and record the 6.

Then 7 x 3 = 21 plus the 5 = 26 (record)

Next place the magic 0 into the units column.

Now 2 x 8 = 16

Carry the 1 and record the 6.

Now 2 x 3 = 6 and add to the 1 carry

Nb. Each number is considered as a unit in this calculation to make it easier.

eg. 30 is 3 and 20 is 2.

167

Next

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38 x 27 = 38

x 27

65

6

0

2

Nb. Each number is considered as a unit in this calculation to make it easier.

eg. 30 is 3 and 20 is 2.

167


Learn!Learn! xxTU x TU – Magic 0

Finally add 266 and 760.

6201Select a

stage.

So 38 x 27 = 1026

11

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Stage 1 ~ 1 Repeated subtraction

24 ÷ 3 =

0

Jump back in 3’s (the divider) until no more can be taken.

2418 21

÷÷ DivisionDivision ~~ Watch and Watch and

Learn!Learn! ÷÷Write the number to divide at the end of a number line.

1512963

-3

Now count the number of jumps. 8 jumps

So 24 ÷ 3 = 8

-3-3-3-3-3-3-3

Select a

stage.

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63 ÷ 3 =

Next


Learn!Learn! ÷÷

3 63

Stage 2 ~ 1 - chunkingTwo ways to set out

or

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Children will look for chunks. First take chunks (multiples) of 10,then 5 and then single units until you have the divided number - 63

63 ÷ 3 =


Learn!Learn! ÷÷

3 6330 + 30 + 3 = 63 so we have taken all chunks possible.

Stage 2 ~ 2

30 (3 x 10)

30 (3 x 10)

3 (3 x 1) Add the chunks.

10 + 10 + 1 = 21

So 63 ÷ 3 = 21

2121

Select a

stage.

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Learn!Learn! ÷÷Stage 3 ~ 1 – Long division

Next

So 198 ÷ 6 = 33

6 198

Children will look for chunks. Try to use multiples of 10, 20, 30 etc to remove the largest possible multiple of 6.(6 x 30)- 180

Record the chunk in brackets and put the answer underneath the original number. Subtract the chunk from the divided number. Then look for more chunks.

18

- 18 (6 x 3)

0

Once all chunks have been taken and 0 or a remainder is left, show the answer at the top by adding the chunks. 30 + 3 = 33

33

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Learn!Learn! ÷÷Stage 3 ~ 2 With remaindersHTU ÷ TU

So 560 ÷ 24 = 23 r 8

24 560

Children will look for chunks. Try to use multiples of 10, 20, 30 etc to remove the largest possible multiple of 24.(24 x

20)- 480

Record the chunk in brackets and put the answer underneath the original number. Subtract the chunk from the divided number. Then look for more chunks.

80

- 72 (24 x 3)

8

Once all chunks have been taken and 0 or a remainder is left, show the answer at the top by adding the chunks. There is not enough to make another 24 so there is a remainder of 8.20 + 3 = 23 r 8

23 r 8

Select a

stage.

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Learn!Learn! ÷÷Stage 4 ~ 1 short division

3 8 1

Regard each digit on its own.Work from left to right.

•How many 3’s are in 8?

Mental Working

•2 with 2 remaining. •Record the 2 above the line. Then carry the remaining 2 over.

22

•Record the 2 next to the one making 21.

•How many 3’s in 21 = 7. Record above the 21.

7

So 81 ÷ 3 = 27

81 ÷ 3 =

Next

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Learn!Learn! ÷÷Stage 4 ~ With remainders

12 2 2 4 Regard each digit on its own.Work from left to right.


Mental Working

•0 with 2 remaining. •Record the 0 above the line. Then carry the remaining 2 over.

02

•Record the 2 next to the two making 22.

•How many 12’s in 22 = 1 – Record above the 22.

1

So 224 ÷ 12 = 18 r8

224 ÷ 12 =10

8 r 8

•Carry the 10 and record how many 12’s in 104.•Record the 8 and remember the 8 remaining.

Next

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Learn!Learn! ÷÷Stage 4 ~ With decimals

4 2 5 0


Mental Working

•0 with 2 remaining.

•Record the 0 above the line. Then carry the remaining 2 over making 25.

02

•How many 4’s in 25 = 6 with 1 remainder. Record above the 25.

6

So 250 ÷ 4 = 62.5

250 ÷ 4 =1

2

•Carry the 1 and record how many 4’s in 10 = 2 with 2 remaining.•Now add a decimal point and carry the 2 making 20.

Select a

stage.

. 0

. 52

•How many 4’s in 20 = 5. Record above

•Only record to a maximum of 2 decimal places.

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