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Progression in Mental and �Written Strategies

PRIMARY

SECONDARY

POST 16

ALTERNATIVE

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Mental Calculations

  • Pupils should learn a range of mental strategies to efficiently derive and recall number facts.
  • The slides below are set out as guidance for a range of essential mental calculation strategies. They are not structured by domain and year group expectation but are often pre-requisite skills needed within written calculations.
  • Schools may wish to use alternative manipulatives, dependant on available equipment and school preference.
  • Pupils should be taught to be flexible by selecting a suitable strategy dependent on the numbers involved but also understand and be encouraged to use personal choice.

Please note that they highlight progression but are not necessarily matched with the national curriculum.

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Written strategies

  • Age stage expectations: �The written strategies outlined in the document are organised according to age stage expectations as set out in the National Curriculum 2014 and the method(s) shown for each year group should be modelled to the vast majority of pupils. However, it is vital that pupils are taught according to the pathway that they are currently working at and are showing to have ‘mastered’ a pathway before moving on to the next one.
  • Schools may wish to use alternative manipulatives, dependent on available equipment and school preference. Ensure that when pupils move from base 10 to place value counters, they understand the unitary value e.g. a 10 counter represents 10 ones.
  • Choosing a calculation method: �Before pupils opt for a written method, they should first consider these steps.

Can I do it in my head using a mental strategy?

Could I use some jottings to help me?

Should I use a formal written method to work it out?

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Mental Calculations

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23 + 5

3 + 5 = 8

so 23 + 5 = 28

Using number bonds

Adding a single-digit number to a 2-digit number

Using partitioning

28 + 5

28 + 5 = 28 + 2 + 3

28 + 5 = 33

Using compensation

28 + 9

28 + 9 = 28 + 10 – 1

28 + 9 = 37

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28 – 5

8 – 5 = 3

So 28 – 5 = 23

Using partitioning

Subtracting a single-digit number from a 2-digit number

Using number bonds

Using compensation

23 – 8

23 – 8 = 23 – 3 – 5

23 – 8 = 15

37 – 9

37 – 9 = 37 – 10 + 1

37 – 9 = 28

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37 + 10

37 + 10 = 47

Adding 10

Adding two 2-digit numbers

Using partitioning with no bridging through a multiple of 10

Using partitioning, bridging through a multiple of ten

23 + 14

23 = 2 tens and 3 ones

14 = 1 ten and 4 ones

23 + 14 = 3 tens and 7 ones

23 + 14 = 37

35 + 17

35 + 17 = 35 + 10 + 7

Adding multiples of 10

23 + 30

23 + 30 = 53

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37 + 19

37 + 19 = 37 + 20 – 1

Using compensation

Adding two 2-digit numbers

Using near doubles (consecutive)

45 + 46

45 + 46 = 45 + 45 + 1

45 + 46 = double 45 + 1

45 + 46 = 90 + 1 45 + 46 = 91

Using near doubles (non consecutive)

25 + 27

25 + 27 = 25 + 25 + 2

25 + 27 = double 25 + 2

25 + 27 = 50 + 2 25 + 27 = 52

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52 – 10

52 – 10 = 42

Subtracting 10

Subtracting two 2-digit numbers

Using partitioning with no bridging through a multiple of 10

38 – 23

38 = 3 tens and 8 ones

23 = 2 tens and 3 ones

38 – 23 = 1 ten and 5 ones

38 – 23 = 15

Subtracting multiples of 10

43 – 20

43 – 20 = 23

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43 – 25

In total 10 + 5 + 3 = 18 has been added to 25 to equal 43.

43 – 25 = 18

Using counting on to find the difference

Subtracting any two 2-digit numbers

Using counting backwards, bridging through a multiple of ten

43 – 25

25 = 20 and 5

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35 – 19

35 – 19 = 35 – 20 + 1

Using compensation

Subtracting two 2-digit numbers

Using adjustment or constant difference

34 – 16

34 – 16 could be rewritten as 38 – 20. The numbers have been adjusted to make the calculation simpler.

The difference between 34 and 16 is the same as the difference between 38 and 20 because 4 has been added to each number.

38 – 20 = 18

34 – 16 = 18

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4.2 + 3.4

3.4 = 3 + 0.4

4.2 + 3.4 = 4.2 + 3 + 0.4

4.2 + 3.4 = 7.6

Adding numbers with decimals

Using compensation

Using partitioning with no bridging through whole numbers

Using partitioning, bridging

through whole numbers

4.7 + 3.5

3.5 = 3 + 0.5

3.4 + 0.9

3.4 + 0.9 = 3.4 + 1 – 0.1

3.4 + 0.9 = 4.3

2.5 + 1.9

2.5 + 1.9 = 2.5 + 2 – 0.1

2.5 + 1.9 = 4.4

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8 + 6 + 2

Using number bonds

Adding three single-digit numbers

8 + 6 + 2 = 16

3 + 3 + 4

Using consecutive numbers

3 + 4 + 5

Using doubles

3 + 3 + 4

3 + 3 + 4 = double 3 + 4

3 + 3 + 4 = 6 + 4

3 + 3 + 4 = 10

3 + 4 + 5 = 4 + 4 + 4

3 + 4 + 5 = 12

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40 x 3

Multiplying a single-digit number by multiples of 10

Multiplying by 10, 100 and 1,000 and multiples of 10

40 x 3 is 10 times bigger than 4 x 3 so the answer will be 10 times bigger

40 x 3 = 120

46 x 10 = 460

Multiplying a number by 10, 100

and 1,000

Multiplying a number with decimals by 10, 100 and 1,000

0.34 x 1,000 = 340

0.34 x 100 = 34

0.34 x 10 = 3.4

46 x 1,000 = 46,000

46 x 100 = 4,600

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Multiplying by multiples of 10 and 100

Multiplying multiples of 10 by multiples of 10

30 x 40

Each step is 10 times bigger.

Each calculation is multiplied by 10, so the answer is becoming 10 times bigger each time.

30 x 40 is 100 times bigger

than 3 x 4

Multiplying multiples of 100 by multiples of 10

700 x 50

30 x 40 = 1,200

700 x 50 is 1,000 times

bigger than 7 x 5

700 x 50 = 35,000

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0.3 x 2 is 10 times smaller than 3 x 2 so the answer will be 10 times smaller

0.3 x 2 = 0.6

Multiplying by tenths

Multiplying a single-digit number by tenths

0.4 x 6 is 10 times smaller than 4 x 6

the answer will be 10 times smaller

Multiplying tenths by tenths

0.3 x 2

0.4 x 0.6

0.4 x 6 is 10 times smaller than 4 x 6

so the answer will be 10 times smaller

0.4 x 0.6 is 10 times smaller than 0.4 x 6

so the answer will be 10 times smaller

0.4 x 0.6 is 100 times smaller than 4 x 6

0.4 x 0.6 = 0.24

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180 ÷ 3

Identifying division facts

Dividing by 10 and 100 and multiples of 10 by a single-digit number

180 ÷ 3 is 10 times bigger than 18 ÷ 3 so the answer is 10 times bigger

180 ÷ 3 = 60

600 ÷ 10 = 60

Dividing a number by 10, 100 and 1,000

Dividing a number with decimals by 10, 100 and 1,000

624 ÷ 10 = 62.4

624 ÷ 100 = 6.24

600 ÷ 100 = 6

6,240 ÷ 1,000 = 6.24

6,000 ÷ 1,000 = 6

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17 x 3

Using partitioning

Multiplying 2-digits by a single-digit

Multiplying by 5

Using doubling

Multiplying by 9 using compensation

24 x 5

24 x 10 = 240

Half of 240 = 120

24 x 5 = 120

17 x 3 = (10 x 3) + (7 x 3)

17 x 3 = 30 + 21 = 51

17 x 3 = 51

To multiply a number by 5, multiply it by 10 and then halve it.

Multiplying a number by 4 is the same as doubling it, then doubling it again.

14 x 4

14 x 4 = 14 x 2 x 2

14 x 4 = 56

14 x 9

14 x 9 = ( 14 x 10 ) – 14

14 x 9 = 126

Instead of multiplying a number by 9,

multiply it by 10 then subtract one group

to be left with 9 groups.

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Double 30

30 = 3 tens

Double 3 = 6

Double 3 tens = 6 tens

Double 30 = 60

Doubling 2-digit numbers

Doubling multiplies of 10

Doubling

Doubling multiplies of 5

Double 35

35 = 30 + 5

Double 30 = 60

Double 5 = 10

Double 35 = 60 + 10

Double 35 = 70

Double 37

37 = 30 + 7

Double 30 = 60

Double 7 = 14

Double 37 = 60 + 14

Double 37 = 74

Double 4.7

4.7 = 4 + 0.7

Double 4 = 8

Double 0.7 = 1.4

Double 4.7 = 8 + 1.4

Double 4.7 = 9.4

Doubling numbers with decimals

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Half of 60

60 = 6 tens

6 ÷ 2 = 3

6 tens ÷ 2 = 3 tens

Half of 60 = 30

Halving 2-digit numbers

Halving multiplies of 10 with an even number of tens

Halving

Half of 72

72 = 70 + 2

Half of 70 = 35

Half of 2 = 1

Half of 72 = 35 + 1

Half of 72 = 36

Half of 158

158 = 100 + 50 + 8

Half of 100 = 50

Half of 50 = 25

Half of 8 = 4

Half of 158 = 50 + 25 + 4

Half of 158 = 79

Halving 3-digit numbers

Halving multiplies of 10 with an odd number of tens

Half of 50

50 = 40 + 10

Half of 40 = 20

Half of 10 = 5

Half of 50 = 20 + 5

Half of 50 = 25

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Written calculations: Addition and Subtraction

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whole

part

part

Tens Frame

Number line

thousands

hundreds

tens

ones

100

1

10

1000

Place Value grid

Base ten

part

part

whole

Part-whole models

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Additive Structure

addend

addend

sum

sum

addend

addend

addend + addend = sum

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Additive Structure

subtrahend

difference

minuend

minuend

subtrahend

difference

minuend - subtrahend = difference

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Reception ELGs

Addition and Subtraction

Number

Numerical Patterns

  • have a deep understanding of number to 10, including the composition of each number;
  • subitise (recognise quantities without counting) up to 5;
  • automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts.
  • verbally count beyond 20, recognising the pattern of the counting system;
  • compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity;
  • explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.

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Composition of numbers

5 + 0

4 + 1

3 + 2

Explore and represent patterns

within numbers up to 10

Doubling facts

Subitise up to 5

7

Automatically recall number bonds up to 5

Explore and represent patterns with odds

and evens

Reception ELGs

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Year 1

Addition and Subtraction

  • read, write and interpret mathematical statements involving addition (+), subtraction (−) and equals (=) signs
  • represent and use number bonds and related subtraction facts within 20
  • add and subtract one-digit and two-digit numbers to 20, including 0
  • solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? − 9

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Understanding teen numbers as a 10 and ones

Can add a one-digit number to a two-digit number within 20

12 + 7 = 19

10 + 1 = 11

10 + 2 = 12

10 + 3 = 13

10 + 4 = 14

0

5

10

15

20

Year 1 addition

?

12

7

12

7

?

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17 – 8

Taking away and counting back (used only for subtracting small numbers)

Year 1 subtraction

0

5

10

15

20

8

?

Can subtract a one-digit number from a two-digit number

20 – 8

20

8

?

20

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Year 2

Addition and Subtraction

  • solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures; applying their increasing knowledge of mental and written methods
  • recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
  • add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and 1s; a two-digit number and 10s; 2 two-digit numbers; adding 3 one-digit numbers
  • show that addition of 2 numbers can be done in any order (commutative) and subtraction of 1 number from another cannot
  • recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems

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tens

ones

tens

ones

44

54

64

74

75

76

77

+10

+10

+10

+1

+1

+1

44 + 33

30 + 3

16

+4

+3

20

23

16 + 7

4 + 3

27 + 30

+10

+10

+10

27

37

47

57

Can add a two-digit number and 1s using concrete objects or pictorial representations

Can add a two-digit number and 10s using concrete objects or pictorial representations

Can add 2 two-digit numbers using concrete objects or pictorial representations

Year 2 addition

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tens

ones

37 – 4

Can subtract a two-digit number and 1s using concrete objects or pictorial representations

Year 2 subtraction

0

5

10

15

20

25

30

35

40

32 – 5

– 2 – 3

Can subtract a two-digit number and 1s using concrete objects or pictorial representations

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Year 2 subtraction

Can subtract a two-digit number and 10s using concrete objects or pictorial representations

tens

ones

53 – 40

13

53

Can subtract a two-digit number using concrete objects or pictorial representations

54 – 23

– 20 – 3

31

54

3

10

10

10

10

10

10

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Year 3

Addition and Subtraction

  • add and subtract numbers mentally, including:�a three-digit number and 1s; a three-digit number and 10s; a three-digit number and 100s
  • add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction
  • estimate the answer to a calculation and use inverse operations to check answers
  • solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction

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hundreds

tens

ones

245

250

255

260

+4

+4

246 + 8

+ 4 + 4

Can add a three-digit number and 10s

Can add a three-digit number and 1s mentally using partitioning

Can add a three-digit number and

100s

Year 3 addition

235 + 40

hundreds

tens

ones

+ 10

+ 10

+ 10

+ 10

hundreds

tens

ones

243 + 300

243

343

443

543

+ 100

+ 100

+ 100

275

265

255

245

235

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tens

ones

hundreds

tens

ones

42 + 31

367 + 185

47 + 36

tens

ones

Can add numbers with up to three digits using the expanded column method

Can add numbers with two digits using the expanded column method

(no regrouping)

Can add numbers with two digits using the expanded column method (regrouping)

Year 3 addition

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235

240

246

250

2

6

246 – 8

– 6 – 2

Can subtract a three-digit number

and 10s

Can subtract a three-digit number and 1s mentally using decomposition (bridging ten)

Can subtract a three-digit number and

100s

Year 3 subtraction

625 – 300

273 – 40

325

425

525

625

10

10

10

10

100

100

100

273

263

253

243

233

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53 – 35

543 – 324

Can subtract numbers with up to three digits using the expanded column method (with exchange)

Can subtract numbers with two digits using the expanded column method (with exchange)

Year 3 subtraction

tens

ones

75 – 31

Can subtract numbers with two digits using the expanded column method (no exchange)

tens

ones

hundreds

tens

ones

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Year 4

Addition and Subtraction

  • add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction �where appropriate
  • estimate and use inverse operations to check answers to a calculation
  • solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

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Thousands

hundreds

tens

ones

3,475 + 1,244

152 + 163

Can add three-digit numbers using the formal column addition method

Can add four-digit numbers using the formal column addition method

Year 4 addition

hundreds

tens

ones

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Year 4 subtraction

Can subtract three-digit numbers using the formal column subtraction method

Can subtract four-digit numbers using the formal column subtraction method

thousands

hundreds

tens

ones

362 – 124

hundreds

tens

ones

3,317 – 1,254

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Year 5

Addition and Subtraction

  • add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
  • add and subtract numbers mentally with increasingly large numbers
  • use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
  • solve problems involving number up to three decimal places

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Year 5 addition

Ten thousands

thousands

hundreds

tens

ones

Can add numbers with more than four-digits

37,056 + 4,863

Can add numbers with wholes and decimals up to three decimal places

13.78 + 8.16

tens

ones

.

tenths

hundredths

.

.

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thousands

Can subtract numbers with more than four-digits

Year 5 subtraction

thousands

hundreds

tens

ones

48,294 – 13,478

ten

thousands

Can subtract numbers with wholes and decimals up to three decimal places

tens

ones

.

tenths

hundredths

.

17.65 – 6.82

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Year 6

Addition and Subtraction

  • perform mental calculations, including with mixed operations and large numbers
  • use their knowledge of the order of operations to carry out calculations involving the four operations
  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
  • solve problems involving addition, subtraction, multiplication and division
  • use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

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Year 6 addition and subtraction

Can subtract numbers with wholes and decimals up to three decimal places with different numbers of digits

Can add numbers with wholes and decimals up to three decimal places with different numbers of digits

57.3 + 32.908

67.26 – 23.917

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Written calculations: Multiplication and Division

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Multiplicative Structure

product

multiplicand

multiplicand

multiplicand

multiplicand

multiplicand

Multiplier (number of equal parts)

multiplicand x multiplier = product

The multiplicand and the multiplier are both factors of the product.

factor x factor = product

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Multiplicative Structure

dividend

quotient (value of part)

quotient (value of part)

quotient (value of part)

quotient (value of part)

quotient (value of part)

divisor (number of equal parts)

dividend ÷ divisor = quotient

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Multiplicative Structure

dividend

quotient (value of part)

quotient (value of part)

quotient (value of part)

quotient (value of part)

quotient (value of part)

remainder

divisor (number of equal parts)

dividend ÷ divisor = quotient plus a remainder

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Quotative division

Quotative and partitive division

There are 32 pupils in a class.

They are put into groups of 4.

There are 32 pupils in a class.

They are put into 4 groups.

There are 4 pupils in each group.

There are 8 groups.

There are 4 groups.

There are 8 pupils in each group.

Partitive division

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EYFS

Multiplication and Division

  • explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally

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Can double numbers and quantities up to 10 using practical objects

Half of 6

Half of 6 = 3

Half of 6 = 3

Half of 8 = 4

Half of 8

Can halve numbers and quantities up to 10 using practical objects with equal sharing

16 = 8 + 8

Reception ELGs

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Year 1

Multiplication and Division

  • count in multiples of twos, fives and tens
  • solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

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Can use concrete objects, pictorial representations and arrays

Can count in 2s

Year 1 multiplication

Can count in 5s

Can count in 10s

?

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Can use concrete objects, pictorial representations and arrays

Year 1 division

10

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Year 2

Multiplication and Division

  • recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers ​
  • calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs ​
  • show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot ​
  • solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

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0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0

5

10

15

20

25

30

35

40

0

10

20

30

40

50

60

70

80

Can make connections between arrays, number patterns, and counting in 2s, 5s and 10s

Can recall and use multiplication facts for the 2, 5 and 10 times tables

Year 2 multiplication

How many twos equal 16?

How many fives equal 40?

How many tens equal 80?

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Can calculate mathematical statements for multiplication using the 2, 5 and 10 times tables

0

5

10

15

5 x 3 = 5 + 5 + 5

Year 2 multiplication

Show that multiplication can be done in any order (commutative)

3 x 5 = 15

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

5 x 3 = 15

0

5

10

15

5 x 3 = 15

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0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0

5

10

15

20

25

30

35

40

0

10

20

30

40

50

60

70

80

Can recall and use division facts for the 2, 5 and 10 times tables

Year 2 division

Can calculate mathematical statements for division using the 2, 5 and 10 times tables

15 ÷ 5 = 3

0

5

10

15

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Year 3

Multiplication and Division

  • recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
  • write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
  • solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects

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6 x 4 = 24

4 x 6 = 24

Understanding commutativity 

Year 3 multiplication

Can multiply 2-digit numbers by 1-digit

14 x 3

14 x 3 = 10 x 3 + 4 x 3

14 x 3 = 30 + 12 = 42

x 3

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Can write mathematical statements for known multiplication and division facts using x, ÷ and =

7 x 3 = 21

3 x 7 = 21

Year 3 multiplication and division

21 ÷ 7 = 3

21 ÷ 3 = 7

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Year 4

Multiplication and Division

  • recall multiplication and division facts for multiplication tables up to 12 × 12
  • use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
  • recognise and use factor pairs and commutativity in mental calculations
  • multiply two-digit and three-digit numbers by a one-digit number using formal written layout
  • solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects

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Can multiply 3 numbers mentally (associative law)

Year 4 multiplication

2 x 3 x 4

Can use the distributive law to multiply 2-digit numbers by a 1-digit number

6 x 32

30

2

6

6 x 30

6 x 2

6 x 32 = 6 x 30 + 6 x 2

6 x 32 = 180 + 12

6 x 32 = 192

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Can multiply a 2-digit number by 1-digit number (no regrouping)

Can multiply a 2-digit number by 1-digit number (regroup)

Can multiply a 3-digit number by 1-digit number (regroup)

Year 4 multiplication

32 x 3

54 x 3

138 x 4

30 × 3

2 × 3

4 × 3

50 × 3

×

+

8 x 4

30 x 4

100 x 4

×

+

+

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Year 4 division

Can divide a 2-digit number

by 1-digit (no regrouping)

Can divide a 2-digit number by 1-digit (with

regrouping)

69 ÷ 3

tens

ones

tens

ones

72 ÷ 3

tens

ones

Can divide a 3-digit number by 1-digit

476 ÷ 7

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Year 5

Multiplication and Division

  • identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers
  • know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
  • establish whether a number up to 100 is prime and recall prime numbers up to 19
  • multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
  • multiply and divide numbers mentally drawing upon known facts
  • divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
  • multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
  • recognise and use square numbers and cube numbers, and the notation for squared ( 2 ) and cubed ( 3 )
  • solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
  • solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
  • solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

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Can multiply a 4-digit number by 1-digit number using short multiplication

Can multiply a 4-digit number by a 2-digit number using long multiplication

Can multiply a 2-digit number by a 2-digit number using long multiplication

Can multiply a 3-digit number by a 2-digit number using long multiplication

Year 5 multiplication

2,169 x 8

23 x 46

254 x 37

1,836 x 24

1

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Can divide a 4-digit number by a 1-digit number

Short division (no remainder)

Can divide a 4-digit number by a 1-digit number

Short division (with remainder)

Year 5 division

8,034 ÷ 6

6,287 ÷ 5

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Year 6

Multiplication and Division

  • multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
  • divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
  • divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
  • perform mental calculations, including with mixed operations and large numbers
  • identify common factors, common multiples and prime numbers
  • use their knowledge of the order of operations to carry out calculations involving the four operations
  • solve problems involving addition, subtraction, multiplication and division
  • multiply one-digit number with up to two decimal places by whole numbers
  • use written division methods in cases where the answer has up to two decimal places

Year 6

Fractions (including decimals and percentages)

  • multiply one-digit number with up to two decimal places by whole numbers
  • use written division methods in cases where the answer has up to two decimal places 3/8

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Year 6 multiplication

Can multiply up to 4 digits by a two-digit whole number using the formal written method of long multiplication

4,132 x 24

Can multiply a one-digit number with up to two decimal places by whole numbers

2.14 x 6

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Can divide numbers up to 4 digits by a two-digit whole number using long division

Year 6 division

Can divide numbers up to 4 digits by a one-digit whole number using long division

465 ÷ 15

496 ÷ 8

I know

8 x 6 = 48

so 8 x 60 = 480

I know

15 x 3 = 45

so 15 x 30 = 450

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Year 6 division

Can divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders or fractions

Can use written division methods in cases where the answer has up to two decimal places

7.62 ÷ 6

372 ÷ 16

372 ÷ 16 = 23 r 4

or

372 ÷ 16 = 23

 

372 ÷ 16 = 23

 

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