Maths Calculations Policy

St Anne’s Calculation Policy

Key Stage One Addition & Subtraction  To find 1 more / 1 less a given number  To find 10 more / 10 less a given number  To know number bonds to 5, 6, 7, 8, 9 & 10 and related inverse e.g. 8 – 6 = 2  To count on in 1s from any given number  To count on & back in 2s from any given number  To count on & back in 10s from any given 2-digit number  To add & subtract 10 to any given 2-digit number  To use number facts to add & subtract 1-digit numbers to 2-digit numbers e.g. Use 4 + 3 to work out 24 + 3, 34 + 3 or e.g. Use 7 – 2 to work out 27 – 2, 37 – 2  To add two or three 1-digit numbers  To know number bonds to 20  To know number bonds to 100  To know partition numbers e.g. hundreds, tens and ones Multiplication & Division  Begin to halve numbers to 40 and multiples of 10 to 100  Double numbers up to 20  Begin to double multiples of 5 to 100  Begin to double 2-digit numbers less than 50 with 1s digits of 1, 2, 3, 4 or 5  Begin to double multiples of 5 to 100  Begin to double 2-digit numbers less than 50 with 1s digits of 1, 2, 3, 4 or 5  To count in 2s, 5s, 10s, & 3s 1

 Begin to learn the ×2, ×3, ×5 and ×10 tables, seeing these as ‘lots of’ e.g. 5 lots of 2, 6 lots of 2, 7 lots of 2  Relate division to grouping e.g. How many groups of 5 in 15?

Lower Key Stage Two Addition & Subtraction  Add multiples and near multiples of 10 and 100  Perform place-value additions without a struggle e.g. 300 + 8 + 50 = 358  Add pairs of ‘friendly’ 3-digit numbers e.g. 320 + 450  Begin to add amounts of money using partitioning  Subtract any two 2-digit numbers e.g. 8 – 2 = 6 e.g. 18 – 6 = 12 e.g. 15 – 8 = 7  Subtract multiples of 5 from 100 by counting up e.g. 100 – 35  Subtract multiples of 10 and 100  Know by heart/quickly derive number bonds to 100 and to £1  Add to the next 100, £1 and whole number e.g. 234 + 66 = 300 e.g. 3·4 + 0·6 = 4  Perform place-value additions e.g. 300 + 8 + 50 + 4000 = 4358  Perform place-value subtractions e.g. 4736 – 706 = 4030  Subtract multiples and near multiples of 10, 100, 1000, £1 and 10p  Subtract multiples of 0·1

2

Multiplication & Division  Know by heart multiplication tables up to x4, x6 and x8 (Y3), All times tables up 12 × 12 (Y4)  Multiply whole numbers by 10 and 100  Multiply three single digit numbers (2x3)x6=  Double numbers up to 50  Double multiples of 5 to 50  To know related division facts  Halve even numbers to 100, halve odd numbers to 20  Recognise factors up to 12 of 2-digit numbers  Multiply whole numbers and 1-place decimals by 10, 100, 1000  Multiply multiples of 10, 100 and 1000 by 1-digit numbers e.g. 300 × 6 e.g. 4000 × 8  Know by heart all the division facts up to 144 ÷ 12  Divide whole numbers by 10, 100, to give whole number answers or answers with 1 decimal place  Divide multiples of 100 by 1-digit numbers using division facts e.g. 3200 ÷ 8 = 400 Upper Key Stage Two Addition & Subtraction  Know number bonds to 1 and to the next whole number  Add to the next 10 from a decimal number e.g. 13·6 + 6·4 = 20  Add numbers with 2 significant digits only, using mental strategies e.g. 3·4 + 4·8 e.g. 23 000 + 47 000  Add 1- or 2-digit multiples of 10, 100, 1000, 10 000 and 100 000 e.g. 8000 + 7000 e.g. 600 000 + 700 000  Add near multiples of 10, 100, 1000, 10 000 and 100 000 to other numbers

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e.g. 82 472 + 30 004  Add decimal numbers which are near multiples of 1 or 10, including money  e.g. 6·34 + 1·99  Know by heart number bonds to 100 and use these to derive related facts e.g. 3·46 + 0·54  Derive, quickly and without difficulty, number bonds to 1000  Add small and large whole numbers where the use of place value or number facts makes the calculation do-able mentally e.g. 34 000 + 8000  Add multiples of powers of 10 and near multiples of the same e.g. 6345 + 199 Add two 1-place decimal numbers or two 2-place decimal numbers less than 1 e.g. 4·5 + 6·3 e.g. 0·74 + 0·33  Subtract numbers with 2 significant digits only, using mental strategies e.g. 6·2 – 4·5 e.g. 72 000 – 47 000  Subtract 1- or 2-digit multiples of 10, 100, 1000, 10 000 and 100 000 e.g. 8000 – 3000 e.g. 60 000 – 200 000  Subtract decimal numbers which are near multiples of 1 or 10, including money e.g. 6·34 – 1·99 e.g. £34·59 – £19·95  Recognise fraction complements to 1 and to the next whole number e.g. 1 2/5 + 3/5 = 2  Use number facts and place value to perform mental subtraction of large numbers or decimal numbers with up to 2 places e.g. 467 900 – 3005 e.g. 4·63 – 1·02  Use number bonds to 1 and 10 to perform mental subtraction of any pair of 1-place or 2-place decimal numbers using complementary addition and including money 4

e.g. 10 – 3·65 as 0·35 + 6 e.g. £50 – £34·29 as 71p + £15

Multiplication & Division  Know by heart all the multiplication facts up to 12 × 12  Multiply whole numbers and 1- and 2-place decimals by 10, 100, 1000, 10 000  Use knowledge of place value and rounding in mental multiplication e.g. 67 × 199 as 67 × 200 – 67  Use doubling and halving as a strategy in mental multiplication e.g. 58 × 5 is half of 58 × 10 e.g. 34 × 4 is 34 doubled twice  Double amounts of money by partitioning e.g. £37·45 doubled is £37 doubled (£74) plus 45p doubled (90p) giving a total of £74·90  Identify common factors, common multiples and prime numbers and use factors in mental multiplication e.g. 326 × 6 is 652 × 3 which is 1956  Use place value and number facts in mental multiplication e.g. 4000 × 6 = 24 000 e.g. 0·03 × 6 = 0·18  Know by heart all the division facts up to 144 ÷ 12  Divide whole numbers by 10, 100, 1000, 10 000 to give whole number answers or answers with 1, 2 or 3 decimal places  Halve amounts of money by partitioning e.g. 1/2 of £75·40 = 1/2 of £75 (£37·50) plus half of 40p (20p) which is £37·70  Know tests for divisibility by 2, 3, 4, 5, 6, 9 and 25  Know square numbers and cube numbers  Reduce fractions to their simplest form  Divide 1- and 2-place decimals by numbers up to and including 10 using place value 5

e.g. 2·4 ÷ 6 = 0·4 e.g. 0·65 ÷ 5 = 0·13 e.g. £6·33 ÷ 3 = £2·11  Halve decimal numbers with up to 2 places using partitioning e.g. Half of 36·86 is half of 36 (18) plus half of 0·86 (0·43)  Know and use equivalence between simple fractions, decimals and percentages, including in different contexts  Recognise a given ratio and reduce a given ratio to its lowest terms

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Year 1  Counting objects Combine 2 groups of objects e.g. 3 + 2 = 5

 Missing numbers need to be placed in all possible places.

3+4= =3+4 3+=7 7=+4 +4=7 7=3+ +=7 7=+  Counting on in ones

 Adding multiples of 10 45 + 30 = 75

7

Year 2  Adjustment Add 9 or 11 by adding 10 and adjusting by 1. This can be extended for adding 19, 21, 19, 31 etc e.g.

Add 9 by adding 10 and adjusting by 1 35 + 9 = 44 +10 35

44

45

-1  Bridging through 10 Children should be able to partition the 7 to relate adding the 2 and then the 5.

8 + 7 = 15 +2 +5

8

10

15

 Partitioning 43 + 24 40 + 20 = 60 3+ 4+7 60 + 7 = 67

8

 Partitioning using an empty number line

Leading to children adding tens in one jump and ones in one jump +30

55

+7

85

92

Year 3  Partitioning using an empty number line bridging through 10

9

 Expanded column addition Horizontal expansion 83 + _42 5 120 125

80 + 3 + 40 + 2 120 + 5 = 125

75 + 66 11 130 141

70 + 5 + 60 + 6 130 +11 = 141

 Column addition with carrying Year 4 (3 digit)

Year 4 (4 digit)

Year 4/5  Compact column addition expanded to 2 decimal places 73. 42 + 84. 73 158. 15 1

(Relating to money & measure)

10

Year 6  Adding numbers with decimals up to 3 places

11

 Subtraction using objects

Year 1

6–1=5  Finding the difference

 Missing number subtraction calculations 10 - ___ = 4

20= ___ - 3

___ - 12= 10

 Subtracting in ones 9 – 4 = 5 -1 -1 -1 -1

Drawing jumps on prepared number line then constructing own empty number lines.

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 Subtracting multiples of 10 from a 2-digit number 57 – 30 – 27 -10

-10

27

37

-10

47

57

Year 2  Bridging through 10 35 - 7 -2

28

-5

30

35

 Counting back on an empty numberline using tens and ones 37 – 12 = 25

13

 Moving towards subtracting tens in one jump & ones in one jump 57 - 38 -8

-30

19

27

57

Year 3 / 4  Complementary addition 84 – 56 = 28 +20 +4

56

+4

60

80

84

 Column Subtraction no exchange up to 3 digits

74 - 41 33

Expanded Column Subtraction no exchange up to 3 digits

70+4 - 40+1 30+3

Year 5 / 6  Decomposition with exchange  Expanded decomposition with exchange 6

72 - 56 16

60 70 - 50 10

+ + +

1 2 6 6 = 16 14

 Decomposition multiple exchange

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Year 1  Counting groups of objects in 2s, 5s & 10s How many legs will 3 teddies have?

2

+

2

+

2

= 6

There are 3 sweets in a bag. How many sweets are there in 4 bags?

Year 1 / 2  Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method. Arrays enable teaching of the commutative law of multiplication.

Also give examples such as 6 x __ = 12

6 x 2 = 12 2 x 6 = 12

2 + 2 + 2 + 2 + 2 + 2 = 12 6 + 6 = 12

16

 Repeated addition using an empty numberline 4 times 6

is

6 + 6 + 6 + 6 = 24

6 0

or 4 lots of 6 or 6 x 4

6

6

6

6

12

18

24

Year 3  Partitioning using the grid method TO X O. Progressing to HTO x O, ThHTO x O

32 x 3 = 96

x 3

30 90

2 6 = 96

Year 4  Developing the grid method. Multiplying numbers up to 4 digits by a 1 or 2 digit number.

Grid method 72 x 38 is approximately 70 x 40 = 2800

x 30 8

70 2 2100 60 560 16

2100 + 60 = 2160 560 + 16 = 567 2160 + 576 = 2736

17

Year 4  Expanded column method 30 + 8 x 7 56 210 266

(8 x 7 = 56) (30 x 7 = 210)

38 x 7 56 210 266

Year 5 / 6

Long multiplication

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Year 1 / 2  Sharing Sharing – 6 sweets are shared between 2 people. How many do they have each?

      Use objects, diagrams and pictorial representations to solve problems involving both grouping and sharing.

Sharing manipulatives equally into groups of 2/3/4/5/10 Introduce the number sentence and division sign 6÷2=3  Grouping Sorting objects into 2s / 3s/ 4s etc How many pairs of socks are there?

There are 12 crocus bulbs. Plant 3 in each pot. How many pots are there?

Jo has 12 Lego wheels. How many cars can she make?

Group manipulatives equally and then introduce the number sentence and division sign e.g. 8 ÷ 2 = 4

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 Develop further using more pictorial representations Practical grouping e.g. in PE 12 children get into teams of 4 to play a game. How many teams are there?

Year 2  Number families / using the inverse operation 18 ÷ 2 = 9 18 ÷ 9 = 2 2 x 9 = 18 9 x 2 = 18

 Empty numberline 18 ÷ 3 = ? Use inverse vocabulary - How many 3’s make 18?

1

2

0

3

3

4

6

5

9

12

6

15

18

Year 2 / 3  Empty numberline with remainders +3 0

+3 3

+3 6

+3 9

12

+3 15

+3 18

r1

r1 19

20

20

Year 3 / 4 / 5  Chunking 72 ÷ 3 3) 72 - 30 42 - 30 12 - 6 6 - 6 0

(10 x 3) (10 x 3) (2 x 3) (2 x 3) 24

Year 5 / 6  Short Division

 Long Division

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