Children move on from dealing mainly with whole numbers to performing arithmetic operations with both decimals and fractions.

**Addition and Subtraction**:

Children will consolidate their use of written procedures in adding and subtracting whole numbers with up to 6 digits and also decimal numbers with up to 2 decimal places. Mental strategies for adding and subtracting increasingly large numbers will also be taught. These will draw upon children’s robust understanding of place value and knowledge of number facts. Negative numbers will be added and subtracted.

**Multiplication and Division**:

Efficient and flexible strategies for mental multiplication and division are taught and practised, so that children can perform appropriate calculations even when the numbers are large, such as 40 000 × 6 or 40 000 ÷ 8. In addition, it is in Years 5 and 6 that children extend their knowledge and confidence in using written algorithms for multiplication and division.

**Fractions**:

Fractions and decimals are also added, subtracted, divided and multiplied, within the bounds of children’s understanding of these more complicated numbers. Children will also calculate simple percentages and ratios.

**Year 5 +**

**Mental calculation**:

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; *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*; *e.g. £34·59 + £19·95*

Use place value and number facts to add two or more ‘friendly’ numbers, including money and decimals; *e.g. 3 + 8 + 6 + 4 + 7*; *e.g. 0·6 + 0·7 + 0·4*; *e.g. 2056 + 44*

**Written Calculation**:

Use column addition to add two or three whole numbers with up to 5 digits

Use column addition to add any pair of 2-place decimal numbers, including amounts of money

Begin to add related fractions using equivalences; *e.g. ½ + 1⁄6 = 3⁄6 + 1⁄6*

Choose the most efficient method in any given situation

**All**:

Add numbers with only 2 digits which are not zeros; *e.g. 3·4 + 5·8*

Derive swiftly and without any difficulty number bonds to 100

Add ‘friendly’ large numbers using knowledge of place value and number facts

Use expanded column addition to add pairs of 4- and 5-digit numbers

**Year 5 –**

**Mental calculation**:

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 1- or 2-digit near multiples of 10, 100, 1000, 10 000 and 100 000 from other numbers: *e.g. 82 472 – 30 004*

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*

Use counting up subtraction, with knowledge of number bonds to 10, 100 or £1, as a strategy to perform mental subtraction; *e.g. £10 – £3·45*; *e.g. 1000 – 782*

Recognise fraction complements to 1 and to the next whole number; *e.g. 1 2⁄5 + 3⁄5 = 2*

**Written Calculation**:

Use compact or expanded column subtraction to subtract numbers with up to 5 digits

Use complementary addition for subtractions where the larger number is a multiple or near multiple of 1000

Use complementary addition for subtractions of decimal numbers with up to 2 places, including amounts of money

Begin to subtract related fractions using equivalences; *e.g. ½ – 1⁄6 = 2⁄6*

Choose the most efficient method in any given situation

**All**:

Derive swiftly and without difficulty number bonds to 100

Use counting up with confidence to solve most subtractions, including finding complements to multiples of 1000; *e.g. 3000 – 2387*

**Year 5 ×**

**Mental calculation**:

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 factors and multiples in multiplication; *e.g. 43 × 6 is double 43 × 3*; *e.g. 28 × 50 is ½ of 28 × 100 = 1400*

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*

Partition 2-digit numbers, including decimals, to multiply by a 1-digit number mentally; *e.g. 6 × 27 as 6 × 20 (120) plus 6 × 7 (42)* ; *e.g. 6·3 × 7 as 6 × 7 (42) plus 0·3 × 7 (2·1)*

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*

**Multiplication and division**:

Use short multiplication to multiply a 1-digit number by a number with up to 4 digits

Use long multiplication to multiply 3-digit and 4-digit numbers by a number between 11 and 20

Choose the most efficient method in any given situation

Find simple percentages of amounts; *e.g. 10%, 5%, 20%, 15% and 50%*

Begin to multiply fractions and mixed numbers by whole numbers ≤ 10; *e.g. 4 × 2⁄3 = 8⁄3 = 2 2⁄3*

**All**:

Know multiplication tables to 11 × 11

Multiply whole numbers and 1-place decimals by 10, 100 and 1000

Use knowledge of factors as aids to mental multiplication; *e.g. 13 × 6 is double 13 × 3*; *e.g. 23 × 5 is ½ of 23 × 10*

Use the grid method to multiply numbers with up to 4 digits by 1-digit numbers

Use the grid method to multiply 2-digit numbers by 2-digit numbers

**Year 5 ÷**

**Mental calculation**:

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

Use doubling and halving as mental division strategies; *e.g. 34 ÷ 5 is (34 ÷ 10) × 2*

Use knowledge of multiples and factors, as well as tests for divisibility, in mental division; *e.g. 246 ÷ 6 is 123 ÷ 3*; *e.g. We know that 525 divides by 25 and by 3*

Halve amounts of money by partitioning; *e.g. ½ of £75·40 = ½ of £75 (£37·50) plus half of 40p (20p) which is £37·70*

Divide larger numbers mentally by subtracting the 10th or 100th multiple as appropriate; *e.g. 96 ÷ 6 is 10 + 6, as 10 × 6 = 60 and 6 × 6 = 36*; *e.g. 312 ÷ 3 is 100 + 4 as 100 × 3 = 300 and 4 × 3 = 12*

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

**Written Calculation**:

Use short division to divide a number with up to 4 digits by a number ≤ 12

Give remainders as whole numbers or as fractions

Find non-unit fractions of large amounts

Turn improper fractions into mixed numbers and vice versa

Choose the most efficient method in any given situation

**All**:

Know by heart division facts up to 121 ÷ 11

Divide whole numbers by 10, 100 or 1000 to give answers with up to 1 decimal place

Use doubling and halving as mental division strategies

Use an efficient written method to divide numbers ≤ 1000 by 1-digit numbers

Find unit fractions of 2- and 3-digit numbers