Written Addition Strategies and Methods – Addition (Draft) Year 3 Year 4 Build on partitioning to develop expanded column addition with Build on expanded column addition to develop compact column two 3-digit numbers addition with larger numbers e.g. 466 + 358 e.g. 1466 + 4868 Use expanded column addition where digits in a column add to more than the column value e.g. 466 + 358 Compact column addition with larger numbers e.g. 5347 + 2286 + 1495 Compact column addition with two or more 3-digit numbers or towers of 2-digit numbers e.g. 347 + 286 + 495 Use expanded and compact column addition to add amounts of money Add like fractions e.g. 83 + 81 + 81 Compact column addition with 3- and 4-digit numbers Recognise like fractions that add to 1 e.g. 41 + 43 e.g. 53 + 52
Mental Subtraction Strategies and Methods – Subtraction (Draft) Year 3 Year 4 Taking away Taking away Use place value to subtract Use place value to subtract 4 7 4 8 e.g. 348 – 300 e.g. 4748 – 4000 3 4 8 e.g. 348 – 40 e.g. 4748 – 8 e.g. 348 – 8 Take away multiples of 10, 100, 1000, £1, 10p or 0·1 Take away multiples of 10, 100 and £1 e.g. 8392 – 50 e.g. 476 – 40 = 436 e.g. 6723 – 3000 e.g. 476 – 300 = 176 e.g. £3·74 – 30p e.g £4·76 – £2 = £2·76 e.g. 5·6 – 0·2 Partitioning Partitioning e.g. 68 – 42 as 60 – 40 and 8 – 2 e.g. £5·87 – £3·04 as £5 – £3 and 7p – 4p e.g. £6·84 – £2·40 as £6 – £2 and 80p – 40p e.g. 7493 – 2020 as 7000 – 2000 and 90 – 20 7 000 – 2 000 7 4 9 3 – 20 20 90 – 20 5 4 7 3 Count back e.g. 6482 – 1301 as 6482 – 1000 (5482) – 300 (5182) – 1 = 5181 Subtract near multiples of 10, 100, 1000 or £1 e.g. 3522 – 1999 e.g. £34·86 – £19·99
Mental Subtraction Written Subtraction of Strategies and Methods – Subtraction (Draft) Year 3 Year 4 Using number facts Using number facts Know pairs which total each number to 20 Number bonds to 10 and 100 and derived facts e.g. 20 – 14 = 6 e.g. 100 – 76 = 24 Number bonds to 100 e.g. 1 – 0·6 = 0·4 e.g. 100 – 48 = 52 e.g. 100 – 35 = 65 0 1 Number bonds to £1 and £10 Subtract using number facts to bridge back through a 10 e.g. £1·00 – 86p = 14p e.g. 42 – 5 = 42 – 2 (40) – 3 = 37 e.g. £10·00 – £3·40 = £6·60 Develop counting up subtraction Expanded column subtraction with 3- and 4-digit numbers e.g. 200 – 167 e.g. 726 – 358 Begin to develop compact column subtraction e.g. 726 – 358
Mental Subtraction Strategies and Methods – Subtraction (Draft) Year 5 Year 6 Taking away Taking away Use place value to subtract decimals Use place value to subtract decimals e.g. 4·58 – 0·08 e.g. 7·782 – 0·08 e.g. 6·26 – 0·2 e.g. 16·263 – 0·2 Take away multiples of powers of 10 Take away multiples of powers of 10 e.g. 15 672 – 300 e.g. 132 956 – 400 e.g. 4·82 – 2 e.g. 686 109 – 40 000 e.g. 2·71 – 0·5 e.g. 7·823 – 0·5 e.g. 4·68 – 0·02 Partitioning or counting back Partitioning or counting back e.g. 3964 – 1051 e.g. 3964 – 1051 e.g. 5·72 – 2·01 e.g. 5·72 – 2·01 Subtract near multiples of powers of 10 Subtract near multiples of 1, 10, 100, 1000, 10 000 or £1 e.g. 360 078 – 99 998 e.g. 86 456 – 9999 e.g. 12·831 – 0·99 e.g. 3·58 – 1·99 Counting up Find a difference between two numbers by counting up from the smaller to the larger e.g. £12·05 − £9·59 e.g. 2009 – 869
Mental Multiplication Strategies and Methods – Multiplication (Draft) Year 3 Year 4 Doubling and halving Grouping Find doubles of numbers to 50 using partitioning Use partitioning to multiply 2-digit numbers by 1-digit numbers e.g. double 48 e.g. 24 × 5 ×5 ×5 Multiply multiples of 100 and 1000 by 1-digit numbers using Use doubling as a strategy in multiplying by 2 tables facts e.g. 18 × 2 is double 18 = 36 e.g. 400 × 8 = 3200 Multiply near multiples by rounding Grouping e.g. 24 × 19 as (24 × 20) – 24 = 456 Recognise that multiplication is commutative Using number facts e.g. 4 × 8 = 8 × 4 Multiply multiples of 10 by 1-digit numbers Know times-tables up to 12 × 12 e.g. 30 × 8 = 240 × 1 2 3 4 5 6 7 8 9 10 11 12 Multiply ‘friendly’ 2-digit numbers by 1-digit numbers 1 1 2 3 4 5 6 7 8 9 10 11 12 e.g. 13 × 4 2 2 4 6 8 10 12 14 16 18 20 11 24 3 3 6 9 12 15 18 21 24 27 30 22 36 Using number facts 4 4 8 12 16 20 24 28 32 36 40 33 48 Know doubles to double 20 5 5 10 15 20 25 30 35 40 45 50 44 60 e.g. double 15 is 30 6 6 12 18 24 30 36 42 48 54 60 55 72 Know doubles of multiples of 5 to 100 7 7 14 21 28 35 42 49 56 63 70 66 84 e.g. double 85 is 170 8 8 16 24 32 40 48 56 64 72 80 77 96 Know ×2, ×3, ×4, ×5, ×8, ×10 tables facts 9 9 18 27 36 45 54 63 72 81 90 88 108 10 10 20 30 40 50 60 70 80 90 100 99 120 11 11 22 33 44 55 66 77 88 99 110 121 132 12 12 24 36 48 60 72 84 96 108 120 132 144