The + and = and missing numbers Continue using a range of equations as in Key Stage 1 and Year 3 but with appropriate numbers. Partition into hundreds, tens and ones and recombine Either partition both numbers and recombine or partition the second number only e.g. 358 + 73 = 358 + 70 + 3 = 428 + 3 = 431 Add or subtract the nearest multiple of 10 or 100, then adjust Continue as in Year 2, 3 and 4 but with appropriate numbers e.g. 458 + 79 = is the same as 458 + 80 - 1 AS4.1 Addition of numbers with at least four digits using formal method of columnar addition 358 +73 431 1 1 3587 +675 4262 1 1 1 The formal, efficient method of columnar addition will involve crossing of boundaries (at the tens, hundreds and/or thousands). Take a systematic approach to teaching this looking at crossing each boundary in turn before mixed practice. Revert to expanded method if children experience difficulties. DF4.6 Extend addition to decimals (same number of decimals places) and adding several numbers (with different numbers of digits). The – and = signs and missing numbers Continue using a range of equations as in Key Stage 1 and Year 3 but with appropriate numbers. Differences Find a difference by counting up, e.g. 8006 – 2993 = 5013. This can be modelled on an empty number line. DF4.6 Use number facts and place value to subtract 6.1 – 0.4 = 5.7 5.7 6.0 6.1 -0. 3 -0 .1 AS4.1 Subtraction with at least four digits using formal method of columnar subtraction For instance, 6467 – 2684 = 3783 Using expanded column subtraction where children experience difficulty with decomposition and need to ‘see’ this. DF4.6 Extend subtraction to decimals (same number of decimals places) and adding several numbers (with different numbers of digits) Video clips: 1. 2. 3, Multiplication Division The x and = signs and missing numbers Continue using a range of equations but with appropriate numbers for Year 4. The ÷ and = signs and missing numbers Continue using a range of equations but with appropriate numbers for Year 4.
MD4.5 TU x U (See Year 3) and HTU x U (Introduced in Year 4 grade-level standards). Partition 23 x 4 = 92 23 x 4 = (20 x 4) + (3 x 4) = (80) + (12) = 92 Use the grid method of multiplication 23 x 7 is approximately 20 x 10 = 200 MD4.3 Sharing and grouping 30 ÷ 6 can be modelled as: Grouping – groups of 6 away and the number of groups counted e.g. 6 + 6 + 6 + 6 + 6 + 0 6 12 18 24 30 Sharing – sharing among 6, the number given to each person. Remainders Note three approaches below: 41 ÷ 4 = 10 r1 +40 +1 41 = (10 x 4) + 1 -1 - 40 MD4.5 TU ÷ U 72 ÷ 5 lies between 50 ÷ 5 = 10 and 100 ÷ 5 = 20 72 50 (10 groups) or (10 x 5) 22 20 (4 groups) or (4 x 5) 2 Answer: 14 remainder 2 MD4.5 HTU ÷ U Can progress from no remainder to remainders. Where remainders are involved, care needs to be taken to ensure they are interpreted correctly in context of problems. 256 ÷ 7 lies between 210 ÷ 7 = 30 and 280 ÷ 7 = 40 256 70 (10 groups) or (10 x 7) 186 140 (20 groups) or (20 x 7) 46 42 (6 groups) or (6 x 7) 4 (36 groups) or (36) Answer: 36 remainder 4 New Mathematics Calculation Policy: Year 5 and Year 6 The exemplification of formal methods here should be taken into account by all Key Stage 2 teachers so children are adequately prepared by Year 5 and into Year 6 to use the means of calculating specified in grade-level standards. Addition & Subtraction