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Multiplication and Division Calculating efficiently and accurately Progression for multiplication and division • • • • • • • Counting Doubling and halving context Multiplication as repeated addition, describing an array and scaling Division as grouping and sharing Understand that multiplication and division are inverses Recall of multiplication and division facts Multiply two / three-digit numbers by 10 / 100 Dice race game Counting in context How many 10p coins are here? How much money is that? How many toes are there on 2 feet? How many gloves in 3 pairs? If Sarah counts in 2s and Nigel counts in 5s, when will they reach the same number? How many lengths of 10m can you cut from 80m of rope? Doubling and halving in context There are 8 raisins. Take half of them. How many have you taken? One snake is 20cm long. Another snake is double that length. How long is the longer snake? I double a number and then double the answer. I now have the number 32. What number did I start with? 94 65 48 30 71 28 36 56 97 32 12 24 51 82 19 77 63 44 53 28 60 96 75 17 43 2 x 3 or 3 x 2 Multiplication 3 plates, 2 cakes on each plate pictures (Children could draw a picture to help them work out the answer) 2 x 3 or 3 x 2 3 plates, 2 cakes on each plate symbols (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Number tracks and number lines (modelled using bead strings) 2 x 3 or 3 x 2 [two, three times] or [three groups of two] 0 2 4 6 Arrays 5 x 3 or 3 x 5 14 x 2 = 28 x 2 10 20 4 8 Array creator 13 x 4 = 52 X 10 3 4 Answer = 52 X 10 3 4 40 12 43 x 6 X 40 3 40 x 6 = 240 6 240 18 3 x 6 = 18 43 x 6 258 1 27 x 34 27 x 34 Approximation: Answer lies between 600 (20 x 30) and 1200 (30 x 40) or 30 x 30 = 900 27 x 34 108 (27 x 4) 810 (27 x 30) 918 Extend to HTU x U, U.t x U and HTU x TU Multiplication grid ITP 6÷2 Division 6 cakes shared between 2 pictures 6 cakes put into groups of 2 (Children could draw a picture to help them work out the answer) 6÷2 6 cakes shared between 2 6 cakes put into groups of 2 symbols (Children could use dots or tally marks to represent objects – quicker than drawing a picture) Number tracks and number lines - grouping (modelled using bead strings) 8÷2=4 6÷2=3 0 2 4 6 Number lines / Arrays 15 ÷ 5 = 3 0 5 10 15 Grouping ITP 67 ÷ 4 = 16 r 3 67 ÷ 4 4 x 10 = 40 4 x 6 = 24 [64] Number dial ITP 97 ÷ 9 = 10 r 7 Efficient methods . . . . 754 ÷ 6 Approximation: Answer lies between 100 (600 ÷ 6) and 150 (900 ÷ 6) Answer = 125 r 4 754 - 600 154 - 120 34 - 30 4 (6 x 100) (6 x 20) (6 x Extend to U.t ÷ U and HTU ÷ TU 5) Efficient methods . . . . Short division 291 ÷ 3 = 97 Estimation: 270 ÷ 3 = 90 97 3 291 2 43.4 ÷ 7 = 6.2 6.2 Estimation: 42 ÷ 7 = 6 7 43.4 1 A Challenge for you! Domino Magic Imagine a domino Add the two numbers together Multiply by five Double Add the larger of the two numbers. What is your number?