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Multiplication and Division why don’t we teach in the traditional way? The compactness of the traditional standard methods, particularly working with the digits of numbers without referring to their values, prevents many children from understanding how the method works. This is particularly true of long division. Many adults who can do long division accurately report that they did not understand the method at the time they were taught it. This can affect their confidence in their own ability. Children that don’t understand the method have nothing to fall back on. Children can not spot if they have made an error as they are not aware of what the answer should approximately be.

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WE:- 1Establish mental methods, based on a knowledge of tables and an understanding of place value. 2With more difficult calculations, approximate first, using mental methods. 3Show children how to set out written calculations using expanded layouts. 4Gradually refine the written record into a more compact and efficient method. 5Extend to larger numbers and to decimals. Encourage children to: olook out for special cases that can still be done mentally; oestimate first. Important teaching principle If, at any stage, a child is making a significant number of errors, they should return to the stage they understood, until ready to move on. Progression towards a compact written method

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Establishing Mental Methods How can you practice multiplication facts? Learning facts Reciting facts Using multiplication charts or grids Singing facts ‘Seeing’ repeated addition Establishing patterns on 100 square Generating patterns on ‘Counter’ or a calculator in constant function Consolidating facts Using board games Auditory games e.g ‘Fizz buzz’ Applying movement to multiples Identifying number sequences / patterns e.g Properties of numbers Multiple Bingo

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Progression in multiplication – using grid method Cheshire Mathematics Team 7x4=4x7

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Progression in multiplication – refining grid method 17 x 14 = 10 4 7 10x10= 100 10x4= 40 7x10= 70 7x4= 28 14 X17 100 (10x10) 40 (10x4) 70 (7x10) 28 (7x4) 238 14 X17 140 (14 x 10) 98 (14 x7) 238

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Progression in multiplication – more difficult example 268 x 53= 200608 50 3 268 X53 10000 3000 400 600 180 24 14204

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Short division or long division? Short division is TU, HTU etc. divided by U e.g. 23 ÷ 4 or 435 ÷ 7 Long division is HTU etc. divided by TU e.g. 236 ÷ 34 =

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Progression to Division Knowing division facts Sharing Grouping ‘Chunking’

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Progression in division: (Sharing) 24 ÷ 4 = Share 24 between 4 groups.

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Progression in division: (Grouping) 24 ÷ 4 = Counting in steps (4, 8, 12, 16, 20, 24)

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Blank number line 12 ÷ 4 = 12 8 4 0 - 4 There are 3 groups of 4. 12 ÷ 4 = 3 ÷

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Progression in division: Step 1 _____ 7 ) 400 - 7 (1 x 7) 393 - 7 (1 x 7) 386 - 7 (1 x 7) 379

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Progression in division: Step 2 _____ 7 ) 400 - 70 (10 x 7) 330 - 70 (10 x 7) 260 - 70 (10 x 7) 190 - 70 (10 x 7) 120 - 70 (10 x 7) 50 - 49 (7 x 7) 1 57r1

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Progression in division: Step 3 _____ 7 ) 400 - 350 (50 x 7) 50 - 49 (7 x 7) 1 57r1

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