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Division

Division. The problems with division. Try these:. 6. 24. What is division?. How would you illustrate this division to a child? What would you draw and what language would you use? 12  3 = 4. Skills in Early Division. 12  3 = 4. Sharing

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Division

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  1. Division Leicestershire Numeracy Team 2003

  2. The problems with division Try these: 6 24 Leicestershire Numeracy Team 2003

  3. What is division? How would you illustrate this division to a child? What would you draw and what language would you use? 12  3 = 4 Leicestershire Numeracy Team 2003

  4. Skills in Early Division 12  3 = 4 Sharing There are three children and 12 cakes. How many can they each have, if I share them out equally? (Sharing 12 things equally into 3 piles. How many in each) Leicestershire Numeracy Team 2003

  5. Skills in Early Division 12  3 = 4 Grouping There are 12 cakes. How many children can have three each? (How many threes are there is 12?) Leicestershire Numeracy Team 2003

  6. Language and division Since the  sign represents both the sharing and grouping aspects of division, encourage the children to read this as ‘divided by’ rather than ‘shared by’. Leicestershire Numeracy Team 2003

  7. 6000  1000 = Would you group or share for this calculation? Leicestershire Numeracy Team 2003

  8. Introducing division • In Year 2 children are encouraged to understand the operation of division as: • sharing equally • grouping or repeated subtraction e.g. How many tens are in 60? Leicestershire Numeracy Team 2003

  9. 18  3 = Leicestershire Numeracy Team 2003

  10. Sharing • Supports an understanding of halving and the 1 to 1 correspondence between objects. • Requires little knowledge or skill beyond counting. • Becomes more difficult to visualise as the divisor increases. • Is inefficient. Leicestershire Numeracy Team 2003

  11. 0 3 6 9 12 15 18 18  3 = Division and number lines Leicestershire Numeracy Team 2003

  12. Modelling division on beadstrings 20  4 = Leicestershire Numeracy Team 2003

  13. 20  4 = Leicestershire Numeracy Team 2003

  14. 20  4 = Leicestershire Numeracy Team 2003

  15. 20  4 = Leicestershire Numeracy Team 2003

  16. 20  4 = Leicestershire Numeracy Team 2003

  17. Key Stage 1 - Calculations • Encourage children to use jottings, as well, to check answers to calculations that have been reached by mental methods Leicestershire Numeracy Team 2003

  18. Grouping • Links to counting in equal steps on a number line. • Requires knowledge of subtraction facts (repeated subtraction) and addition facts (counting up). • Is more efficient than sharing as the divisor increases. • Provides a firmer basis on which to build children’s understanding of division. Leicestershire Numeracy Team 2003

  19. Introducing division • In Year 3 and 4 children also need to know that: • dividing a whole number by 1 leaves the number unchanged: e.g. 12  1 =12 • 16  2 does not equal 2  16 • division reverses multiplication (the inverse) – this allows them to solve division calculations by using multiplication strategies (18  3 by counting the hops of 3 to 18) • there will be remainders for some division calculations (to be expressed as whole-number remainders). Leicestershire Numeracy Team 2003

  20. How many eights in 48? •        •        •        •         •        •        Leicestershire Numeracy Team 2003

  21. Continuing division • In Year 4 children need to begin to : • relate division and fractions • use a written method for division (chunking). Leicestershire Numeracy Team 2003

  22. the number to be divided 2 3 the divisor  Leicestershire Numeracy Team 2003

  23. 3 the number to be divided 2  the divisor Leicestershire Numeracy Team 2003

  24. the number to be divided 2  3 the divisor Leicestershire Numeracy Team 2003

  25. Teaching chunking - partitioning 72  5 Partition 72 in to a convenient multiple of 5 + the rest 72 = 50 + 22 Divide each part 50 ÷ 5 = 1022 ÷ 5 = 4 rem 2 Recombine the parts Answer: 14 remainder 2 Leicestershire Numeracy Team 2003

  26. 5 x 10 or 10 groups of 5 5 x 4 or 4 groups of 5 40 45 50 55 60 65 70 72 0 5 10 15 20 25 30 35 Teaching chunking - number line 72 ÷ 5 = Grouping - How many 5’s are there in 72? Adding groups of 5 Leicestershire Numeracy Team 2003

  27. Teaching chunking - vertical 5 x 1 = 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50 72  5 = 72 50 (5 x 10) 22 20 (5 x 4) 2 Answer: 14 remainder 2 Leicestershire Numeracy Team 2003

  28. Using calculators for repeated subtraction The constant function To calculate 72  5 using repeated subtraction Press 5 - - = then press 72 Leicestershire Numeracy Team 2003

  29. Teaching chunking - larger numbers 256  7256 = 210 + 46210 ÷ 7 = 3046 ÷ 7 = 6 remainder 4 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = 70 256  7 = 256 210 (7 x 30) 46 42 (7 x 6) 4 or Answer: 36 remainder 4 Leicestershire Numeracy Team 2003

  30. Continuing division • In Year 5 and 6 children also need to understand: • that a number cannot be divided by zero • how a quotient can be expressed as a fraction and as a decimal fraction • how to interpret the display when dividing with a calculator. Leicestershire Numeracy Team 2003

  31. 185 people go to the school concert. They pay £1.35 each. How much ticket money is collected? Programmes cost 15p each. Selling programmes raises £12.30 How many programmes are sold? £ Show your method you may get a mark. Leicestershire Numeracy Team 2003

  32. Leicestershire Numeracy Team 2003

  33. Solve these word problems To make a box pieces of wood 135mm long have to be cut from a 2.5m length. How many lengths of wood can be cut? Train fares cost £14.50. I have £52. How many people can I take on the journey? Leicestershire Numeracy Team 2003

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