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division Leicestershire Numeracy Team Division

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division Leicestershire Numeracy Team The problems with division Try these:

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division Leicestershire Numeracy Team 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

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division Leicestershire Numeracy Team = 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) Skills in Early Division

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

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division Leicestershire Numeracy Team 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.

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division Leicestershire Numeracy Team = Would you group or share for this calculation?

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division Leicestershire Numeracy Team 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?

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division Leicestershire Numeracy Team =

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division Leicestershire Numeracy Team 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.

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division Leicestershire Numeracy Team = Division and number lines

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division Leicestershire Numeracy Team Modelling division on beadstrings 20 4 =

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division Leicestershire Numeracy Team =

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division Leicestershire Numeracy Team =

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division Leicestershire Numeracy Team =

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division Leicestershire Numeracy Team =

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division Leicestershire Numeracy Team Key Stage 1 - Calculations Encourage children to use jottings, as well, to check answers to calculations that have been reached by mental methods Q29 12c2b2a3All 4% 12%27%61%31%

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division Leicestershire Numeracy Team 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 childrens understanding of division.

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division Leicestershire Numeracy Team 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 = 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).

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division Leicestershire Numeracy Team How many eights in 48?

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

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division Leicestershire Numeracy Team the divisor the number to be divided

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division Leicestershire Numeracy Team the divisor the number to be divided

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division Leicestershire Numeracy Team the divisor the number to be divided

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

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division Leicestershire Numeracy Team ÷ 5 = Grouping - How many 5s are there in 72? Adding groups of 5 Teaching chunking - number line x 10 or 10 groups of 5 5 x 4 or 4 groups of 5

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division Leicestershire Numeracy Team Teaching chunking - vertical 72 5 = (5 x 10) (5 x 4) 2 Answer: 14 remainder 2 5 x 1 = 5 5 x 2 = 10 5 x 5 = 25 5 x 10 = 50

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division Leicestershire Numeracy Team Using calculators for repeated subtraction The constant function To calculate 72 5 using repeated subtraction Press =then press 72

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division Leicestershire Numeracy Team Teaching chunking - larger numbers 7 x 1 = 7 7 x 2 = 14 7 x 5 = 35 7 x 10 = = (7 x 30) (7 x 6) = ÷ 7 = ÷ 7 = 6 remainder 4 or Answer: 36 remainder 4

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division Leicestershire Numeracy Team 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.

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division Leicestershire Numeracy Team 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. £

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division Leicestershire Numeracy Team

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division Leicestershire Numeracy Team 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 £ I have £52. How many people can I take on the journey?

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