350 likes | 411 Vues
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
E N D
Division Leicestershire Numeracy Team 2003
The problems with division Try these: 6 24 Leicestershire Numeracy Team 2003
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
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
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
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
6000 1000 = Would you group or share for this calculation? Leicestershire Numeracy Team 2003
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
18 3 = Leicestershire Numeracy Team 2003
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
0 3 6 9 12 15 18 18 3 = Division and number lines Leicestershire Numeracy Team 2003
Modelling division on beadstrings 20 4 = Leicestershire Numeracy Team 2003
20 4 = Leicestershire Numeracy Team 2003
20 4 = Leicestershire Numeracy Team 2003
20 4 = Leicestershire Numeracy Team 2003
20 4 = Leicestershire Numeracy Team 2003
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
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
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
How many eights in 48? • • • • • • Leicestershire Numeracy Team 2003
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
the number to be divided 2 3 the divisor Leicestershire Numeracy Team 2003
3 the number to be divided 2 the divisor Leicestershire Numeracy Team 2003
the number to be divided 2 3 the divisor Leicestershire Numeracy Team 2003
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
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
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
Using calculators for repeated subtraction The constant function To calculate 72 5 using repeated subtraction Press 5 - - = then press 72 Leicestershire Numeracy Team 2003
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
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
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
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