Lesson 20 Heads and tails

Heads and tails

   
Overview Resources
Pupils record the number of heads they get in five samples of ten tosses of a coin. They contrast the variation in the percentage of heads in their samples of ten with the way the percentage approaches more and more closely to 50% as the class data is cumulated. This introduces the idea of sampling variation. Then they look at the pattern of the frequency of runs of heads in the whole class data. The frequency roughly halves between runs of one and runs of two, and continues to halve with each longer run. They discuss this in terms of probability. Coins
Worksheets 1-5 copied on to A3 or A2
Aims Curriculum links
Models of probability and chance. Data handling: probability and proportions.
EPISODE 1
Samples and proportions
Pupils test the idea that there is a 50-50 chance of getting a head when you throw a fair coin. They toss a coin in batches of 10 throws then combine their samples into samples of 50. They treat the probability of the event in terms of a percentage between 0 and 100%.

Pupils discuss reasons why the difference from 50% is smaller in the larger sample than for samples of 10.
EPISODE 2
Cumulative class table and chart
Pupils collate all their experimental data in a cumulative table, working out at each addition of a sample the percentage of the heads to the new total, noting how it oscillates, but draws nearer to the 50%. The teacher makes corresponding points on a graph to show this oscillation and convergence. Pupils discuss how this approach can be applied in other situations e.g. to see if the chances of boys and girls being born are equal.
EPISODE 3
Comparing runs of heads
Pupils trawl the data again for more information, collecting the frequency of runs of heads, i.e. where a head is immediately followed by another and so on, throughout their samples of 50. They then make a cumulative table and represent the totals for each run of 2,3, 4, etc. heads, as a bar chart. They reflect on the ‘halving pattern’ shown in the bar chart and on how previous events affect future ones.

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Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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