Lesson 16 Three dice
Episode 1
Reasoning | Resources: Blank ‘tickets’ (small pieces of paper), Worksheet 1, dice in three different colours |
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Whole class preparation | |
Accessible start for all, with little mathematical sense. Personal preferences dominate e.g. ‘birthday dates’ and ‘numbers I like.' Gradual understanding of context, mathematically. Range of possible outcomes. Minimum and maximum. Teacher demonstration of what pupils should do on their own. |
![]() Hand out blank ‘tickets’ and ask each pupil to write on it a number they like. Collect the slips of paper and draw six ‘from a hat’ listing the numbers on the board as the first ‘class ticket’. Include numbers less than 3 and over 18, hoping that some pupils will object. At this point clarify that there are minimum and maximum possible outcomes, or a range of possible outcomes. Replace the impossible numbers with possible ones. Accept repeats — they have to be ‘hit’ separately. |
Independent and collaborative pupils’ work often requires coaching on taking turns. But it should not be lengthy ‘busy work'. | ![]() Ask the class to describe the results. Typical answers: ‘There are more hits for the middle numbers, ‘easier to score 10 than 3 or 18,’ there are more ways of getting 8 than 3'. Leave the tally table of scores on the board as a model for the pair work. |
Pair and small group work | |
Beginning of recognition that middle numbers are more likely to come up. Pupils change selection of numbers based on own experience only, or on intuitively recognising probability patterns. The move to collecting the class results allows the effect of sample size on sample variation to be evident. |
![]() Encourage pairs to review their results, perhaps asking; What do you notice? and What numbers would be best to choose for a ticket? Then ask pupils to choose another six numbers and repeat for a further 25 dice rolls. |
Distribution of scores is now evident. Variations between groups are recognised as minor as well as random and cancel each other. | Whole class sharing and discussion![]() First find out which groups hit all the numbers in their first ticket? How early or late in the 25 throws? Which did not hit all the numbers? Which scores seemed to come up least? Discuss the changes they made to their numbers for their second ticket and why. Some pupils would have just used the numbers that came up most and avoided the ones that didn't, without going further. Some pupils would intuitively approach difference within the range, e.g.‘end numbers are no good’ and ‘middle numbers come up more’ At this point you can move to collect all the data from all the groups. List the number of hits for each score for each group and calculate the frequency. This allows comparisons of groups and recognition that there is a ‘bulge’ in the middle of the range. |
Whole class reflection How is choosing numbers for the three dice game different from choosing numbers for the National Lottery? Pupils should talk about the ‘hits’ being not actually random, some scores being more likely than others, and scores can be repeated. |
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