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# Mathematics Matters Lesson Accounts 53 - Horse Racing and Probability

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Created on 29 May 2008 by ncetm_administrator
Updated on 17 June 2008 by ncetm_administrator
 Mathematics Matters Lesson Accounts A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

# Lesson Account 53 - Horse Racing and Probability

 Written by H Tanner Organisation Unknown Age/Ability Range Y8

(a) What was the mathematical task(s)?
Horse racing game to demonstrate probability of getting different totals on 2 dice. (Done with special needs Y8). Horses labelled 1-12 down the side of the board. 6 “fences”, drawn as vertical lines down the board.

Teacher chooses horse number 6 and invites pupils to choose other horses to bet on.

Teacher invites a pupil to roll 2 dice.

The horse with the total from the dice moves forward one fence.

Atmosphere of playing a competitive game was generated. Game is played and as it progresses, pupils quickly realise that some horses are a bad bet!

After the game the teacher asks the class to think about what they have learned and to discuss with their friends which horse they should bet on next. After a few minutes the teacher takes suggestions and the game is played again.

The need to sort out thinking leads to the class beginning to generate a sample space. After a couple of iterations, the teacher begins to formalise the learning and the creation of a formal sample space.

(c) How could you tell that the task(s) achieved the intended purposes?  Do you have any evidence?
Buzz in the classroom and desire to bet on 6.  Clarity of pupils’ final explanations.

Stahl (2002) 101 Red Hot Maths Starters, London: Letts ISBN: 1-84085-696-3

(e) Can you say why you chose this example?  What criteria were in your mind?
Enjoyment of the game led to cognitive conflict between initial naive ideas and experience of the game.  Initially the class thought all values equally likely but the game demonstrated otherwise.  Playing the game also hinted as to why 6 was the best bet through experience with examples.

The task helps pupils to build a feel for the shape of a probability distribution before defining it formally. The approach roots the concept in a practical experience rather than in a theoretical algorithm.  Children are encouraged to build their own abstract mathematical concepts from a solid concrete base, rather than merely being presented with the ideas of other people.

The emphasis on pupils articulating their own thinking, discussion and prediction allowed the teacher access to the pupils’ ideas and misconceptions and provided opportunities for the scaffolding of learning, leading eventually to an understanding of formal, abstract mathematics.

## Values & Principles

 Conceptual understanding and interpretations for representations

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