Playing with Probability - Efron's Dice

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I have some dice that are coloured green, yellow, red and purple...

Lesson idea. A lesson activity to explore probability with dice. We are used to the idea of transitivity, where we can ascribe an order to events. Efron’s dice are non-transitive and probability methods that the pupils are familiar with can be used to explore how to play a game using them.

Teaching approach. Efron's dice provide a discussion(ta) topic for joint reasoning(ta) - whole class(ta) or in group work(ta). Pupils can explore aspects of mathematical thinking(ta) particularly with relation to probability. (edit)

Resource details
Title Playing with Probability - Efron's Dice
Topic Probability
Teaching approach
Learning Objectives

Understanding the worth of probability tables and how to use them to solve a problem.

Format / structure

A wiki page also available as a downloadable Word document.

Age of students / grade

KS4,  KS3,  Secondary

Useful information

Large wooden dice that are coloured green, yellow, red and purple with stickers to show numbers (see this page).
Any practical probability starting point carries the risk that the results will not, in the short term, produce the expected results. This is a useful discussion point.

Files and resources to view and download

This resource was adapted from resources contributed by Mark Dawes