Playing with Probability  Efron's Dice
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 nontransitive 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  [[Topics/ProbabilityProbability]] 
Teaching approach  [[Teaching Approaches/Whole classWhole class]], [[Teaching Approaches/Mathematical thinkingMathematical thinking]], [[Teaching Approaches/Group workGroup work]], [[Teaching Approaches/ReasoningReasoning]], [[Teaching Approaches/DiscussionDiscussion]] 
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. 
Subject  [[Resources/MathsMaths]] 
Age of students / grade  [[Resources/KS4KS4]], [[Resources/KS3KS3]], [[Resources/SecondarySecondary]]

Useful information  Large wooden dice that are coloured green, yellow, red and purple with stickers to show numbers (see this page).

Files and resources to view and download  Playing with Probability  Efrons Dice/Activity and as a download File:Efron's Dice Activity.doc. 
Acknowledgement  This resource was adapted from resources contributed by Mark Dawes 