Dice duels

## Description

A dice has been weighted (loaded) to favour one of the six numbers. Roll the dice to work out which is the favoured face. Explore how many rolls are needed for you to be reasonably sure of a conclusion. Make biased dice. Test ideas about bias by rolling a loaded dice on its own or with a fair dice. For the dice pair, look at the sum of the two numbers rolled. Look at demonstrations of the mathematical principles of bias. Compare the shape of theoretical data distributions with experimental results. This learning object is a combination of 3 objects in a series of 11 learning objects.

## Key learning objectives

• Students collect and handle data about random events to test conjectures about variation and bias.
• Students interpret frequency graphs to compare experimental results with theoretical probabilities.
• Students compare the shape of theoretical and experimentally derived data distributions in situations where there is bias.
• Students relate the shape of data distributions to statements about sample variation, sample size and bias.

## Educational value

• Provides scenarios for students to use dice as a means to explore relationships between bias, proportions, sample size, random variation and statistical distributions.
• Demonstrates that conclusions based on small sample sizes can be incorrect due to random variation.
• Includes scenarios involving a range of even and uneven distributions.
• Introduces mathematical ideas underpinning uneven distributions via an on-screen tutorial.
• Automatically collates experimental results and displays them as frequency graphs.

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