Chance and Data Investigation

This year, the 34 Year Group have been working on a Chance and Data investigation every week. Here is the detail of the investigation they will be exporing from this week.

The students roll two dice in a simulated game of Aussie Rules football. They play all four quarters in a competition against a partner and the scores are similar to the real thing. This simple dice simulation has the fun of a game, but also involves many number, chance and data concepts. Collecting class data allows analysis of several aspects of the mathematics. We then move into using a computerised model, which allows for long term patterns to be explored, and empirical results can be compared with theoretical expectations.

 Learning outcomes and related concepts
• Whole number skills
• Probability comparisons and calculations
• Collection and organisation of group data
• Probability distributions
• Concept of expected results
• Calculation of averages
• The mathematical investigative process (Working Mathematically)

 Learning stages
1. Building the simulation model with dice
2. Small group work playing the game
3. Coding and collecting group esults
4. Discussing and analysing the data
5. Investigations using computer simulation - calculating empirical probabilities
6. Conclusion and summary

 Features
Connecting to (and modeling) a recreational game: Most investigations benefit from an interesting context and games can be a great source of these. However, it is the conversion of the game into an investigation that frames the learning. Use of concrete materials: Each student rolls two dice; the first rolled being the goals and the second the behinds. The concreteness makes the entry to the puzzle accessible to all.
Non-threatening: The randomness of the game and the easy entry skills makes the game appealing. Having 'entered' the game context, students can then be informally exposed to various mathematical ideas at a level that suits their confidence and ability. Collecting group data: The game is a played in pairs, but the decision to invite students to list the scores on the board cleverly sets the scene to change from a game into a whole group investigation. The data, being generated by students provides important 'ownership' and any stories or patterns in the data are 'their stories'. Empirical versus theoretical calculations: At several places throughout the investigations calculations are performed in both modes, allowing students to see and discuss the relative merits of each.