Appendix 6: Maths of Lotto – Overview

This is an anti-gambling lesson. Or at least one designed to show the mathematical realities behind Lotto games. Does the community understand the true chances? If not, then they may be exploitable. It is presented as a whole class game which becomes an investigation involving probability, combination theory, statistics and working mathematically. A computer simulation of the game allows a problem solving extension, and provides a basis for analysis of the realities of real lotto games.

“After this lesson one of my students called them ‘Looto” games

Mathematics Content Outcomes\Links To Official Curriculum Documents

• Probability and expectation
• Combination theory and simple proportion
• Statistics
• Interdisciplinary learning
• Working mathematically – mathematical modeling

Lesson Stages

1. Discussion of real lotto games and demonstration of the simple 6:2 game
2. Estimation of chances in the 6:2 game
3. Play 10 games – record results on board
4. Check results against perceptions – is there a difference? – reasons for the difference
5. Explaining the real chances - are all pairs (or groups) equally likely?
6. Are you superstitious? – the psychology of choices
7. Playing and analysing other simple games eg. 7:2, 8:2, 7:3, 5:3, 10:2, ….
8. Computer simulation
9. Analysing real Lotto games and where the money goes
10. Educating the public – do they know their real chances?

Straw Vote

Please rate each of the following features (out of 10) as to its contribution to the overall quality of the learning experience.

 1 Modelling a real context as a class game [   ] 2 Collecting initial class perceptions (Estimation) [   ] 3 Incidental or informal learning opportunities [   ] 4 First principles analysis of how many pairs are in the barrel [   ] 5 Opportunity for strategy development [   ] 6 Computer simulation [   ] 7 The ‘superstition’ analysis - is each pair equally likely? [   ] 8 Non-threatening [   ] 9 Openness - mixed ability - suits many grade levels? [   ] 10 Relevance outcome i.e addressing a social issue - educating the public [   ]

This lesson is fully documented (pending), including the software simulation, within the Maths300 project. www.maths300.esa.edu.au

Lovitt, C., Clarke, D. (2011) A Designer Speaks. Educational Designer, 1(4).