# Final Eight

### Task 1 ... Years 4 - 10

#### Summary

Team competition sports usually have a process for working out season champions that involves top teams playing off in a defined sequence. This task explores the Final Eight system of the Australia Football League (AFL) as an example of how mathematics is applied to design these play-off systems and provides a playing board to support those who need to adapt the investigation to the National Rugby League (NRL).

#### Materials

• Two dice
• Team cards (pre-cut)
• Position cards (pre-cut)
• Playing board (for both AFL & NRL)
Enlarge to A3 and print.

#### Content

• collecting and organising data
• mathematical modelling of a real-life situation
• probability and chance

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

The fact that two football codes in Australia use different finals structures to determine the season winner, shows that devising these play-offs is serious business. They have to be workable, fair and make money. Build your initial investigation around the game most suited to your students, then offer them the opportunity to compare their outcomes with those possible using the alternative structure.

Other possible iceberg investigations for this task are:

• For either AFL or NRL or both:
Of the 28 combinations, which can meet in the Grand Final?
• Design and investigate a different final eight structure?
• Design and investigate a final four or final six structure?
• Using Final Eight as a guide, investigate the finals structure of your favourite sport.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

Changing this lesson to a whole class investigation requires multiple copies of the board based on one per group of 8 and two dice per group. Students write their name on a slip of paper. This is placed where they finish on the 'ladder' at the end of the season (first to eighth) and that position is decidedly randomly; perhaps using a shuffled suite of cards Ace to 8 from which the students draw their position. The investigation is focussed on the fairness of this particular finals system and involves data gathering and representation, probability and reasoning skills.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 149, Sporting Finals which also includes a reproducible copy of the board. The lesson offers a powerful extension of the investigation through companion software.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Final Eight task is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 9 & 10

The Sporting Finals lesson is an integral part of:

• MWA Chance & Measurement Years 9 & 10