Task 122 ... Years 2 - 8
SummaryThe Australian Football League (AFL) provides the setting for this language and logic puzzle. It doesn't matter if this is not your local code because the logic is still accessible. Later your local sporting code - football or other - can be used to challenge students to make their own puzzles.
The major aspect is the provision of concrete materials (cards) which make the task accessible to, and popular with, almost all students. Another feature is a kinaesthetic option where the class members can 'act out' the ladder positions. Include the way points are assigned for a win, loss or draw and you have another challenge.
An extension of the task offers an excellent way to introduce selections and arrangements (permutations and combinations). The teacher (or the students) can choose the conditions for the problem to manage the difficulty of the challenges.
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
The solution to the puzzle (from the top of the ladder) is:
Hawthorn, Fremantle, Essendon, Carlton, Brisbane, Sydney, Adelaide, Melbourne, Collingwood, Geelong, Richmond, Kangaroos, West Coast, St. Kilda, Port Adelaide, BulldogsTo support students to discover this, refer to the Working Mathematically process and ask what strategies a mathematician might use for this problem. They have the cards, which enable them to make a model, but what to do now. Guess & check, break the problem into smaller parts and draw a diagram all offer possibilities. One of the smaller parts, for example, is the clue:
West Coast won the same number of games as St. Kilda.The consequence is that they must be near each other on the ladder.
Whole Class InvestigationTasks 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.
Use a set of cards about 20cm square and write the team names, one per card. This allows the problem to be acted out with 16 class members who each hold a card. Also, the acting out can be confirmed by students folding and tearing scrap paper (two pieces per pair and eight sections in each) to make team cards. Transcribe the clues to the whiteboard or a duplicated sheet (copyright prevents you photocopying the card) and you are away.
Strategies teachers have used with the whole class and these tools include:
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 69, Football Ladder, which includes several clue sets.
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 Football Ladder task is an integral part of:
The Football Ladder lesson is an integral part of: