Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
How high can a high jumper jump? How can a high jumper jump higher without jumping higher? Read on...
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These four problems require some logical thinking and a willingness to work systematically. Routes to a solution are not immediately obvious so working on the problems could help students to develop their resilience, an important quality for mathematical problem-solvers.
Before introducing the task:
"Mathematicians need to be resourceful problem-solvers who don't give up, who talk to each other and share good ideas, who work strategically and systematically. The answers won't be immediately obvious, so these problems will test your ability to work as mathematicians."
The problems could be used in several ways:
Hand out this worksheet and invite students to work on all four problems in pairs.
Cut the worksheet into the four separate problems and invite different groups to work on different problems.
Work on one or two of the questions together as a class and then invite students to use each other's useful insights to solve the remaining problems.
While students are working, circulate and listen for useful insights. Where appropriate, bring the class together so that students can share successful strategies with the rest of the class.
The following key questions or prompts could be offered to students who are stuck:
What do you know? Write it down.
What can you deduce from what you know? Write it down.
Is there a good way of representing what you know, to make it clear?
For other problems that require systematic and logical thinking see Two and Two, Product Sudoku and Cinema Problem.
Of the four problems, Football Champ and Hockey use very similar techniques, so one could be solved as a class before students are given the second to apply any useful methods they have devised.