Why do this problem?
This problem offers an engaging context for exploring simple combinations. To succeed in this task it is necessary for students to work systematically.
Show the picture of the 4-4-2 formation. "Does anyone know what this football formation is called?" Invite students to explain why it's called 4-4-2. "Does anyone know any other formations?" Write on the board any suggestions; common suggestions might be 5-3-2, 3-5-2, and 4-4-3.
"What is special about all these sets of numbers?" They add up to ten, there are three numbers.
"I would like you to find all the possible football formations. You have three rows of players, defenders, midfielders and strikers. How many different ways can you share the ten players between the three rows?"
Give students some time to work on the problem. As they are working, circulate and look for different approaches. Bring the class together for a mini-plenary and invite any students who are working systematically to explain their approach to others, perhaps by writing on the board the first few formations they found, and then inviting the class to speculate on which formation they would write
down next. Then give the class time to finish off the problem, using systematic approaches to make sure they find all the possibilities.
Finally, bring the class together to discuss which formations could plausibly be used in a football game, and why some of them would not be sensible.
If I had one striker, how many different ways could I arrange the defence and midfield?
If I had two strikers, how many different ways could I arrange the defence and midfield?
This collection of problems
encourages students to work systematically.
Students could start by exploring formations for a five-a-side team in order to develop the systematic thinking skills they need to tackle the main challenge.