Shapely Pairs

Why do this problem?

The game provides a powerful and engaging context for working on properties of triangles/quadrilaterals. Two other related problems are Quadrilaterals Game and Property Chart

Possible approach

This game can easily be played in groups. The rules are clear: after a brief demonstration students could be left to play the game. To encourage discussion and peer support, ask students to play as pairs; both must agree on the "final answer" before it counts. Again, to spread ideas and strategies around the class, you could organise a rotation or two so that all pairs move on and play a new pair.

Key questions

• How many different sorts of triangle can be used to fit a particular card?
• Is your opponents' drawing clear, correct and convincing?

Possible support

Share out two or three sets of the cards (or big A4 versions) among all the students in the class, show a triangle on the board and ask students to stand if they have a card that describes it. The duplication of cards should generate useful conflict if people with the same card disagree.

It might be useful to have a worksheet available with lots of different triangles as 'ideas' or to save some students having to draw the shapes.

Possible extension

• How many triples of cards lead to possible triangles?
• What is the greatest number of cards which will all apply to the same triangle?
• Make your own version of this game, deciding what to put on the cards.