Why do this problem?
Teachers may be interested in Gillian Hatch's article Using
Games in the Classroom
in which she analyses what goes on when
geometrical mathematical games are used as a pedagogic
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.
After a period of play, invite the class to share their
thoughts on the game. Were there any particularly 'good' cards? any
particularly 'bad' card? Are there any mathematical insights that
could be discussed?
Allocate the three questions from the problem
to different pairs/fours to work on and ask them to report back at
the end of the lesson.
- How many different sorts of triangle can be used to fit a
- Is your opponents' drawing clear, correct and convincing?
- 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
As an alternative game, group the students into small teams,
shuffle the cards, and play it like charades: the only way to give
clues to the property on the card is to draw appropriate triangles
for the members of your team. Each team could have a minute at a
time, and the winning team is the one who gets through most
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.