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'Property Chart' printed from https://nrich.maths.org/

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Why do this problem?

This game provides an interesting context in which to consider the properties of quadrilaterals (or triangles), and has a particular focus on the combinations of properties that are possible.

Possible approach

Quadrilaterals Game could be used either at the beginning or at the end of this problem.

Use the instructions on the problem page to set up and play the game in pairs. As you circulate, rather than praising the winner of each game, praise charts that are fuller when the game ends - or at least where you believe all of the possible shapes have been drawn. Once a game has been 'won', encourage the pair to work together to check if there were any spaces that could have been filled - or to convince each other that the remaining spaces cannot be filled.

Once students have had a chance to play and explore the game, bring the whole group together to share what they have noticed. Were there any cards which they found easy or difficult to draw shapes for? Which were the best and worst combinations of cards? Encourage a range of opinions, and where there is disagreement, challenge students to justify their ideas and convince each other.

Next, introduce the questions at the end of the problem. Students could work on them in their pairs, or in new groups of three or four. Remind them to use the ideas from the whole group discussion, and to use what each student learnt from playing the game. Groups could draw their final grids, and then look around the room at each others' grids. How many different complete grids can the whole group come up with?

Key questions

  • Which shapes are most useful in this game?
  • Which property cards are 'good' and 'bad' and why?
  • Tell me two cards where there is no shape that works for both.

Possible support

The game could be played as a whole class - shuffle and arrange the property cards on the board so that everyone has the same question. Groups of 3 or 4 then work together filling in the grid and checking each others work. A correct shape or gap will earn 10 points, but each incorrect shape or gap will lose 10 points. After a set time, all the grids are displayed, and students try to find errors in the other groups' work, in order to establish the scores and the winners. They may be ready to try the problem as stated after this!

Another way in to the problem could be to produce some partly completed grids and ask students to finish them, or produce some completed grids with a few deliberate errors for students to find and correct.

 

Possible extension

If only the quadrilaterals are visible on the board can you identify the property cards in each position? In what other ways can you adapt/invert/develop this game to make new and possibly harder challenges?

Suggest students have a go at Shapely Pairs

 

Additional comment

Teachers may be interested in Gillian Hatch's article Using Games in the Classroom in which she analyses what goes on when mathematical games are used as a pedagogic device.