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## 'Property Chart' printed from http://nrich.maths.org/

### 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

Use the instruction on the

problem
page to set up and play the game for about half a lesson, then
move the group on to the questions at the end of the problem.

### 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 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?

### 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.

### 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.