### Why do this problem :

This problem can be a good way to demonstrate mathematics emerging
out of play.

### Possible approach :

Using wood blocks (trominoes from three squares, like dominoes
from two), arranged as a tower, a game of coordination and
experimentation begins as players try not to topple the stack.

Pick up one of the pieces of wood and begin posing some
questions about it.

- Can these blocks form a square ? - other than the three side by
side used for each layer in the stacking game.

Let the questions flow and get pursued. Try to encourage
adjustment rather than abandonment when a line of questioning
appears to run out. For example a five by five square can't be made
because each block contributed three squares of area and there are
25 to be covered, so there must be a hole. OK, given there's a
hole, can you make a square ?

### Key questions :

- What questions can you pose ? (offer an example : what
rectangles can and cannot be made ?)

- Which seem like good questions to pursue ?

- (later) What were our questions ? Where has each question taken
us in what we now see or understand ? What came out of this that we
didn't know already or didn't expect ?

### Possible extension :

Equal
Equilateral Triangles is a good next step.

### Possible support :

Create a competition to produce all rectangles up to side length
10.

Perhaps use a digital camera or the camera in a mobile phone to
catch arrangements quickly. A drawing record may sap energy that
might be used more effectively pursuing the task.