### Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

### 2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

### Screwed-up

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

# Transformation Game

### Why play this game?

This game provides an opportunity to practise a lot of transformations in the context of a game. The scoring system encourages the use of combinations of transformations. Opponents usually watch for cheating and errors, so there is built-in feedback for students. The structure of a game encourages students to play strategically.

### Possible approach

Play a demonstration game, teacher vs a couple of students working together. It would be useful to have the playing board drawn or projected on the board for this. Ask students to play in pairs to get used to the game, and to make a note of any questions they might have.
With the class all together, allow time to answer the questions that have arisen.

Explain that students will be playing in pairs agains other pairs, and that they will have some time to prepare. In their pairs, suggest that students ensure they know where the triangles would go, forwhatever transformation card they get, and encourage them topractise making more complex transformations.
Organise a competition between pairs.

Use the time available to give positive feedback to those who get hightotal scores (even if they do not win) and to those who use combined transformations.

### Key questions

Where can we get to from here?
How would you get to the high scoring triangles? Which cards would you need to have?

### Possible extension

Students could be restricted to moves which involve more than one transformation.

Other aspects could be altered - students could agree fair rules between themselves.

Ask students to design their own version of the game, perhaps changing the shape, the transformations on the cards and the size of the grid. They could play the game to decide what scores are appropriate for their new version.

### Possible support

Students might want to redesign some of the transformation instruction cards, so that the information about how to move is clearer to them. The teacher will need to decide whether they should use their own cards, or whether they could keep them visible as a reference to check the meaning of the printed cards.

Explain that the group will be playing this game in teams against the teacher later on, and that they have most of the lesson to work on strategy. Maybe kids could start with a couple of cards, then come and ask for more when they are sure that they know where each triangle would go, and then two more etc.

When a team plays the teacher, make sure that they discuss and agree on the moves.