### Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

### Napoleon's Hat

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

### 30-60-90 Polypuzzle

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

# Power Match

### Why do this problem?

This interactivity gives students an opportunity to become familiar with logarithmic scales.

### Possible approach

This activity can be played in pairs as a game, or individually. When a flag is incorrectly placed, can students understand why? This is good for rooting out errors in understanding. For example, $10^{1.5}$ is not half way between 10 and 100.
Alternatively it could be used as a starter or plenary with the whole class working together on an interactive whiteboard to decide where to place the green dot for each target.

### Key questions

Which two powers of ten will the target be between?
Which one is it closer to?
What is the value of the halfway point between two powers of ten?

### Possible extension

Students could go on to explore scientific contexts for logarithms, such as the pH scale in the problem Mixing pH.

### Possible support

A Question of Scale introduces logarithmic scales by inviting students to consider orders of magnitude of scientific quantities.