# Communicating and reflecting - September 2009, Stage 4&5

This month NRICH gets involved in the conversational side of mathematics, with problems which naturally lead to discussion and sharing of ideas and methods. Which forms of communication and presentation of the mathematics will prove to be the most effective? Through discussion and explanation you will refine your thinking and perhaps make connections with other areas of mathematics.

## Problems

### Chances Are

##### Age 14 to 16 Challenge Level:

Which of these games would you play to give yourself the best possible chance of winning a prize?

##### Age 14 to 16 Challenge Level:

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

### Carbon Footprints

##### Age 14 to 16 Challenge Level:

Is it really greener to go on the bus, or to buy local?

### Pythagoras Proofs

##### Age 14 to 16 Challenge Level:

Can you make sense of these three proofs of Pythagoras' Theorem?

##### Age 14 to 16 Challenge Level:

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

### Model Solutions

##### Age 16 to 18 Challenge Level:

How do these modelling assumption affect the solutions?

### The Wrong Stats

##### Age 16 to 18 Challenge Level:

Why MUST these statistical statements probably be at least a little bit wrong?

### Dangerous Driver?

##### Age 16 to 18 Challenge Level:

Was it possible that this dangerous driving penalty was issued in error?

### Notty Logic

##### Age 16 to 18 Challenge Level:

Have a go at being mathematically negative, by negating these statements.