# Representations and models - May 2012, Stage 4&5

It can be useful to use different ways of looking at mathematical ideas. This month we look at how alternative representations and models help us to develop understanding of the underlying mathematical concepts.

## Problems

### What Numbers Can We Make Now?

##### Stage: 3 and 4 Challenge Level:

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

### Take Three from Five

##### Stage: 3 and 4 Challenge Level:

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

### Pair Products

##### Stage: 4 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

##### Stage: 4 Challenge Level:

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

### Trig Reps

##### Stage: 5 Challenge Level:

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

### Polar Bearings

##### Stage: 5 Challenge Level:

What on earth are polar coordinates, and why would you want to use them?

### Maths Shop Window

##### Stage: 5 Challenge Level:

Make a functional window display which will both satisfy the manager and make sense to the shoppers