# Representations and models - May 2012, All Stages

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

### Matching Numbers

##### Stage: 1 Challenge Level:

Can you find different ways of showing the same number? Try this matching game and see!

### How Do You See It?

##### Stage: 1 and 2 Challenge Level:

Here are some short problems for you to try. Talk to your friends about how you work them out.

### How Would We Count?

##### Stage: 1 and 2 Challenge Level:

An activity centred around observations of dots and how we visualise number arrangement patterns.

### That Number Square!

##### Stage: 1 and 2 Challenge Level:

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

### Different Sizes

##### Stage: 1 and 2 Challenge Level:

A simple visual exploration into halving and doubling.

### Let Us Divide!

##### Stage: 2 Challenge Level:

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

### Matching Fractions

##### Stage: 2 Challenge Level:

Can you find different ways of showing the same fraction? Try this matching game and see.

### What Numbers Can We Make?

##### Stage: 3 Challenge Level:

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

### Always a Multiple?

##### Stage: 3 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

### 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