### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Colour Wheels

## Colour Wheels

Imagine a wheel with different coloured markings - red, green and blue painted on it at regular intervals.
As the wheel goes round, a trail is painted on the ground.
RGBRGBRGBRGBRGBRGB ... ...

This text is usually replaced by the Flash movie.

Satisfy yourself that you can predict where the blues will appear.
How about the red and green marks?

Can you predict the colour of the 18th? 19th? 31st? 59th? 299th? 3311th? 96 312th?
How did you work it out?

Now consider the wheels that produce:

BBYGBBYGBBYG ... ...
BYBRBYBRBYBRBYBR ... ...
RRRBBYRRRBBYRRRBBYRRRBBYRRRBBY ... ...
RRBRRRRBRRRRBRRRRBRRRRBRR ... ...

This text is usually replaced by the Flash movie.

What will the 24th colour be in each case? The 49th colour? The 100th?
How did you work it out?

You could continue this investigation by asking yourself some "what if ...?" questions:

A wheel has six markings. Where would red be painted on it so that the 100th mark made is red?

What other wheels (with more/fewer markings) would give you a red in the 100th position?

### Why do this problem?

This activity, included in a month when we are focusing on visualising, challenges pupils to form pattern images in their heads. The problem encourages them to use this imagery to recognise, describe, and manipulate pattern. This leads on to opportunities to build up generalisations using words, and this links with aspects of arithmetic, (multiples and divisibility).

### Possible approach

You could introduce this activity orally. Start off by asking the group to imagine a wheel with a blue mark painted on the edge and a red mark painted on the opposite edge. Say that you place it on the ground and roll it. Ask them to talk in pairs about what they think they would see on the ground if the paint was still wet. Share ideas amongst the whole group. Encourage learners to describe using just words at first, rather than using pictures or objects.

Once the blue, red, blue, red ... pattern has been established, ask a few questions like "Can you predict the colour of the third/fifth/tenth/hundredth mark?". Give learners plenty of time to think about each question and at this stage, you can allow them to draw/write if they want to. When discussing their responses, encourage clear explanations. Did they have to draw $100$ marks?

You can then go on to the problem as it is written. You may want to continue working orally to start with, but you could always show the children the animations of the wheel/s or have a large disc/cylinder as a prop.

When it comes to drawing their ideas together, look for learners who express their explanations clearly in terms of multiples. Many children will be able to investigate their own wheels and to ask their own questions, and their work would make an impressive display.