### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

### Fence It

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

# Charlie's Mapping

##### Stage: 3 Challenge Level:

Before starting to explore Charlie's mapping, you might want to watch a short video explaining how to use the NRICH Number Plumber.

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Charlie has created a new mapping which you can access by clicking on the picture below. The initial challenge is to figure out what Charlie's mapping does. You can drop some numbers into the mapping, and see what comes out.

Test your ideas by predicting the outputs for some different inputs.

Then try to build your own mapping which does the same job.

There are many ways of doing this which are not as complicated as the way Charlie chose! Try to find more than one, and explain why they do the same job.

Only reveal the hidden parts of Charlie's mapping once you have been succesful.

Click on the picture to explore Charlie's mappings.

As you explore Charlie's mappings, you will notice points appearing on the graph. The input number is the x coordinate, and the output number is the y coordinate.
Create some other function machines using the NRICH Number Plumber, and observe the outcomes on the graph.

Mathematicians like to ask themselves questions about what they notice.
What possible questions could you ask?

These questions may lead you to make conjectures - something which you believe to be true but need to investigate further in order to convince yourself.