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### 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.

# Exploring Simple Mappings

##### Stage: 3 Challenge Level:

Ed from St Peters College noticed that:

If the numbers aren't changed ($\times2$ and $+3$), the final answer will always be odd.
When the values of the $2$ and $3$ are changed, from an even and an odd, to an odd and an even, the answer will be the same type as the number placed in the input box at the start:
if the input is even, the answer will be even
if the input is odd, the answer will be odd

Thomas from Wilson's School noticed that:

The higher the numbers you are multiplying by, the steeper the gradient of the graph.

The addition or subtraction determines where the graph cuts the y-axis.

Rajeev from Fair Field Junior School in Radlett summarised his findings clearly here
He started to consider the equations of perpendicular lines. You can go to Perpendicular Lines if you would like to explore this further.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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