### Complex Partial Fractions

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.

### Agile Algebra

Observe symmetries and engage the power of substitution to solve complicated equations.

### Graphs of Changing Areas

Use graphs to gain insights into an area and perimeter problem, or use your knowledge of area and perimeter to gain insights into the graphs...

# Steve's Mapping

##### Age 16 to 18 Challenge Level:

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

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Steve has created two mappings which you can access by clicking on the picture below. The initial challenge is to figure out what Steve's mappings do. You can drop some numbers into the mappings, and see what comes out.

Test your ideas by predicting the outputs for some different inputs.
Only reveal the hidden parts of the mapping once you are certain you know what is going on.
Can you find an input which gives the same output for both mappings?

Click on the picture to explore Steve's mappings.

As you explore Steve'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.