# Working Backwards, Leaping Forwards

### Working backwards, leaping forwards

In mathematics lessons, you might be given a question and asked to work out the answer, but these problems are a little bit different! To solve them, you'll need to think about the relationships between functions and operations and their inverses, and work backwards in order to leap forward!

##### Age 7 to 14 Challenge Level:

What is the smallest number of answers you need to reveal in order to work out the missing headers?

##### Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

##### Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

##### Age 14 to 16 Challenge Level:

Can you find the hidden factors which multiply together to produce each quadratic expression?

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

Can you match the charts of these functions to the charts of their integrals?

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

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

##### Age 14 to 18 Challenge Level:

Learn how solving inverse problems can save lives in this article from Plus Magazine

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