# Understanding Inverse Relationships

### Understanding inverse relationships

Working backwards is an important part of mathematical problem solving. In this feature, we share problems that encourage students to think about the relationships between processes and their inverses.

##### 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:

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 16 to 18 Challenge Level:

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