# What Does it All Add up To?

##### Age 11 to 18

Challenge Level

### Why do this problem?

This problem, along with the rest of the problems in the Proof for All (st)ages feature, provides an excellent context for observing, conjecturing and thinking about proof, and for appreciating the power of algebra.

### Possible approach

*This problem featured in an NRICH Secondary webinar in January 2022.*

*These printable cards for sorting may be useful: *

What Does it All Add Up To Proof Sort

### Key question

Is there a way to represent the sum of four consecutive numbers that will help to explain the patterns you noticed?

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### Possible support

Encourage students to work in pairs on the proof sorting exercise.

Before embarking on this problem, students could take a look at

Three Neighbours.

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### Possible extension

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