# Noticing Patterns

The key to solving these problems is to notice patterns or properties. Encouraging students to organise their work in a systematic way will allow them to notice what might not otherwise be obvious.

### Summing Consecutive Numbers

##### Stage: 3 Challenge Level:

This problem offers a simple context for students to explore, make generalisations and prove conjectures, working numerically and algebraically.

### 1 Step 2 Step

##### Stage: 3 Challenge Level:

This problem is inaccessible without looking at simpler cases, and thus helps students to see the value of specialising in order to generalise.

### Pick's Theorem

##### Stage: 3 Challenge Level:

This problem allows students to consolidate their understanding of how to calculate the area of irregular shapes, while offering an opportunity to explore and discover an interesting result.

### What's Possible?

##### Stage: 4 Challenge Level:

As well as introducing the difference of two squares, this problem allows students to explore, conjecture and use algebra to justify their results.