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: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:1

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: Challenge Level:2 Challenge Level:2

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