# Patterns that lead to algebra and proof - October 2010, Stage 3&4

Mathematicians are fascinated by pattern - one writer has even described 'pattern sniffing' as a mathematical behaviour. In this month's activities and problems we invite you to discover patterns, describe them in different ways and begin to think about how you can convince yourself, and others that you have sniffed out all there is to find!

## Problems

##### Stage: 3 Challenge Level:

Think of a number... follow the machine's instructions. I know what your number is! Can you explain how I know?

##### Stage: 3 Challenge Level:

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

### Special Numbers

##### Stage: 3 Challenge Level:

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

##### Stage: 4 Challenge Level:

Explore the two quadratic functions and find out how their graphs are related.

##### Stage: 4 Challenge Level:

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

##### Stage: 4 Challenge Level:

Here are some more quadratic functions to explore. How are their graphs related?

### Weekly Challenges

##### Stage: 4 and 5 Challenge Level:

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.