# Generic examples - March 2012, Stage 1&2

Sometimes it is possible to state what is general by perceiving the structure in just one example. Vivid proofs of generalisations can be located in a particular, well-chosen example. This month we invite you to explore and notice what is generalisable in carefully chosen generic examples.

## Problems

### Walking Round a Triangle

##### Stage: 1 Challenge Level:

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

### Two Numbers Under the Microscope

##### Stage: 1 Challenge Level:

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

### Odd Times Even

##### Stage: 1 Challenge Level:

This problem looks at how one example of your choice can show something about the general structure of multiplication.

### Round a Hexagon

##### Stage: 2 Challenge Level:

This problem shows that the external angles of an irregular hexagon add to a circle.

### Take Three Numbers

##### Stage: 2 Challenge Level:

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

### Three Neighbours

##### Stage: 2 Challenge Level:

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

### Square Subtraction

##### Stage: 2 Challenge Level:

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?