# Noticing and Explaining Patterns

Some mathematicians say that mathematics is the science of patterns. Here we invite you to explore some situations and notice the patterns that emerge, before going on to explain and perhaps prove them.

### Odd Square

Think of a number, square it and subtract your starting number. Is there something special about the number you are left with?

### Summing Consecutive Numbers

Watch the video to see what Charlie can do with consecutive numbers. There are plenty of patterns to notice and explain...

Choose a few numbers and add them up in pairs. You'll be surprised how much there is to discover...

### Pairwise Puzzler

I thought of 4 numbers - can you figure them out from 6 clues? Can you figure out 5 numbers from 10 clues? 6 numbers from 15 clues...

### Pair Products

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. Try it a few times - notice anything?

### Differences

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number? Explore this and other related questions, and see if you can prove your findings.

### Shake to Solve

Sometimes real progress in maths comes when you find a way of looking at a problem in two different ways.