### Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

### Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

### Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

# An Appearing Act

##### Stage: 3 and 4

This resource is part of "Dotty Grids - Exploring Area"

You may wish to print out some dotty paper.

Take an 8 by 8 square, and cut it up like this:

Rearrange the pieces to make a 13 by 5 rectangle:

It seems we can use the same pieces to make two shapes with different areas!
Can you explain why?

Can you perform this “magic trick” by splitting squares of other sizes in a similar way?

Which squares are least obvious?

What patterns are there in the square sizes?

Want to share what you've done? Got any interesting questions or ideas?