### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# What Two ...?

### Why do this problem?

This problem is a short challenge that may introduce pupils to the idea of square numbers and square roots. It can also be opened up in all sorts of ways (see the 'Possible extension' section below).

### Possible approach

You may want to give learners this challenge as you are taking the register, for example, as it does not need much explanation.

Sharing ways of approaching the solution will be valuable, however, as children are likely to have done different things. Some might have used trial and improvement, some may have used a calculator to find the square root.

### Key questions

Perhaps you could try two consecutive numbers and see how close you are?
Do you have sense of how big the numbers will be?

### Possible extension

This problem can be extended in all sorts of ways by asking 'what if ...?' questions. This sheet gives you some suggestions.

### Possible support

A calculator is likely to be useful.