### 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?

# Spelling Circle

### Why do this problem?

This problem links English and mathematics, and will help children become familiar with numbers that are, and are not, factors of $12$. You can also focus on learners' justifications and explanations of why certain arrangements of letters work. You may find this sheet of 'blanks' useful.

### Key questions

How many spaces for letters do you have?
Where do you find the first letter?
What could the next letter be? And the next?
When you're using your own word, what happens if you put the letters in every second space ... every third space ... every fourth space?
Can you explain why?

### Possible extension

Learners can be encouraged to find all the possible ways of arranging one word. How do they know they have them all? They could also try using words with a different number of letters, and changing the number of sections in the circle. Can they move the letters by any number of spaces?

### Possible support

Some children will find it helpful to start by writing the word continuously round the circle.