### Counting Counters

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

### Cuisenaire Squares

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

# Lost Books

### Why do this problem?

This problem requires learners to work systematically and use logical thinking about numbers. Much of it can be done practically which opens up possibilities for different types of learning. It could be very useful for getting learners to develop rules for how something works.

### Key questions

Where do odd (and even) numbers come on the sheets?
What is the last number always divisible by?
What do the two numbers on a sheet add to?
Have you made a table of your results?
Can you make any predictions about how the numbering will go?

### Possible extension

An extension can be made by finding out about patterns of numbering the pages of books (possibly a child's picture book) which has pages which fold in.

### Possible support

Suggest starting by cutting a sheet of A$4$ paper to cut into $4$. This is made into a little book by putting the sheets together and folding. The pages can then be numbered starting on the outside at $1$.