This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?

A game in which players take it in turns to choose a number. Can you block your opponent?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Can you make square numbers by adding two prime numbers together?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

This activity creates an opportunity to explore all kinds of number-related patterns.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

An introduction to proof by contradiction, a powerful method of mathematical proof.

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either. . . .

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

These two group activities use mathematical reasoning - one is numerical, one geometric.