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

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

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

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. . . .

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?

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

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

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

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

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.