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

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

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?

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

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. . . .

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

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.

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

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