Properties of Numbers: Multiples, Factors, Primes, Square and Cube Numbers

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.

Can you fill in this table square? The numbers 2-12 were used to generate it with just one number used twice.

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?