Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Can you rearrange the cards to make a series of correct mathematical statements?

How many different cubes can be painted with three blue faces and three red faces? A boy (using blue) and a girl (using red) paint the faces of a cube in turn so that the six faces are painted. . . .

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

A walk is made up of diagonal steps from left to right, starting at the origin and ending on the x-axis. How many paths are there for 4 steps, for 6 steps, for 8 steps?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

Relate these algebraic expressions to geometrical diagrams.

Can you work through these direct proofs, using our interactive proof sorters?

Daniel used connections between each of the ideas to help him solve the problem. He explained his thinking very well.

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.