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
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.
This is a beautiful result involving a parabola and parallels.
Can you invert the logic to prove these statements?
Can you work through these direct proofs, using our interactive
Daniel used connections between each of the ideas to help him solve
the problem. He explained his thinking very well.
Go to last month's problems to see more solutions.
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.