Visualising and representing

problem
Like a circle in a spiral

Age

7 to 16

Challenge level

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
problem
Shape mapping

Age

7 to 11

Challenge level

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?
problem
Rearrange the square

Age

5 to 7

Challenge level

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
problem
Peg rotation

Age

7 to 11

Challenge level

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
problem
Twice as big?

Age

7 to 11

Challenge level

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
problem
Triangle numbers

Age

11 to 14

Challenge level

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
problem
Noughts and crosses

Age

11 to 14

Challenge level

Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.
problem
Route to infinity

Age

11 to 14

Challenge level

Can you describe this route to infinity? Where will the arrows take you next?
problem
Multiples grid

Age

7 to 11

Challenge level

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
problem
Tricky triangles

Age

5 to 7

Challenge level

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?