Visualising and representing

problem

Pyramid Numbers

Age

7 to 11

Challenge level

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
problem

Square to L

Age

7 to 11

Challenge level

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
problem

Dicey

Age

7 to 11

Challenge level

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
problem

Knight's Swap

Age

7 to 11

Challenge level

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
problem

Midpoint Triangle

Age

7 to 11

Challenge level

Can you cut up a square in the way shown and make the pieces into a triangle?
problem

A Flying Holiday

Age

7 to 11

Challenge level

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.
problem

Colour Wheels

Age

7 to 11

Challenge level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
problem

Paw Prints

Age

7 to 11

Challenge level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
problem

Painted Faces

Age

7 to 11

Challenge level

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
problem

More Building With Cubes

Age

7 to 11

Challenge level

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!