Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Use the isometric grid paper to find the different polygons.

What's the greatest number of sides a polygon on a dotty grid could have?

What shape and size of drinks mat is best for flipping and catching?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.