Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

Chippy the Robot goes on journeys. How far and in what direction must he travel to get back to his base?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you find all the different triangles on these peg boards, and find their angles?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you find triangles on a 9-point circle? Can you work out their angles?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

Vidhya from Kensri School in India sent in a very well reasoned solution for this problem.

Tobi and Charles explain how you would find the total number of crossings for any number of sticks.

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

A virtual geoboard that allows you to create shapes by stretching rubber bands between pegs on the board. Allows a variable number of pegs and variable grid geometry and includes a point labeller.

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

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.