How many right angles can you make using two sticks?
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
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.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
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?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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
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
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.
Neil has successfully generalised his results for the Multiplication square.
Neat proofs of two results about the golden ratio are demonstrated here.
Suggestions for worthwhile mathematical activity on the subject of
angle measurement for all pupils.
Can you deduce the pattern that has been used to lay out these
Take it in turns to make a triangle on the pegboard. Can you block
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.