Angles - July 2005, All Stages

Problems Right Angle Challenge

Age 5 to 7 Challenge Level:

How many right angles can you make using two sticks? Nine-pin Triangles

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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's Journeys

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 7 to 11 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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? Age 14 to 16 Challenge Level:

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? Sine and Cosine for Connected Angles

Age 14 to 16 Challenge Level:

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. Figure of Eight

Age 14 to 16 Challenge Level:

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 ? Octa-flower

Age 16 to 18 Challenge Level:

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? Cubestick

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

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.