Angles - July 2005, All Stages

Problems

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Right Angle Challenge

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

How many right angles can you make using two sticks?

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Sweeping Hands

Stage: 2 Challenge Level: Challenge Level:1

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.

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Chippy's Journeys

Stage: 2 Challenge Level: Challenge Level:1

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

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Nine-pin Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Triangles All Around

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Triangle Pin-down

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Triangles in Circles

Stage: 3 Challenge Level: Challenge Level:1

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?

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Subtended Angles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Right Angles

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Pegboard Quads

Stage: 4 Challenge Level: Challenge Level:1

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?

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Sine and Cosine for Connected Angles

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Figure of Eight

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

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Octa-flower

Stage: 5 Challenge Level: Challenge Level:1

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?

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Cubestick

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Walls

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.