Pinboard Task

Task 1 Task 2 Task 3 Task 4

Task 5 Task 6 Task 7

NC Level 3 to 8

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Pinboard Task 1

Take it in turns to add a band to the board to make any of the shapes you are allowing.A band can share a peg with other bands, but the shapes must not overlap (except along the edges and pegs).

A player loses when they cannot make a shape on their turn.

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http://nrich.maths.org/2872

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Pinboard Task 2

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

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http://nrich.maths.org/2852

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Pinboard Task 3

How many different triangles can you make which consist of the centre point and two of the points on the edge?

Can you find the angle at the centre point each time?

Can you find the other two angles in each triangle?

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http://nrich.maths.org/2844

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Pinboard Task 4

How many DIFFERENT quadrilaterals can be made by joining the dots on the circle? (There are eight evenly-spaced dots.)

Can you work out the angles of all your quadrilaterals?

http://nrich.maths.org/962

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Pinboard Task 5

Choose two points on the edge of the circle. Call them A and B. Join these points to the centre, C. What is the angle at C?

Join A and B to a point on the edge. Call that point D. What is the angle at D?

What do you notice?

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http://nrich.maths.org/2845

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Pinboard Task 6

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

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http://nrich.maths.org/2847

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Pinboard Task 7

This problem is in two parts. The first part consists of four similar challenges which provide building blocks to help you to solve the final challenge. You could work on them with others, but if you are working on your own, you may not need to attempt all four.Of course, you are welcome to go straight to the Final Challenge!

In this problem, you will be working with cyclic quadrilaterals. A cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. There is an interactivity at the bottom of the page which you can use to create cyclic quadrilaterals.

http://nrich.maths.org/6624