Construction - September 2005, All Stages

Problems

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Chairs and Tables

Stage: 1 Challenge Level: Challenge Level:1

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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Mrs Trimmer's String

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

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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Complete the Square

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Complete the squares - but be warned some are trickier than they look!

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Dotty Relationship

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

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

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Stringy Quads

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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Yin Yang

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

Can you reproduce the Yin Yang symbol using a pair of compasses?

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Keep Your Distance

Stage: 3 Challenge Level: Challenge Level:1

Can you mark 4 points on a flat surface so that there are only two different distances between them?

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Property Chart

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

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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Shapely Pairs

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

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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Three Tears

Stage: 4 Challenge Level: Challenge Level:1

Construct this design using only compasses

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Triangle in a Triangle

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

Can you work out the fraction of the original triangle that is covered by the inner triangle?

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Half a Triangle

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

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

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Trig Rules OK

Stage: 5 Challenge Level: Challenge Level:1

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...

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Pentabuild

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

Explain how to construct a regular pentagon accurately using a straight edge and compass.

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Vecten

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

Join in this ongoing research. Build squares on the sides of a triangle, join the outer vertices forming hexagons, build further rings of squares and quadrilaterals, investigate.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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