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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > 2D Geometry, Shape and Space > Other polygons

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Pick's Theorem

Stage: 3 Challenge Level: Challenge Level:1

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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Where Are They?

Stage: 2 Challenge Level: Challenge Level:1

Use the isometric grid paper to find the different polygons.

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Flip Your Mat!

Stage: 2 and 3 Challenge Level: Challenge Level:1

What shape and size of drinks mat is best for flipping and catching?

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Shaping It

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

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

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Shapely Lines

Stage: 1 Challenge Level: Challenge Level:1

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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Board Block Challenge

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

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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Watch Those Wheels

Stage: 1 Challenge Level: Challenge Level:1

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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Pentagonal

Stage: 4 Challenge Level: Challenge Level:1

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

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Lafayette

Stage: 2 Challenge Level: Challenge Level:1

What mathematical words can be used to describe this floor covering? How many different shapes can you see inside this photograph?

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From One Shape to Another

Stage: 2

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

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Overlapping Circles

Stage: 2 Challenge Level: Challenge Level:1

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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Kite

Stage: 3 Challenge Level: Challenge Level:1

Derive a formula for finding the area of any kite.

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LOGO Challenge - Following On

Stage: 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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Same Shapes

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

How can these shapes be cut in half to make two shapes the same shape and size? Can you find more than one way to do it?

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Playground Snapshot

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

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Icosagram

Stage: 3 Challenge Level: Challenge Level:1

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

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Star Gazing

Stage: 4 Challenge Level: Challenge Level:1

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.