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

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Spokes

Stage: 5 Challenge Level: Challenge Level:1

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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What Shape and Colour?

Stage: 1 Challenge Level: Challenge Level:1

Can you fill in the empty boxes in the grid with the right shape and colour?

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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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Egyptian Rope

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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Hex

Stage: 3 Challenge Level: Challenge Level:1

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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Round and Round the Circle

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Sweets in a Box

Stage: 2 Challenge Level: Challenge Level:1

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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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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Tessellation Interactivity

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

An environment that enables you to investigate tessellations of regular polygons

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Lighting up Time

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

A very mathematical light - what can you see?

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Two Regular Polygons

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

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

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LOGO Challenge 11 - More on Circles

Stage: 3 and 4 Challenge Level: Challenge Level:1

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

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First Forward Into Logo 2: Polygons

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

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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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Shuffles

Stage: 5 Challenge Level: Challenge Level:1

An environment for exploring the properties of small groups.

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Shedding Some Light

Stage: 2 Challenge Level: Challenge Level:1

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

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The Dodecahedron

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

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

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Dodecawhat

Stage: 4 Challenge Level: Challenge Level:1

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

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LOGO Challenge 9 - Overlapping Polygons

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

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Shapes on the Playground

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

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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Cube Paths

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

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

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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.

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Hexagon Transformations

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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Part the Polygons

Stage: 2 Short Challenge Level: Challenge Level:1

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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Bracelets

Stage: 2 Challenge Level: Challenge Level:1

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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Clock Hands

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

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.