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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 > Equilateral triangles

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Can You Explain Why?

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

Can you explain why it is impossible to construct this triangle?

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Cut it Out

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

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Of All the Areas

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

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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Chain of Changes

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

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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Colouring Triangles

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

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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Sorting Logic Blocks

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

This interactivity allows you to sort logic blocks by dragging their images.

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Jig Shapes

Stage: 1 Challenge Level: Challenge Level:1

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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Logic Block Collections

Stage: 1 Challenge Level: Challenge Level:1

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

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Sorting Shapes

Stage: 1 Challenge Level: Challenge Level:1

This activity challenges you to make collections of shapes. Can you give your collection a name?

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Shaping Up

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

What do these two triangles have in common? How are they related?

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Triangle Shapes

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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Impossible Triangles?

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

Which of these triangular jigsaws are impossible to finish?

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The Square Hole

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

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

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Equal Equilateral Triangles

Stage: 4 Challenge Level: Challenge Level:1

Using the interactivity, can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

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Overlapping Again

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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Making Maths: Equilateral Triangle Folding

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

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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Triangular Hexagons

Stage: 2 Challenge Level: Challenge Level:1

Investigate these hexagons drawn from different sized equilateral triangles.

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Tessellating Transformations

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

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

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Gold Yet Again

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

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

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Triangle Animals

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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Posting Triangles

Stage: 1 Challenge Level: Challenge Level:1

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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LOGO Challenge 6 - Triangles and Stars

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

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

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LOGO Challenge 5 - Patch

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

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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Tri-five

Stage: 2 Challenge Level: Challenge Level:1

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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Six to Four

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

Move four sticks so there are exactly four triangles.


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