There are **18** NRICH Mathematical resources connected to **Sets of shapes**, you may find related items under Physical and Digital Manipulatives.

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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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Here are shadows of some 3D shapes. What shapes could have made them?

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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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How many different shapes can you make by putting four right- angled isosceles triangles together?

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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Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

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On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

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

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You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

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A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

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You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

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Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

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

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This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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How can you put five cereal packets together to make different shapes if you must put them face-to-face?