List

Being Resilient - Geometry

Nine Colours
problem
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Nine Colours

Age
11 to 16
Challenge level
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Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Triangles to Tetrahedra
problem
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Triangles to Tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Reflecting Squarely
problem
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Reflecting Squarely

Age
11 to 14
Challenge level
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In how many ways can you fit all three pieces together to make shapes with line symmetry?
Cuboids
problem
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Cuboids

Age
11 to 14
Challenge level
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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Same length
problem
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Same length

Age
11 to 16
Challenge level
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Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Isosceles Triangles
problem
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Isosceles Triangles

Age
11 to 14
Challenge level
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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Kite in a Square
problem
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Kite in a Square

Age
14 to 18
Challenge level
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Can you make sense of the three methods to work out what fraction of the total area is shaded?