Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 How many faces does a cube have, and so how many squares are in its net?
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6.
2 A net is a square with a triangle on each side. Write how many triangles it has, and how many faces the finished solid has.
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4 triangles and 5 faces — a square pyramid.
3 How many triangles are in the net of a hexagonal pyramid?
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6.
Level 2 · Core
4 This net folds into a cube. Which face ends up opposite B?
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Going round the band A, B, C, D, the face two along from B is D.
5 In the same net, write the face opposite T and the face opposite C.
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T is opposite U, and C is opposite A.
6 A net has two identical triangles and three rectangles. How many faces does the solid it makes have?
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2 + 3 = 5 faces — a triangular prism.
Level 3 · Challenge
7 Think about a straight strip of six squares in a row.1 It has the right number of squares for a cube.
2 It folds into a cube.
3 Folding it makes two squares overlap.
Which statements are correct?
2 It folds into a cube.
3 Folding it makes two squares overlap.
Which statements are correct?
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Six squares is the right count (1 ✓), but the strip wraps round and the ends land on each other, so it does not fold into a cube (3 ✓, 2 ✗). 1 and 3.
8 A net is made of one hexagon and six triangles. Write the number of faces of the solid, and the number of its vertices.
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7 faces and 7 vertices.
9 A cube net is a band of four squares with one cap already placed above the band. How many different positions are there for the last square?
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It can sit below any of the four columns of the band: 4 positions.