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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.A net of six squares folds into a cube. One square is shaded. Which square ends up opposite the shaded one?[4]
Text description of the figure
A net of six squares in a cross shape: a vertical column of four squares labelled 1, 2, 3, 4 from the top, with square 5 attached to the left of square 2 and square 6 attached to the right of square 2. Square 1 is shaded.
- Asquare 2
- Bsquare 3
- Csquare 4
- Dsquare 5
- Esquare 6
2.On a standard die opposite faces add to 7. Two dice are stacked. The touching faces show 3 on the upper die and 5 on the lower. What number is on the bottom face?[4]
- A1
- B2
- C3
- D4
- E5
3.A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?[4]
Text description of the figure
Two views side by side. The view from above is a solid 2 by 2 square of four cells. The view from the front is a solid 2 by 2 square, so the solid is two columns wide and reaches two cubes high.
- A4
- B5
- C6
- D7
- E8
4.How many lines of symmetry does a regular hexagon have?[4]
- A2
- B3
- C4
- D6
- E12
5.A cube 3 units on each side is built from unit cubes and painted all over the outside. How many of the small cubes have no paint on them at all?[4]
- A0
- B1
- C6
- D8
- E27

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Answer key — Math Kangaroo practice

Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.

1.B — square 3KA-0005Nets and folding, 2D to 3D
- AI picked the square directly next to the shaded one in the net, but neighbours in the net share an edge on the cube.
- CI counted to the far end of the column, assuming the square furthest away in the net is the one opposite.
- DI picked one of the side flaps because it is not touching the shaded square in the drawing.
- EI picked the other side flap for the same reason, without tracking what happens as the net folds.
2.B — 2KA-0016Dice and cube face relationships
- AI used the upper die's touching face instead of the lower one, so I worked from 3 rather than 5.
- CI gave the number on a touching face itself rather than the number opposite it.
- DI subtracted 3 from 7 because I confused which die was sitting on which.
- EI gave the lower die's upward face, which is the number I was told, not the hidden one underneath.
3.C — 6KA-0081Views of a solid: top, front, side
- AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
- BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
- DI added an extra cube that neither view requires.
- EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.
4.D — 6KA-0085Line and rotational symmetry
- AI checked only the vertical and horizontal folds and stopped there.
- BI counted the lines through opposite corners and forgot the ones through opposite edges.
- CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
- EI counted each line twice, once from each end.
5.B — 1KA-0089Building and counting with unit cubes
- AI assumed every small cube touches the outside somewhere.
- CI counted the cubes at the centre of each face, which are painted on one side.
- DI counted the corner cubes, which are the most painted rather than the least.
- EI gave the total number of small cubes instead of the unpainted ones.

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