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5 on the sheet, 5 match these filtersReshuffle Start overseed 1

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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 25 points

1.A square sheet is folded in half top to bottom, then in half left to right. One hole is punched through all the layers. How many holes are in the unfolded sheet?[5]
Text description of the figure
Three steps in a row: a square sheet, the same sheet folded in half top to bottom into a wide rectangle, and that rectangle folded in half left to right into a small square with a single punched hole near its centre.
- A1
- B2
- C4
- D6
- E8
2.A circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?[5]
Text description of the figure
A square with a circle drawn inside it, the circle touching the midpoint of each of the four sides. The region inside the square but outside the circle is shaded.
- A0.1
- B0.2
- C0.3
- D0.5
- E0.8
3.A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?[5]
Text description of the figure
The floor of a room, 8 metres by 4 metres, drawn flat, with one 8-metre-by-2-metre wall unfolded upwards from its far edge. A straight line joins the ant's starting corner on the floor to the opposite corner on the unfolded wall.
- A9.2
- B10
- C11
- D12
- E14
4.A square sheet is folded in half, then in half again. Two holes are punched through all the layers. How many holes are there when it is unfolded?[5]
- A2
- B4
- C6
- D8
- E16
5.On a die, opposite faces add to 7. A die rests on a table with 3 on top. What do the four side faces add up to?[5]
- A10
- B12
- C14
- D17
- E18

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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.C — 4KA-0020Paper folding and hole punching
- AI forgot that the punch goes through every layer at once, not just the top one.
- BI undid only one of the two folds before counting the holes.
- DI doubled for the first fold and then added two more rather than doubling a second time.
- EI counted a fold that was never made, doubling three times instead of twice.
2.B — 0.2KA-0052Area by subtraction (shaded regions)
- AI estimated by eye from the four corner pieces without comparing them to the whole square.
- CI used a diameter of 5 instead of a radius of 5 when working out the circle's area.
- DI assumed the circle covers half the square because it touches all four sides.
- EI found the fraction covered by the circle and gave that instead of the fraction outside it.
3.B — 10KA-0082Shortest paths on and around shapes
- AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
- CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
- DI chose an unfolding that gives a longer straight line and did not compare it with the others.
- EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.
4.D — 8KA-0134Paper folding and hole punching
- AI forgot that the punch goes through every layer, not just the top one.
- BI undid only one of the two folds before counting.
- CI doubled twice for the folds but added the second hole instead of doubling for it too.
- EI counted three folds instead of two, doubling one time too many.
5.C — 14KA-0139Dice and cube face relationships
- AI subtracted only the top face from 21, forgetting the hidden bottom face as well.
- BI guessed four middling numbers and added them without using the total of all six faces.
- DI subtracted only the bottom face of 4 from the total of 21.
- EI added the four largest numbers on the die rather than the four that are actually at the sides.

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