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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 19 points

1.Which of these arrangements of six squares cannot be folded into a closed cube?[3]
Text description of the figure
Four arrangements of six squares labelled A to D. A is a T shape, B is a straight line of six squares, C is a staircase of pairs, and D is a cross with a column of four and one square on each side.
- Athe T shape
- Bthe straight line of six
- Cthe staircase
- Dthe cross
- Ethey all fold
2.Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
- AA
- BB
- CH
- DT
- EZ
3.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
- A3 times
- B6 times
- C9 times
- D12 times
- E27 times
4.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
- A30
- B60
- C90
- D120
- E240
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.B — the straight line of sixKA-0048Nets and folding, 2D to 3D
- AI assumed any arrangement that is not a simple line must fail to fold.
- CI thought a staircase would overlap when folded, without tracking a single face through the fold.
- DI picked the cross because it looks unusual, even though it is the most familiar cube net there is.
- EI checked that each arrangement had six squares and assumed six squares is enough.
2.C — HKA-0142Line and rotational symmetry
- AI found the vertical fold and assumed a horizontal one must work too.
- BI found the horizontal fold and stopped without testing the vertical one.
- DI counted the vertical fold twice rather than testing a horizontal one.
- EI mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.
3.C — 9 timesKA-0042Scaling and similar figures
- AI applied the length scale factor straight to the area.
- BI doubled the scale factor because area involves two dimensions, instead of squaring it.
- DI multiplied the scale factor by four, as though area scaled with the number of sides.
- EI cubed the scale factor, which is the rule for volume rather than area.
4.D — 120KA-0148Clock geometry: hands, angles, times
- AI gave the angle for a single hour mark rather than the four marks between the hands.
- BI counted two hour marks instead of four.
- CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
- EI measured the angle the long way round the clock face instead of the smaller one.
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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