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Math Kangaroo practice

Name: ______________________Date: ____________9 questions · 32 points

1.Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
- Aodd, 47
- Bodd, 49
- Ceven, 48
- Deven, 49
- Eodd, 45
2.On the number line shown, the marks are equally spaced. What number does the arrow point to?[3]
Text description of the figure
A number line with equally spaced tick marks. The leftmost tick is labelled 0 and the rightmost is labelled 60, with five unlabelled ticks evenly spaced between them. An arrow points to the fourth tick from the left.
- A4
- B24
- C30
- D40
- E50
3.In the number 4073, what is the value of the digit 7?[3]
- A3
- B7
- C70
- D700
- E4000
4.What is 1 + 2 + 3 + ... + 20?[3]
- A190
- B200
- C210
- D220
- E420
5.Each shape stands for a whole number. A triangle plus a triangle plus a triangle is 12, and a triangle plus a square is 9. What is the square?[3]
- A3
- B4
- C5
- D6
- E8
6.The four-digit number 27_4 is divisible by 3. Which digit could go in the gap?[4]
- A1
- B2
- C3
- D4
- E6
7.The two digits of a number are swapped and the number gets bigger by 36. Which of these could be the number?[4]
- A13
- B15
- C24
- D41
- E62
8.Which of these numbers can be divided exactly by both 4 and 9?[4]
- A96
- B117
- C132
- D144
- E153
9.How many two-digit numbers have both of their digits odd?[5]
- A10
- B20
- C25
- D45
- E50

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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 — odd, 49KA-0002Parity of numbers (odd/even behavior)
- AI decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.
- CI paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.
- DI added correctly but then labelled 49 as even because I had already decided the pairs would make it even.
- EI added only the first six numbers and stopped before including the thirteen.
2.C — 30KA-0006Number lines and betweenness
- AI counted the tick marks and gave the position number instead of reading the value on the scale.
- BI worked out that each gap is worth 10 but then counted only as far as the tick before the arrow.
- DI counted the tick marks rather than the gaps between them, so every gap came out one step too small.
- EI counted the gaps from the right-hand end instead of from zero.
3.C — 70KA-0055Place value and digit positions
- AI gave the last digit of the number instead of looking at the 7 at all.
- BI gave the digit itself rather than what it is worth in the position it sits in.
- DI counted the positions from the left, so I read the 7 as being in the hundreds place.
- EI gave the value of the largest digit instead of the value of the 7.
4.C — 210KA-0057Clever regrouping (pair to round numbers)
- AI paired the numbers from the outside in but left the 20 out of every pair, so I added only up to 19.
- BI estimated the total as a round number instead of working it out.
- DI used eleven pairs of 20 instead of ten pairs of 21.
- EI multiplied 20 by 21 and forgot that pairing counts every number twice.
5.C — 5KA-0061Operation puzzles and cryptarithms
- AI solved for the triangle and gave that instead of the square.
- BI found the triangle is 4 and gave that number, without going on to the second equation.
- DI halved the 12 instead of dividing it by the three triangles.
- EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.
6.B — 2KA-0011Divisibility rules: 2, 3, 4, 5, 9, 10
- AI added the known digits to get 13 and then checked whether the missing digit itself was a multiple of 3.
- CI chose 3 because the question mentioned dividing by 3, without testing the digit sum at all.
- DI tested the last two digits, which is the rule for 4, not the rule for 3.
- EI added the digits but left out the 4 at the end, so my sum was four too small.
7.B — 15KA-0056Place value and digit positions
- AI checked that the digits differ and stopped, without working out how much the swap actually changes the number.
- CI saw a difference of 2 between the digits and expected that to give a change of 36.
- DI ignored the direction: swapping this number makes it smaller, not bigger.
- EI picked a number whose digits differ by 4 without noticing that the larger digit is already in front.
8.D — 144KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10
- AI checked that it divides by 4 and stopped without testing the 9.
- BI checked the digit sum for 9 and stopped without testing the 4.
- CI saw an even number with a digit sum of 6 and treated 6 as good enough for 9.
- EI tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.
9.C — 25KA-0135Digit-constraint puzzles
- AI counted the odd numbers in one row of ten and treated that as the whole answer.
- BI used four odd digits instead of five, forgetting that 9 is odd.
- DI counted every two-digit number that is itself odd, which only fixes the last digit.
- EI let the first digit be any of ten values rather than only the five odd ones.

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