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Math Kangaroo practice

Name: ______________________Date: ____________6 questions · 23 points

1.The first three patterns are made of dots and follow a rule. How many dots will the fifth pattern have?[3]
Text description of the figure
Three dot patterns in a row. The first has one column of 2 dots with a single dot above it, making 3. The second has two columns of 2 dots with a single dot above, making 5. The third has three columns of 2 dots with a single dot above, making 7.
- A9
- B10
- C11
- D13
- E14
2.A pattern of tiles repeats: black, black, white. What colour is the 100th tile?[3]
- Ablack
- Bwhite
- Cit depends where you start counting
- Dgrey, because the pattern breaks
- Ethere is no 100th tile
3.Beads are threaded in the repeating order red, green, blue, yellow. What colour is the 30th bead?[4]
- Ared
- Bgreen
- Cblue
- Dyellow
- Eit depends where you start
4.Each row of a grid starts 3 more than the row above. Each cell is 1 more than the one to its left. The top-left cell is 1. What is in row 4, column 3?[4]
Text description of the figure
A grid four rows by four columns. The first row reads 1, 2, 3, 4 and the second row reads 4, 5, 6, 7. The remaining rows are blank, and the cell in row 4, column 3 is shaded.
- A9
- B10
- C12
- D13
- E15
5.A staircase of blocks has 4 blocks in the first step, 7 in the second and 10 in the third. How many blocks are in the eighth step?[4]
- A22
- B24
- C25
- D28
- E32
6.Squares of dots grow: 1 dot, then 4, then 9, then 16. How many dots are in the seventh square?[5]
- A25
- B36
- C42
- D49
- E64

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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 — 11KA-0008Continuing a visual pattern
- AI continued the pattern to the fourth stage and stopped one stage early.
- BI counted only the columns of two and forgot the single dot sitting on top of each pattern.
- DI continued the pattern one stage too far and gave the sixth pattern instead of the fifth.
- EI doubled the third pattern's count, assuming the pattern doubles rather than grows by a fixed amount.
2.A — blackKA-0108Repeating cycles and position mod n
- BI got a remainder of 1 but read the last colour of the repeat rather than the first.
- CI thought the pattern had no fixed first tile, even though tile one is given.
- DI assumed a repeating pattern must eventually change.
- EI assumed the pattern runs only for as many tiles as one repeat contains.
3.B — greenKA-0014Repeating cycles and position mod n
- AI got a remainder of 2 but started counting the colours at zero, which shifted me back one bead.
- CI counted the seven whole repeats and then counted three more beads instead of two.
- DI divided 30 by 4, got 7 remainder 2, and used the last colour of a repeat as though the remainder were zero.
- EI thought the repeating pattern had no fixed starting point, even though bead one is given.
4.C — 12KA-0105Patterns in tables and grids
- AI stopped at row 3, taking two steps down from the top instead of three.
- BI found where row 4 starts but forgot to move across to the third column.
- DI moved three columns across instead of two, counting columns rather than steps between them.
- EI took four steps of 3 downwards instead of three, counting rows rather than the gaps between them.
5.C — 25KA-0109Arithmetic sequences and the nth term
- AI added the step of 3 six times instead of seven, stopping at the seventh step.
- BI multiplied 3 by 8 without adding the first step's blocks.
- DI multiplied the step of 3 by 8 and added 4, taking one step too many.
- EI multiplied the first step's 4 blocks by the step number instead of following the pattern.
6.D — 49KA-0138Growth patterns and figurate numbers
- AI continued the pattern to the fifth square instead of the seventh.
- BI stopped one square short, giving the sixth instead of the seventh.
- CI added 6 to the sixth square's 36, treating the differences as constant.
- EI continued one square too far and gave the eighth.

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