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Worksheet generator
Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
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1.A 3 by 3 board is drawn. How many 2 by 2 squares can be found on it, if they must line up with the grid?[3]
Text description of the figure
A square board divided into a 3 by 3 arrangement of nine equal small squares.
A1
B2
C4
D6
E9
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.The L-shaped figure is made of unit squares. What is its perimeter?[3]
Text description of the figure
An L-shaped figure made of unit squares: a vertical column 3 squares tall and 1 square wide, with 2 extra squares attached along the bottom to the right, so the shape covers 5 unit squares in total.
A5
B10
C12
D14
E16
4.Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
A10
B14
C16
D20
E24
5.What is 1 + 2 + 3 + ... + 20?[3]
A190
B200
C210
D220
E420
6.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
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.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
9.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
10.Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?[5]
A0
B1
C2
D3
Eit cannot be decided
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 9 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
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-0001Counting by position (sliding window)
AI split the board into separate 2 by 2 blocks and only one whole block fitted, so I answered one.
BI slid the square across the top row and found two positions, then forgot it can also move down.
DI counted the four sliding positions and then added the two whole rows of the board as well.
EI counted the nine small squares on the board instead of the 2 by 2 squares.
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 — 12KA-0013Perimeter and area of rectilinear shapes
AI counted the unit squares that make up the shape, which is the area rather than the perimeter.
BI walked around the outline but skipped the two short steps at the inner corner.
DI added the perimeters of the two rectangles the shape is made of, counting the shared edge twice.
EI counted the edges of all five unit squares, which counts every internal edge as well.
4.C — 16KA-0050Working backwards
AI added the 4 and the 6 and stopped, forgetting to undo the halving.
BI doubled the 6 first and then added the 4, reversing the steps in the wrong order.
DI doubled the total at the end rather than doubling only the amount left after the first spend.
EI doubled twice because spending half felt like it needed undoing more than once.
5.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.
6.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.
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.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.
9.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.
10.B — 1KA-0017Truth-tellers and liars
AI assumed everyone could be lying at once without checking that Cal's statement would then be true.
CI found one consistent truth-teller and added another without testing whether both could hold together.
DI assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.
EI gave up after one assumption led to a contradiction, instead of trying the other assumption.