Worksheet generator

1.D — 6KA-0003Counting shapes hidden inside a figure

• AI counted only the three small triangles I could see as separate cells and stopped there.
• BI counted the three small triangles and added the whole big one, but forgot the two made of two cells.
• CI found the three small ones and one pair, but missed the second pair of neighbouring triangles.
• EI assumed every choice of two of the four lines would make a triangle, without checking each one.

2.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.

3.D — 30KA-0007Working backwards

• AI added the 6 and the 9 and stopped, forgetting to undo the halving at the start.
• BI undid the steps in the order they were written instead of reversing the order as well as the operations.
• CI doubled the 9 first and then added the 6, which reverses the steps in the wrong order.
• EI doubled twice because giving half away felt like it should be undone more than once.

4.C — 14KA-0009Counting cubes in a stack, including hidden ones

• AI counted only the cubes on the bottom layer and treated the rest as decoration.
• BI counted only the cubes whose faces I could actually see in the drawing.
• DI assumed every layer was a full 3 by 3 square and multiplied 9 by 2 for two layers.
• EI assumed the stack was a solid 3 by 3 by 3 block because it sits in a corner.

5.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.

6.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.

7.B — 2KA-0016Dice and cube face relationships

• AI used the upper die's touching face instead of the lower one, so I worked from 3 rather than 5.
• CI gave the number on a touching face itself rather than the number opposite it.
• DI subtracted 3 from 7 because I confused which die was sitting on which.
• EI gave the lower die's upward face, which is the number I was told, not the hidden one underneath.

8.C — 16KA-0019Multi-step arithmetic word problems

• AI found what one child has left and gave that instead of the total for all four.
• BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
• DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
• EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.

9.D — 9KA-0046Counting by position (sliding window)

• AI cut the board into four separate 2 by 2 blocks instead of sliding the square one step at a time.
• BI counted the three sliding positions along the top and doubled them for two rows.
• CI counted the positions along the top row and down the left column and added them.
• EI counted the sixteen small squares on the board rather than the 2 by 2 squares.

10.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.

11.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.

12.B — 3KA-0068Tree diagrams

• AI read the two in exactly two heads as the answer rather than as a condition to count.
• CI counted the outcomes with two or more heads, so I included the three-head one as well.
• DI counted the orderings of three different objects instead of listing the eight outcomes.
• EI gave the total number of possible outcomes rather than the number with exactly two heads.

13.A — 3KA-0076Casework

• BI included 0 and 7 as a pair, even though both numbers have to be bigger than zero.
• CI counted both orders of each pair, even though swapping does not make a new way.
• DI counted every starting number from 1 to 7 without checking which pairs repeat.
• EI counted both orders and also allowed pairs of equal numbers.

14.C — 6KA-0081Views of a solid: top, front, side

• AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
• BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
• DI added an extra cube that neither view requires.
• EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.

15.D — 6KA-0085Line and rotational symmetry

• AI checked only the vertical and horizontal folds and stopped there.
• BI counted the lines through opposite corners and forgot the ones through opposite edges.
• CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
• EI counted each line twice, once from each end.

16.B — 1KA-0089Building and counting with unit cubes

• AI assumed every small cube touches the outside somewhere.
• CI counted the cubes at the centre of each face, which are painted on one side.
• DI counted the corner cubes, which are the most painted rather than the least.
• EI gave the total number of small cubes instead of the unpainted ones.

17.C — CalKA-0091Elimination grids

• AI used Bo's clue and forgot the very first clue, which rules Ana out directly.
• BI read Bo's clue as telling me what Bo has rather than what Bo does not have.
• DI stopped after using each clue once, without going back to see what the ticks had ruled out.
• EI applied Bo's clue but never came back to Ana's, so I left two people in the running.

18.B — 60KA-0093Weighing and balance puzzles

• AI halved the apple's weight, as if one apple balanced two pears.
• CI assumed a pear must weigh the same as an apple because the two sides balance.
• DI multiplied the apple's weight by three halves the wrong way round, making the pear heavier.
• EI gave the total weight of the two apples rather than the weight of one pear.

19.B — Bo onlyKA-0096Truth-tellers and liars

• AI took Ana's statement at face value without checking whether a truthful person could say it.
• CI decided nobody was lying without testing Ana's statement against that assumption.
• DI believed Ana's statement even after concluding she was a liar, which is what a liar's statement cannot be.
• EI gave up when Ana's statement looked circular, instead of testing one assumption all the way through.

20.B — Box X is not redKA-0099Reading a logical statement precisely

• AI read the rule backwards, as if being heavy were what makes a box red.
• CI assumed not red must mean one particular other colour, when the rule says nothing about which.
• DI contradicted the rule I was given rather than applying it to box X.
• EI decided one fact could not settle anything, without testing what would follow if X were red.

21.A — Yes, alwaysKA-0102Informal proof by contradiction

• BI found one pair that works and assumed the argument depended on that particular card.
• CI tried a couple of selections, did not find a pair, and stopped looking.
• DI looked for a pattern in the numbers rather than at how many pairs there are to avoid.
• EI thought the answer depended on which six were taken, when the counting settles it for every choice.

22.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.

23.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.

24.B — 21.5KA-0115Multi-step arithmetic word problems

• AI halved the 60 pencils before giving any away.
• CI subtracted 17 from one box of 12 rather than from the whole 60.
• DI gave the number of pencils left over rather than what each child gets.
• EI gave the starting number of pencils without doing either of the steps.

25.B — 7KA-0131Back-solve from the answer choices

• AI tested the first choice, got 13, and picked it anyway because it was close.
• CI added the 3 to 17 instead of subtracting it, then halved the 20 that gave me.
• DI subtracted 3 from 17 and gave that without halving it.
• EI added 3 to 17 instead of undoing the addition by subtracting it.

26.D — 21KA-0132Eliminate impossible choices by bounding

• AI did not try one five and four twos, so I judged this total impossible.
• BI missed the combination of two fives and three twos.
• CI stopped listing after two fives and never reached three fives and two twos.
• EI forgot the case where every coin is a five, which is allowed by the wording.

27.B — 9KA-0150Try small cases first

• AI counted one diagonal from each corner and stopped there.
• CI counted three diagonals from each corner but forgot that each one gets counted from both ends.
• DI counted every line joining two corners, including the six sides.
• EI multiplied six corners by three diagonals each and never halved.