Worksheet generator

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 — 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.

4.B — 3 centsKA-0010Money and change

• AI found the smallest amount that cannot be made rather than the largest one.
• CI did not notice that 7 is 2 plus 5, so I marked it as impossible without testing it.
• DI only tried using coins of one kind at a time and never mixed the two denominations.
• EI assumed odd amounts are impossible because one of the coins is even.

5.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.

6.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.

7.C — 14KA-0051Complementary counting

• AI counted the multiples of 3 and gave that instead of the numbers that are not multiples.
• BI counted 21 as a multiple of 3 inside the range, so I removed one too many.
• DI removed only the multiples of 3 that are also even, so I subtracted three instead of six.
• EI gave the size of the whole range and forgot to remove anything at all.

8.C — 9KA-0072Systematic listing

• AI counted only the numbers with two identical digits, like 11, 22 and 33.
• BI required the two digits to be different, even though repeats are allowed.
• DI allowed a fourth digit that was not in the list.
• EI counted three-digit numbers instead of two-digit ones.

9.D — 55KA-0118Reading tables, charts, and graphs

• AI read the axis as going up in ones and added the gridline heights instead of the values.
• BI gave the tallest bar rather than the total of all four.
• CI added only three of the four bars, missing the shortest one.
• EI read the shortest bar as 10 rather than 5, because the axis steps in fives.

10.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.

11.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.

12.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.

13.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.

14.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.

15.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.

16.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.

17.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.

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.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.

21.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.

22.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.

23.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.

24.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.

25.D — 19KA-0018Complementary counting

• AI counted the codes that avoid 3 entirely and gave that as my answer without subtracting.
• BI counted the codes with a 3 in the first position only and forgot the other two positions.
• CI counted the codes with exactly one 3 and forgot the ones with two or three of them.
• EI counted every possible code and forgot to remove the ones with no 3 at all.

26.E — 14KA-0133Counting shapes hidden inside a figure

• AI counted the nine small squares and stopped, missing every larger one.
• BI counted the small squares and the whole board, forgetting the middle size entirely.
• CI found the 2 by 2 squares by splitting the board into blocks, getting two instead of four.
• DI slid the 2 by 2 square across and down but missed one of its four positions.

27.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.

28.D — DeeKA-0136Ordering and ranking from clues

• AI ignored the very first clue, which rules Ana out of the front directly.
• BI put Bo at the front, but Bo must have Ana immediately in front of him.
• CI forgot that Cal is fixed at the back of the line.
• EI stopped once two arrangements seemed possible, without testing whether the second one actually fits every clue.

29.C — 750KA-0137Multi-step arithmetic word problems

• AI poured out half instead of a third and then forgot to add the 150 ml back.
• BI poured out the third correctly but never added the 150 ml.
• DI assumed the 150 ml added back was the same as the amount poured out, so nothing changed.
• EI added the 150 ml to the full jug without pouring anything out first.

30.C — 4KA-0140The multiplication principle

• AI counted the codes that do start with A rather than the ones that do not.
• BI counted the letters available for the first position instead of counting whole codes.
• DI counted every arrangement of the three letters and forgot the restriction.
• EI allowed letters to repeat, which the words each exactly once rule out.