Worksheet generator

1.C — 12KA-0062Factors, multiples, LCM and GCD by listing

• AI found a number that divides both but not the largest one, stopping at the first that worked.
• BI used the difference between 36 and 24 divided by 2 rather than a common factor.
• DI used a factor of 36 without checking that it also divides 24.
• EI found the least common multiple instead of the greatest common divisor.

2.B — 8KA-0100Working backwards

• AI undid the operations in the order they were written instead of in reverse order.
• CI gave the final answer back, assuming the three steps cancelled each other out.
• DI doubled the 11 and subtracted the 6 but forgot the final halving that undoes the doubling.
• EI undid only the halving and stopped there without touching the other two steps.

3.C — 65KA-0103Recursive rules

• AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
• BI generated one term too few, giving the fifth term instead of the sixth.
• DI doubled six times and subtracted 1 only once at the end.
• EI generated one term too many, giving the seventh instead of the sixth.

4.C — 55KA-0107Growth patterns and figurate numbers

• AI stopped at the eighth triangle, losing count while adding the rows.
• BI gave the ninth triangle instead of the tenth, being one row short.
• DI gave the eleventh triangle, adding one row too many.
• EI squared the position number, which describes square patterns rather than triangular ones.

5.B — 4KA-0111Age problems

• AI aged only the child and left the mother's age unchanged.
• CI looked for when the mother is four times as old rather than three times.
• DI used the age difference of 24 and halved it, without checking the ratio it gives.
• EI gave the difference between their ages, which never changes, instead of a number of years.

6.D — 1200KA-0128Check units and re-read before bubbling

• AI worked entirely in metres and gave the answer in square metres.
• BI multiplied 30 by 0.4 without converting the metres to centimetres at all.
• CI converted 0.4 m to 4 cm rather than 40 cm.
• EI converted 0.4 m to 400 cm, moving the decimal point one place too far.

7.E — 408KA-0129Sanity-check with a second method

• AI worked out 17 times 20 and forgot to add the 17 times 4 part.
• BI worked out 17 times 4 as 28 instead of 68 when adding the parts together.
• CI worked out 17 times 4 as 48 instead of 68 when adding the parts together.
• DI made a carrying slip of ten in the final addition of the two parts.

8.C — 7KA-0077The pigeonhole principle

• AI answered with the luckiest case, where the first three balls happen to match.
• BI found the worst case of two of each colour and forgot to take one more.
• DI multiplied the three colours by the three balls I need, rather than thinking about the worst case.
• EI worked from the number of balls of each colour rather than from the number of colours.

9.B — 2KA-0094Weighing and balance puzzles

• AI assumed one weighing could separate nine possibilities, but it has only three outcomes.
• CI split the coins into halves each time, which wastes the balance's third outcome.
• DI weighed the coins one against another in pairs rather than in groups.
• EI compared each coin with a known good one in turn, which always works but is nowhere near the fewest.

10.D — No, because the number of moves is oddKA-0097Parity arguments

• AI assumed enough moves can undo anything, without asking what each move preserves.
• BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
• CI reached for the number of items rather than for what a single swap actually changes.
• EI thought the choice of swaps could change the outcome, when every swap has the same effect.