Worksheet generator

1.B — 7KA-0064Fractions of a quantity

• AI divided 28 by 7 instead of taking a quarter of it.
• CI found three quarters of 16 by mistake, mixing up the class size.
• DI found how many did travel by bus and gave that instead of how many did not.
• EI subtracted the 4 quarters as if they were 4 students.

2.C — 750KA-0113Unit conversion

• AI worked in kilograms and gave the answer in kilograms when grams were asked for.
• BI converted 2.5 kg to 250 g rather than 2500 g.
• DI subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.
• EI subtracted without converting at all, taking 2.5 away from 1750.

3.E — 86400KA-0124Estimate to the nearest choice

• AI gave the number of minutes in a day instead of the number of seconds.
• BI gave the number of seconds in one hour rather than in a whole day.
• CI multiplied the 24 hours by a round thousand instead of converting properly.
• DI multiplied 60 by a round thousand, using one conversion and inventing the other.

4.C — 2/5KA-0141Number lines and betweenness

• AI compared the bottom numbers and assumed a bigger denominator means a bigger fraction.
• BI saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.
• DI checked that it is bigger than one third but never checked it against one half.
• EI compared the top numbers only and ignored what the bottoms do to the size.

5.E — Not all birds can flyKA-0146Reading a logical statement precisely

• AI read some cannot as meaning none can, which is a far stronger claim.
• BI chose a statement that directly contradicts the one I was given.
• CI read some as meaning a majority, when it only guarantees at least one.
• DI read some as meaning exactly one, when it means at least one.

6.A — 1KA-0053Remainders and modular cycles

• BI found the cycle 2, 4, 1 but read the remainder of 30 divided by 3 as one instead of zero.
• CI counted the cycle positions from zero, which shifted my answer one step along.
• DI divided 30 by 7 and used that remainder rather than the remainder of the powers.
• EI assumed the remainder would be one less than the divisor because the power is large.

7.B — 15KA-0074Selections of a few objects

• AI doubled the group size instead of counting pairs.
• CI allowed a student to be paired with themselves, adding six impossible pairs.
• DI counted each pair twice, once in each order, and forgot to halve.
• EI multiplied 6 by 6, counting every ordered pair including a student with themselves.

8.C — 18KA-0084Area by dissection and rearrangement

• AI added the two different side lengths without doubling for the opposite pair.
• BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
• DI gave the perimeter of the whole square instead of one of the pieces.
• EI gave the area of the square rather than the perimeter of a piece.

9.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.

10.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.

11.A — 3KA-0116Combined work rates

• BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
• CI halved the slower pipe's time rather than adding the two rates.
• DI averaged the two times, which would only be right if the pipes took turns.
• EI added the two times, which makes two pipes slower than one - an impossible answer.

12.D — 120KA-0148Clock geometry: hands, angles, times

• AI gave the angle for a single hour mark rather than the four marks between the hands.
• BI counted two hour marks instead of four.
• CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
• EI measured the angle the long way round the clock face instead of the smaller one.

13.C — 6KA-0025Counting up to symmetry

• AI also treated bracelets that are mirror images as the same, but only rotations were allowed.
• BI divided the number of beads by itself rather than dividing the number of arrangements by the number of rotations.
• DI divided the 24 arrangements by 2 instead of by the 4 rotations of a circle of four beads.
• EI counted every arrangement in a line and forgot that rotating a bracelet gives the same bracelet.

14.E — 9KA-0037Last-digit behavior of products and powers

• AI assumed a number this large has no reachable last digit and gave up on the cycle.
• BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
• CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
• DI assumed the units digit of any power of 7 is always 7.

15.C — 4KA-0040The pigeonhole principle

• AI answered with the lucky case, where the first two socks happen to match.
• BI used the number of colours as my answer without adding one for the sock that must repeat.
• DI worked from the number of socks of each colour instead of the number of colours.
• EI took the whole drawer, guaranteeing a pair but far more socks than are needed.

16.A — Yes, and many orders workKA-0049Parity of numbers (odd/even behavior)

• BI found one arrangement that works and assumed a problem this fiddly could only have one answer.
• CI saw five odd numbers against four even ones and called that a mismatch, when a row of nine needs exactly five of one and four of the other.
• DI blamed the length of the row rather than checking how many odd and even numbers it has to hold.
• EI decided the first number settles it without checking that starting even would need five even numbers, and only four exist.

17.C — 55KA-0078Extremal / worst-case counting

• AI found the smallest possible total of the other nine and gave that instead of what is left.
• BI assumed the biggest number could be at most half the total.
• DI made the other nine numbers all equal to 1, forgetting that they have to be different from each other.
• EI ignored the other nine numbers entirely, as if the biggest could take the whole total.

18.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.

19.D — No, because the two colours cannot balanceKA-0101Coloring arguments

• AI checked that 100 divides by 4 and treated that as proof that a covering exists.
• BI assumed a covering must exist somewhere and that I simply had not found it yet.
• CI gave a reason that is not even true, since 100 really is a multiple of 4.
• EI thought orientation could rescue it, but every turn of a T covers the same mixture of colours.

20.D — 25KA-0106Inferring a rule from examples

• AI used the rule add 4, which fits the first example but not the others.
• BI found a rule from two examples only and never tested it against the third.
• CI doubled the input and forgot the extra one that every example needs.
• EI used double and add five, which fits none of the examples exactly.