Worksheet generator

1.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.

2.D — ThursdayKA-0021Remainders and modular cycles

• AI found the remainder 2 but counted the two days starting from today rather than starting from tomorrow.
• BI divided 100 by 7 and used the quotient of 14, treating the leftover days as if there were none.
• CI remembered there was a remainder but used a remainder of 1 instead of working it out.
• EI counted 100 divided by 7 as 14 remainder 3 instead of remainder 2.

3.E — 60KA-0026Percentages and simple discounts

• AI worked out the size of the discount and gave that as the new price instead of subtracting it.
• BI treated a quarter off as half off and took the price down to 40.
• CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
• DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.

4.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing

• AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
• BI added the two intervals together rather than looking for a time that is a multiple of both.
• DI found a common multiple but not the least one, landing on a later coincidence.
• EI multiplied the two intervals together instead of finding their least common multiple.

5.C — 70KA-0055Place value and digit positions

• AI gave the last digit of the number instead of looking at the 7 at all.
• BI gave the digit itself rather than what it is worth in the position it sits in.
• DI counted the positions from the left, so I read the 7 as being in the hundreds place.
• EI gave the value of the largest digit instead of the value of the 7.

6.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.

7.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.

8.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.

9.C — 4KA-0161Remainders and modular cycles

• AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
• BI used a remainder of 1 rather than 2 when dividing 50 by 3.
• DI doubled my way to 2 cubed = 8 and used 8 minus 2.
• EI assumed a large power of 2 must eventually be divisible by 7.

10.A — 1KA-0169Remainders and modular cycles

• BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
• CI read the cycle backwards and landed on the entry before the right one.
• DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
• EI assumed a power that large must be divisible by 5.

11.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.

12.D — 15KA-0024Ratio as parts of a whole

• AI found what one part is worth and gave that as my answer instead of multiplying it back up.
• BI divided 40 by the five blue parts instead of by the eight parts that make the whole.
• CI read the ratio 3 to 5 as meaning 3 out of every 5 and worked from that.
• EI found the value of one part correctly but then multiplied by 5 instead of 3, giving the blue counters.

13.D — 16KA-0033Means, and working backwards from a mean

• AI subtracted the two means from each other and gave the difference as the removed number.
• BI assumed the removed number must be the new mean, since the mean dropped to 11.
• CI assumed removing a number equal to the old mean is what changes the mean.
• EI added the two totals instead of subtracting one from the other.

14.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.

15.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.

16.D — 2550KA-0058Clever regrouping (pair to round numbers)

• AI found the sum of 1 to 50 and forgot that every term here is twice as big.
• BI used 49 pairs instead of 25, losing one pair from the count.
• CI estimated the answer as a round number rather than pairing properly.
• EI paired the terms but forgot that pairing counts every number twice, so I never halved.

17.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.

18.A — 1KA-0149Last-digit behavior of products and powers

• BI assumed every power of 3 ends in 3.
• CI found the cycle 3, 9, 7, 1 but counted its positions from zero, landing one step early.
• DI used a remainder of 2 instead of 0 when dividing 100 by the cycle length of 4.
• EI assumed a number this large has no reachable last digit, rather than looking for a repeat.

19.D — 12KA-0060Operation puzzles and cryptarithms

• AI added the digits of 132 instead of working out what A and B must be.
• BI found A + B correctly and then halved it, as if the question wanted one digit.
• CI spotted the 11 in the working and gave that instead of the sum it multiplies.
• EI found a pair of digits by trial and misadded them by one.

20.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.