Worksheet generator

1.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.

2.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.

3.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.

4.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.

5.D — 4320KA-0059Estimation and order of magnitude

• AI worked out the drips in an hour and stopped there.
• BI multiplied by the 24 hours but forgot the 60 minutes in each one.
• CI used 6 hours in a day, thinking of waking hours rather than a whole day.
• EI used 600 minutes in an hour rather than 60.

6.C — 5KA-0061Operation puzzles and cryptarithms

• AI solved for the triangle and gave that instead of the square.
• BI found the triangle is 4 and gave that number, without going on to the second equation.
• DI halved the 12 instead of dividing it by the three triangles.
• EI subtracted the wrong way round, taking 9 from a number instead of taking the triangle from 9.

7.C — 200 gKA-0151Ratio as parts of a whole

• AI worked out the part size correctly and then answered for the sugar instead of the flour.
• BI split the 320 grams into two halves instead of into eight equal parts.
• DI took three fifths of 320 rather than five eighths, using the ratio numbers as a fraction of each other.
• EI divided 320 by the 5 in the ratio and stopped, treating 5 as the number of parts.

8.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.

9.B — 4% lowerKA-0065Percentages and simple discounts

• AI applied only the decrease and forgot that the price had already risen.
• CI assumed a rise and a fall of the same percentage cancel each other out exactly.
• DI got the size of the change right but the direction wrong.
• EI added the two percentages together instead of applying them one after the other.

10.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.