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 — 6KA-0054Counting shapes hidden inside a figure

• AI counted only the three small rectangles drawn as separate cells and stopped there.
• BI counted the three small rectangles and the whole one, and forgot the two made of two cells.
• DI counted a rectangle made of the left and right cells, even though they are not next to each other.
• EI assumed any pair of the four vertical lines makes a rectangle without checking each one.

3.C — 6KA-0067Tree diagrams

• AI counted the puddings only and forgot that the main course is also a choice.
• BI added the number of mains to the number of puddings instead of multiplying them.
• DI used three puddings as well as three mains, without reading how many puddings there are.
• EI doubled the answer, as if the order of the two courses made a different meal.

4.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.

5.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.

6.A — 3KA-0076Casework

• BI included 0 and 7 as a pair, even though both numbers have to be bigger than zero.
• CI counted both orders of each pair, even though swapping does not make a new way.
• DI counted every starting number from 1 to 7 without checking which pairs repeat.
• EI counted both orders and also allowed pairs of equal numbers.

7.C — 8KA-0012Casework

• AI counted each pair of digits once instead of counting both orders, such as 17 and 71.
• BI listed the pairs starting from 1 and 7 and forgot the number 80, where the second digit is zero.
• DI included 08 as a two-digit number, but a two-digit number cannot start with zero.
• EI counted both orders of every pair and then counted the pairs that reverse to themselves twice as well.

8.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.

9.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.

10.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.