Worksheet generator

1.C — 14KA-0009Counting cubes in a stack, including hidden ones

• AI counted only the cubes on the bottom layer and treated the rest as decoration.
• BI counted only the cubes whose faces I could actually see in the drawing.
• DI assumed every layer was a full 3 by 3 square and multiplied 9 by 2 for two layers.
• EI assumed the stack was a solid 3 by 3 by 3 block because it sits in a corner.

2.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.

3.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.

4.A — 56KA-0163Selections of a few objects

• BI counted ordered selections, so I counted the same three people once for every order they could stand in.
• CI multiplied the 8 members by the 3 places, which counts something quite different from a selection.
• DI divided the 336 ordered selections by 3 instead of by 3 factorial.
• EI chose 2 people rather than 3.

5.A — 60KA-0172Selections of a few objects

• BI chose any 4 from all 9 people and ignored the two-and-two requirement.
• CI added the two counts instead of multiplying them.
• DI treated the choices as ordered, counting the same committee several times.
• EI used 5 x 4 x 2 or a similar shortcut rather than counting each selection properly.