Worksheet generator

1.A — the rectangleKA-0004Line and rotational symmetry

• BI found the vertical fold that works and assumed a second one must work as well without testing it.
• CI saw that the star looks very symmetric and picked it without counting how many lines of symmetry it actually has.
• DI counted the horizontal fold and then counted the vertical one too, even though the two halves do not match.
• EI only tested vertical folds on every shape and concluded that no shape had two lines.

2.C — 90 degreesKA-0032Clock geometry: hands, angles, times

• AI gave the angle for one hour mark instead of the three hour marks between the hands.
• BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
• DI used a third of the clock face rather than a quarter of it.
• EI read 3 o'clock as the hands pointing in opposite directions.

3.E — 24KA-0038Building and counting with unit cubes

• AI added the three measurements together instead of multiplying them.
• BI counted one layer of 4 by 3 and forgot that the block is two layers tall.
• CI read the block as 3 by 3 by 2 because the drawing hid the far column.
• DI counted only the cubes whose faces I could actually see in the picture.

4.B — the straight line of sixKA-0048Nets and folding, 2D to 3D

• AI assumed any arrangement that is not a simple line must fail to fold.
• CI thought a staircase would overlap when folded, without tracking a single face through the fold.
• DI picked the cross because it looks unusual, even though it is the most familiar cube net there is.
• EI checked that each arrangement had six squares and assumed six squares is enough.

5.C — HKA-0142Line and rotational symmetry

• AI found the vertical fold and assumed a horizontal one must work too.
• BI found the horizontal fold and stopped without testing the vertical one.
• DI counted the vertical fold twice rather than testing a horizontal one.
• EI mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.

6.A — 150 degreesKA-0170Angles on lines, in triangles, in polygons

• BI found the exterior angle and answered with that instead of the interior one.
• CI used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.
• DI gave the total of all twelve interior angles rather than one of them.
• EI used a ten-sided polygon by mistake.

7.C — 9 timesKA-0042Scaling and similar figures

• AI applied the length scale factor straight to the area.
• BI doubled the scale factor because area involves two dimensions, instead of squaring it.
• DI multiplied the scale factor by four, as though area scaled with the number of sides.
• EI cubed the scale factor, which is the rule for volume rather than area.

8.B — 40KA-0080Properties of triangles and quadrilaterals

• AI subtracted 100 from 180 and then divided by four instead of by two.
• CI assumed the two equal angles are always 45 degrees.
• DI gave what is left after taking 100 from 180 without splitting it between the two angles.
• EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.

9.C — 6KA-0081Views of a solid: top, front, side

• AI used the view from above only, giving one cube per square, and ignored the height the front view demands.
• BI made just one column two cubes tall, forgetting that the front view is two cubes high across its whole width.
• DI added an extra cube that neither view requires.
• EI assumed the solid is a filled 2 by 2 by 2 block, which is the largest that fits rather than the smallest.

10.D — 6KA-0085Line and rotational symmetry

• AI checked only the vertical and horizontal folds and stopped there.
• BI counted the lines through opposite corners and forgot the ones through opposite edges.
• CI assumed a hexagon behaves like a rectangle with a couple of extra folds.
• EI counted each line twice, once from each end.

11.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.

12.B — 30 cmKA-0155Scaling and similar figures

• AI kept the difference of 4 cm between the two sides instead of keeping their ratio.
• CI added 20 to 12 rather than scaling 12.
• DI used the scale factor upside down and multiplied 12 by 8/20 instead of 20/8.
• EI multiplied 12 by 1.5, the ratio between the original sides, instead of by the enlargement factor.

13.B — 50 sq cmKA-0164Scaling and similar figures

• AI scaled the area by 5/3, using the side ratio directly instead of its square.
• CI multiplied the area by 2.5, halfway between the side ratio and its square.
• DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
• EI multiplied by 5 and ignored the 3 in the ratio entirely.

14.B — 10KA-0082Shortest paths on and around shapes

• AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
• CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
• DI chose an unfolding that gives a longer straight line and did not compare it with the others.
• EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.

15.C — 14KA-0139Dice and cube face relationships

• AI subtracted only the top face from 21, forgetting the hidden bottom face as well.
• BI guessed four middling numbers and added them without using the total of all six faces.
• DI subtracted only the bottom face of 4 from the total of 21.
• EI added the four largest numbers on the die rather than the four that are actually at the sides.