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 — 12KA-0013Perimeter and area of rectilinear shapes

• AI counted the unit squares that make up the shape, which is the area rather than the perimeter.
• BI walked around the outline but skipped the two short steps at the inner corner.
• DI added the perimeters of the two rectangles the shape is made of, counting the shared edge twice.
• EI counted the edges of all five unit squares, which counts every internal edge as well.

3.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.

4.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.

5.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.

6.E — the two diagonals are the same lengthKA-0079Properties of triangles and quadrilaterals

• AI confused a rectangle with a square, which is only one special kind of rectangle.
• BI remembered a fact about squares and rhombuses and applied it to every rectangle.
• CI counted the two diagonals as lines of symmetry, which only works for a square.
• DI used the angle sum of a triangle on a four-sided shape.

7.B — 24KA-0083Perimeter and area of rectilinear shapes

• AI subtracted 6 from 20 and gave that, which is neither a side nor an area.
• CI took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.
• DI multiplied the perimeter by half the known side instead of finding the missing side first.
• EI used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.

8.B — 75KA-0088Angles on lines, in triangles, in polygons

• AI added the three angles wrongly, getting 295 instead of 285.
• CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
• DI repeated one of the given angles instead of computing the missing one.
• EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.

9.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.

10.E — (7, 3)KA-0145Grid coordinates and lattice reasoning

• AI moved left instead of right, subtracting the 4 rather than adding it.
• BI moved left and up, reversing both directions.
• CI swapped the two coordinates round before moving.
• DI moved up instead of down, adding the 2 rather than subtracting it.

11.C — 100 degreesKA-0152Angles on lines, in triangles, in polygons

• AI found the smaller of the two unknown angles and stopped before doubling it.
• BI split the remaining 150 degrees into two equal halves instead of a one-to-two split.
• DI split the remainder evenly into 75 and 75, then doubled one of them.
• EI assumed that the largest angle in a triangle like this must be a right angle.

12.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.

13.B — square 3KA-0005Nets and folding, 2D to 3D

• AI picked the square directly next to the shaded one in the net, but neighbours in the net share an edge on the cube.
• CI counted to the far end of the column, assuming the square furthest away in the net is the one opposite.
• DI picked one of the side flaps because it is not touching the shaded square in the drawing.
• EI picked the other side flap for the same reason, without tracking what happens as the net folds.

14.B — 2KA-0016Dice and cube face relationships

• AI used the upper die's touching face instead of the lower one, so I worked from 3 rather than 5.
• CI gave the number on a touching face itself rather than the number opposite it.
• DI subtracted 3 from 7 because I confused which die was sitting on which.
• EI gave the lower die's upward face, which is the number I was told, not the hidden one underneath.

15.C — 84KA-0027Area by subtraction (shaded regions)

• AI gave the area of the square that was cut out instead of the area that remains.
• BI subtracted the side length of the small square from the area of the big one.
• DI subtracted 4 rather than the small square's area of 16.
• EI gave the area of the whole square and forgot that a piece had been removed.

16.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.

17.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.

18.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.

19.C — 18KA-0084Area by dissection and rearrangement

• AI added the two different side lengths without doubling for the opposite pair.
• BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
• DI gave the perimeter of the whole square instead of one of the pieces.
• EI gave the area of the square rather than the perimeter of a piece.

20.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.

21.B — 1KA-0089Building and counting with unit cubes

• AI assumed every small cube touches the outside somewhere.
• CI counted the cubes at the centre of each face, which are painted on one side.
• DI counted the corner cubes, which are the most painted rather than the least.
• EI gave the total number of small cubes instead of the unpainted ones.

22.C — 8KA-0147Circles: radius, diameter, and touching circles

• AI subtracted the radii, which is the answer when one circle sits inside the other.
• BI averaged the two radii instead of adding them.
• DI multiplied the radii together rather than adding them.
• EI added the two diameters instead of the two radii.

23.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.

24.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.

25.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.

26.C — 4KA-0020Paper folding and hole punching

• AI forgot that the punch goes through every layer at once, not just the top one.
• BI undid only one of the two folds before counting the holes.
• DI doubled for the first fold and then added two more rather than doubling a second time.
• EI counted a fold that was never made, doubling three times instead of twice.

27.B — 0.2KA-0052Area by subtraction (shaded regions)

• AI estimated by eye from the four corner pieces without comparing them to the whole square.
• CI used a diameter of 5 instead of a radius of 5 when working out the circle's area.
• DI assumed the circle covers half the square because it touches all four sides.
• EI found the fraction covered by the circle and gave that instead of the fraction outside it.

28.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.

29.D — 8KA-0134Paper folding and hole punching

• AI forgot that the punch goes through every layer, not just the top one.
• BI undid only one of the two folds before counting.
• CI doubled twice for the folds but added the second hole instead of doubling for it too.
• EI counted three folds instead of two, doubling one time too many.

30.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.