Which side of the landmark?

Twenty-four positions, one figure

A solid figure can be turned into twenty-four different positions and still be the same figure. Six faces can be the one pointing at you, and for each of those the figure can be spun four ways. Six fours are twenty-four.

The paper shows you one of those positions and asks you to recognise another.

Everything else on that line is a genuinely different figure — not a trick of the drawing. That is worth saying, because children often suspect these questions of being unfair, and they are not.

At this level the turn is usually a tip onto another face, often followed by a spin.

The C.U.B.E. method

C — Count the cubes. Expect counting to rule out nothing at all this year, because the paper builds the wrong options with the same number on purpose. Do it anyway; it takes five seconds and it catches the one paper that forgets.

U — The unique bit. Choose a landmark and commit to it: the lone cube, the tallest column, the arm that sticks out sideways.

B — Both sides. What sits to the left of your landmark, and what sits to the right?

E — Eliminate. Predict first, then read the options.

The B is where the marks are.

Telling a turn from a reflection

Here is the reliable test, and it is worth more than any amount of staring.

Pick your landmark cube. Now say a sentence about it out loud: the tall column is on its left, the flat arm is on its right.

Turn the figure any way you like. That sentence stays true.

Reflect it, and the sentence reverses.

That is the whole difference, and it is the only test that still works when the drawing looks convincing.

Turning a figure in your head

Do not try to move the whole thing at once. Working memory holds four to seven things, and a nine-cube figure will not fit.

So move one thing. Decide which face is going to end up pointing at you. Work out where your landmark cube goes. Only then rebuild the rest around it.

And if an option survives your landmark check, check a second feature before committing — because two features agreeing is a rotation, and one feature agreeing is a coincidence.

Where do pupils lose marks?

Choosing the mirror image. The biggest cause of lost marks at this level. It survives the cube count, the outline and the silhouette, and fails only on which side of the landmark things sit.

Matching the outline instead of the arrangement. One option has the right cubes with one moved a place — it matches from a single viewpoint and stops matching the moment you check a second face.

Turning the whole figure at once.

Reading the options before predicting. Every wrong option was written from a real pupil error, and one of them will talk you out of the right answer.

How can we practise this at home?

Build a small asymmetric figure from blocks — nine or so cubes, with one obvious sticking-out arm — and turn it slowly while your child says where the arm has gone before it arrives.

Then the important half: build the mirror image of it alongside, and let them try to turn one into the other. Failing to do that, physically, with their hands, teaches the mirror trap in a way no diagram manages.