Nothing floats: counting cubes you cannot see

Count first, every time

On any question showing a figure built from cubes, the first move is to count the cubes and write the number down.

Think about why that works. If you take a set of blocks and turn them, does the number of cubes change? No. Turning never adds a cube and never takes one away.

So a set with a different number is out. Straight away, no matter how much it looks right.

On most block-matching questions, counting alone gets rid of two of the four wrong options — half the work done before you have thought about shape at all.

Nothing floats

Which leaves the harder half of the counting: the cubes you cannot see.

The rule is one sentence, and children accept it immediately because it is obviously true rather than something to memorise:

Nothing floats. If a cube has air underneath it, there is a cube you cannot see holding it up — and it counts.

That finds nearly every hidden cube in an 11+ figure. The rest are hidden behind others, and those are found by counting layer by layer rather than by looking.

Turning is not flipping

On questions asking which set of loose blocks builds the figure, there is one more rule, and it is the one that separates people who are good at this from people who are nearly good at it.

You may turn a block any way up. You may never flip it over.

Hold up both hands. Same shape, same fingers, same size. Now turn one so it matches the other exactly. You cannot — one is the mirror image of the other.

Some blocks are exactly like that, and the wrong options will include one: right number of cubes, right-looking shape, and it can never be turned to fit.

If you find yourself wanting to flip a block over to make it work, that is the trap.

Where do pupils lose marks?

Missing a hidden cube, usually one underneath rather than behind.

Flipping instead of turning.

Counting the whole figure at once and getting a different answer each time.

Checking blocks one at a time. Every block might fit the figure somewhere on its own — the question is whether they all fit at the same time.

How can we practise this at home?

Real cubes, and the game is: build it, then count it, then take it apart and count again as it comes down. The second count is the check, and children enjoy catching themselves out.

Then the specific drill for hidden cubes: build something with an overhang, so a cube is clearly being held up by one that cannot be seen from the front, and ask for the total before it is dismantled.

The hands demonstration for flipping takes ten seconds and is worth doing once, properly. It tends not to need repeating.