Count the piles, not the cubes

One stack is still one square

This is the idea the whole question type is built on, so it is worth picturing properly.

Imagine one cube on the table, and you are looking straight down on it. You see a square.

Now put a second cube on top and look down again. Nothing has changed. You still see one square, because the top cube sits exactly over the bottom one and hides it completely.

So a stack of two cubes, or three, or ten, is still only one square from above.

Which is why counting the cubes is the wrong thing to count. You count the piles.

Dot them and count them

The method, and it is the same every time:

Read which way you are being asked to look — from above, from the front, or from the side — and underline it.

Dot every square you would see from that direction. From above, that is one dot per pile, not one per cube. From the front or the side, take each column in turn and give it one dot for every level of its tallest stack — a tower of three shows three squares, one above another. A cube directly behind another gets no extra dot, because depth does not show in a front view.

Count the dots. That number is how many squares the right answer must have.

Cross out every option with a different number. It does not matter how right they look — a wrong count is a wrong answer, and this usually removes two or three options in about ten seconds.

From above, from the front, from the side

The same figure has more than one flat view, and which one you want depends entirely on where you are standing.

From above, you see how the blocks are spread out across the table — but not how tall anything is. A tower of four cubes and a single cube look identical.

From the front, it is the other way round. Now you see how high everything is, but not how far back it goes. Two cubes one behind the other sit in exactly the same square. So a front view can have several squares in one column: as many as the tallest stack in that line, front to back.

Here are all three views of one solid, drawn for this page. It is built from seven cubes in supported stacks: the back row has stacks 1, 0 and 3 cubes high, and the front row has 2, 1 and 0.

From above: four stacks, so four squares.

From the front (looking from the edge marked on the diagram): the three columns reach heights 2, 1 and 3 — the taller stack in each line, front to back — so six squares.

From the right-hand side, reading front to back: heights 2 and 3, so five squares.

Same solid, three different counts, and the question names which one it wants.

Where do pupils lose marks?

Not reading which way they are looking. Three directions give three different answers, and all three are usually sitting there.

Letting depth show. In a front view, a block at the back and a block at the front occupy the same square. Depth does not exist in a flat view.

Matching on the outline. Two views can share an outline and differ inside it. Check the inside, not just the edge.

Counting cubes instead of piles when looking from above.

How can we practise this at home?

Building blocks, Lego, sugar cubes — anything stackable. Build something small, then ask your child to draw what it looks like from above before they move.

Then move round and look. The gap between the drawing and the reality is the lesson, and it closes quickly.

The other useful game costs nothing: build a shape behind a book, describe only its view from above, and see whether they can build the same thing. They usually can't, and working out why teaches exactly what a plan view does and does not tell you.