Block counting turns up in almost every non-verbal reasoning paper, and it is one of the most commonly dropped marks in the whole test.
The reassuring part: children do not usually get these wrong because they cannot reason. They get them wrong because of one specific habit, and it takes about a minute to explain.
The mistake
They count the cubes they can see.
That is it. That is the whole thing.
A block counting question shows a stack of cubes drawn in three dimensions. Some cubes are visible. Some are completely hidden behind or underneath the ones you can see, and the question is asking how many cubes are in the stack altogether, hidden ones included.
A child who counts only what is drawn will get a consistent, confident, wrong answer. And because it feels right, they will not check it.
This is worth saying plainly to your child, out loud, once: if a cube is holding another cube up, that cube exists, even though you cannot see it.
The method that works
Do not count cubes. Count layers.
- Start at the bottom layer and work up. The bottom layer is almost always a full rectangle, because everything above it has to rest on something.
- For each layer, work out the rectangle it would be if it were complete: rows multiplied by columns.
- Subtract the gaps you can actually see in that layer.
- Add the layers together.
Counting layers rather than cubes works because it forces the question "what must be underneath this?" at every step, which is exactly the question the trap depends on you not asking.
Worked example
Picture a stack three cubes wide, three cubes deep and three cubes high, with one corner cube missing from the very top layer.
Counting what you can see: you would get somewhere around 16 or 17, depending on the angle of the drawing. Most of the middle of the stack is invisible.
Counting layers:
- Bottom layer: 3 x 3 = 9
- Middle layer: 3 x 3 = 9
- Top layer: 3 x 3 = 9, minus the one missing corner = 8
Total: 26.
The gap between 16 and 26 is not a small error. It is the whole question, and it is the difference between a mark and no mark.
Practice questions
Read each description, work it out on paper, then check. Resist the urge to guess before writing anything down.
A stack four wide, two deep and two high, complete with no gaps.
Show the answer
16. Two layers of 4 x 2. 8 + 8. Nothing hidden matters here, which is why it is first: get the layer habit going on an easy one.
A stack three wide, three deep and two high, with two cubes missing from the top layer.
Show the answer
16. Bottom 3 x 3 = 9. Top 3 x 3 = 9, minus 2 = 7. 9 + 7 = 16.
A stack two wide, two deep and four high, complete.
Show the answer
16. Four layers of 2 x 2. Tall thin stacks are where children most often undercount, because from most angles you can only see two faces.
A staircase: bottom layer three wide and one deep, middle layer two wide and one deep, top layer one cube.
Show the answer
6. 3 + 2 + 1. Staircases look harder than they are. There is nothing hidden at all, but children often assume there must be.
A stack five wide, two deep and two high, with three cubes missing from the top layer.
Show the answer
17. Bottom 5 x 2 = 10. Top 5 x 2 = 10, minus 3 = 7. 10 + 7 = 17.
A stack three wide, three deep and three high, with the entire top layer missing except its four corners.
Show the answer
22. Bottom 9, middle 9, top layer is only the four corners = 4. 9 + 9 + 4 = 22. This one catches children who see a mostly empty top layer and stop concentrating.
What to do if your child got several wrong
Do not drill more questions yet. Go back to the sentence at the top: if a cube is holding another cube up, that cube exists. Say it, show it with actual bricks if you have any in the house, then come back to these six.
Physical bricks for five minutes are worth more than twenty more questions on paper, because the trap is a habit of looking rather than a gap in reasoning.
Where this fits in the 11+
Non-verbal reasoning is one of the four sections of the Kent Test and appears in most other selective papers too. It is also the section children meet coldest, for a simple structural reason: non-verbal reasoning is not on the national curriculum. Schools do not teach it, so unless a child has practised it deliberately, the exam hall is the first place they see it.
That is why it is worth disproportionate attention in the last few weeks before a test. The content cannot be learned late, but the question formats absolutely can, and format familiarity is most of the mark.
If you want the visual versions of these, with the full range of rotations, reflections, series and analogies alongside them, that is what The Revision Wizard's non-verbal reasoning bank is for. Every question is levelled, and the ones your child gets wrong come back around automatically rather than being quietly forgotten.
More free practice sets are on the way. If there is a question type your child keeps losing marks on, come and say hi on Instagram and tell me which one - it will go to the front of the queue.