Count the single blocks, including the ones you cannot see. That one instruction solves most 3D building block questions, and it is the step children skip.
The hidden blocks are the whole question
A solid drawn on paper shows you perhaps two thirds of itself. The rest is behind, or underneath, holding the visible part up.
A child who counts only what they can see will undercount every time. And the questions are built knowing that: the wrong answers are usually the undercounts.
So the rule is to count what must be there, not what is drawn. If a block sits in mid air in the picture, something is underneath it, and that something is a block you count.
A counting method that does not go wrong
- Count by layer, bottom first. How many blocks in the bottom layer, including those hidden at the back?
- Write the number down before moving up. Do not hold three numbers in your head.
- Count the next layer. Repeat to the top.
- Add the layers.
- Sanity check: nothing floats. Every block above the bottom layer must rest on one below it.
Layer by layer is more reliable than counting the whole shape at once, because it turns one hard problem into three easy ones.
Learn to name the pieces
Many questions do not ask how many blocks there are. They ask which piece completes a solid, or which pieces build it. That needs a vocabulary of shapes.
| Piece | Made of | Spot it by |
|---|---|---|
| Single | 1 cube | Fills a single gap |
| Double | 2 cubes in a line | Fills a straight gap of two |
| Triple | 3 cubes in a line | A straight bar |
| L shape | 3 or 4 cubes turning a corner | Fits an inside corner |
| T shape | 4 cubes, three in a line plus one | Fits a notch in the middle of a run |
Teach a child to name what they are looking at. "That is an L" is a faster thought than describing the shape to themselves each time, and under timed conditions that matters.
Which piece completes the solid
Work it as a subtraction rather than a search.
- Count the blocks in the finished solid, including hidden ones.
- Count the blocks already in place.
- Subtract. Now you know how many cubes the missing piece has, which usually eliminates most options immediately.
- Only then look at the shape of the remaining candidates.
Counting first and shape second is the opposite of what children do naturally, and it is far quicker.
See our guide to cube nets and our free timed spatial section, which uses both types.
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Count in single blocks, and count the ones you cannot see
3D building blocks is a similar situation to cube nets, and it really is a unique subject within non-verbal. But the teaching of it is simple.
We get them to start counting in single blocks. So when you have an L shape, or a triple block, or a double block, or a single block, we start by getting them to count the number of single blocks, in counting form, including the ones in the rear and any hidden ones.
Then they use that concept to work out which block is being requested. Alongside the counting, they learn to identify a triple block, a double block, a single block, an L block and a T block. Once they can name the pieces and count what is actually there rather than what they can see, they can work towards the answer in an educated way instead of guessing.
Mushtaque Ahmed, Founder of GrammarPath and Bright Mentors
Frequently asked questions
How do you count cubes in 11+ 3D building block questions?
Count by layer, starting at the bottom, and write each layer's total down before moving up. Include every block hidden at the back or underneath, because a block that appears to float must be resting on something, and that something counts.
Why does my child undercount blocks?
Because they count only what is drawn. A solid on paper hides the blocks behind and underneath it, and the wrong answers in these questions are usually the undercounts, so the mistake is anticipated by whoever wrote the paper.
What shapes come up in 3D building block questions?
Single cubes, doubles and triples in a line, L shapes turning a corner, and T shapes of three in a line plus one. Teaching a child to name them is worth it, because recognising an L is far faster under time pressure than describing the shape to themselves.
How do you work out which piece completes a solid?
As a subtraction. Count the blocks in the finished solid including hidden ones, count the blocks already in place, and subtract. That tells you how many cubes the missing piece has and usually eliminates most options before you even look at their shape.
Are 3D building block questions hard to teach?
No, and that is the good news. The method is simply counting in single blocks, layer by layer, including the hidden ones, and then learning to recognise the standard pieces. Children improve quickly once they stop trying to judge it by eye.