Primary 5 · Mathematics
P5 shapes and spatial reasoning
Spatial questions punish trusting the picture. A drawing of a stacked solid shows one side, and a child counts the cubes they can see and stops. The cubes hidden behind are still there. Here is where the count comes up short.
- Level
- P5
- Usually taught
- Term 4
- Covers
- 1 concept
What changes at P5
In Primary 5, spatial reasoning is about reading three-dimensional shapes from flat drawings. Your child counts unit cubes in a stacked solid, imagines it rotated, and matches a solid to its views from different sides.
The whole challenge is that a drawing is flat and the solid is not. A single picture cannot show every cube, so part of the skill is knowing which cubes must be there even though you cannot see them.
The sentence that costs the mark
This solid is built from unit cubes. How many cubes are there in total?
What the working usually does
countvisible=7
Counts every cube the drawing shows from the front. It is a careful count, just of the ones you can see.
What the question asked
countall=10
Counts layer by layer and adds the cubes hidden behind, because the drawing shows only one side of the solid.
The visible count is not careless. It is an accurate count of every cube you can see. The mistake is trusting the drawing, which hides the cubes tucked behind the ones in front, and a drawing only ever shows one side of a solid.
The same question, worked properly
Count the cubes you can see
visible cubes = 7Start with the cubes the drawing shows from the front. There are 7 of them. This is where most counts stop.
Look for the cubes hidden behind
hidden behind = 3This is the step that fails. The left tower is two cubes deep, so behind each of its three front cubes sits another you cannot fully see. A drawing only shows one side.
Add them up
7 + 3 = 10Seven visible cubes plus three hidden ones makes 10 unit cubes in the whole solid.
Check a second way
tower 6 + steps 4 = 10Count it differently to be sure. The two-deep left tower is 3 × 2 = 6 cubes, and the bottom steps add 4 more. Same total, 10.
How can you tell it has clicked?
You can check this with a real object. Ask your child to count the cubes, then ask: are there any you cannot see from where you are looking? That question is the whole lesson.
If they remember to add the hidden ones, they have understood that a drawing shows one side. If they stop at the visible count, that is the exact habit to change.
One thing to try tonight
Build a small stack with real blocks or sugar cubes. Look at it from one side and ask how many there are, then walk around it.
The cubes that were hidden were there the whole time. A drawing only ever gives you one view, so the hidden ones have to be reasoned in, not seen.
What your child will meet in this topic
- Spatial Reasoning
Most Singapore schools introduce this in Term 4, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
Reading hidden structure from a flat drawing is the foundation for nets, the volume of solids, and the cross-sections that come in secondary school. It starts with trusting the structure over the single view.
A child who checks for hidden cubes reads any solid correctly. One who counts only what shows is short every time the shape has depth.
The methods your child will use here
Each one is the same method wherever it turns up, so it is worth learning once.
More in Primary 5
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.