Primary 5 · Mathematics
P5 volume of cube and cuboid
Volume and area feel like the same kind of question, and the working looks almost identical. The difference is one extra dimension, and it shows up only in whether the answer ends in cm² or cm³.
- Level
- P5
- Usually taught
- Term 2
- Covers
- 2 concepts
What changes at P5
At Primary 5, volume is the amount of space a solid fills, found by multiplying three measurements: length, breadth and height. A cube is the simplest case, the same side used three times.
The rule is one line, and the arithmetic is small. The difficulty is that a volume looks almost exactly like an area on the page, and the only thing separating them is the third measurement and the little ³ on the unit.
The sentence that costs the mark
A cuboid is 8 cm long, 5 cm broad and 3 cm tall. Find its volume.
What the working usually does
only8 × 5=40 cm²
Multiplies only the two sides of one face and stops. That gives the area of the face, in cm², not the volume of the box.
What the question asked
3 ×8 × 5=120 cm³
Multiplies the third dimension too, the 3 cm height. Three dimensions give a volume, in cm³.
Both are clean multiplications ending on a believable number, and 40 looks as reasonable as 120. The only tell is the mark on the unit: cm² is a flat area, cm³ is a solid volume, and only the third dimension makes it cm³.
The same question, worked properly
Volume needs all three
length, breadth AND heightA volume fills a solid, so it needs all three measurements. Length and breadth alone only cover a flat face, not the space inside.
Multiply three, not two
8 × 5 × 3This is the step that fails. Multiply all three: 8 × 5 × 3, not just 8 × 5. Stopping at two gives the area of one face, which is where the mark is lost.
Work it out
8 × 5 × 3 = 120The order does not matter, the product is the same either way. It comes to 120.
Give the cubic unit
120 cm³Three lengths multiplied make a cubic unit, so the ³ says it is a volume. A cm² or a bare cm here is the giveaway that only two dimensions were used.
How can you tell it has clicked?
You do not need to do the multiplication to check this. Look at the unit on the answer: a volume ends in cm³, with a small three. If it says cm², a dimension was missed.
A child who understands multiplies three measurements and writes cm³. A child who stops at two has found the area of one face, and the wrong unit is the quiet sign of it.
One thing to try tonight
Fill a small box with sugar cubes or dice, one layer at a time. One layer is length × breadth, and the number of layers is the height. Count the whole box and you have multiplied three numbers, which is the volume.
One flat layer on its own is only a face. Ask your child to point at a single layer, then at the whole box, and say which one the question is asking for. That is the area-versus-volume line, made of dice.
What your child will meet in this topic
- Volume of a Cuboid
- Volume of Liquid
Most Singapore schools introduce this in Term 2, 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
Multiplying three dimensions is the base for the harder P6 volume work: compound solids, liquid levels in a tank, and rate of flow, where the same length × breadth × height sits inside a longer question.
A child who always counts three dimensions, and checks the unit, carries that forward. A child who stops at a face loses the same mark again in P6, now hidden inside a bigger solid.
The same topic in other years
It comes back each year and gets harder, so it helps to see what came before and what is coming.
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.