Packing is not dividing: volume
The Short Answer
Volume is the space inside a solid — length times width times height for a cuboid, in cubic units. The question the 11+ actually asks is often different: how many small cubes fit inside a larger box. That is a packing question, and dividing one volume by the other gives the wrong answer whenever the sizes do not divide neatly.
What is a volume question?
The space inside a solid. For a cuboid, length × width × height, and the answer is in cubic units because you are counting cubes.
That much your child has. The 11+ asks three harder things: packing, working backwards, and counting the parts of a solid quickly.
Packing is not dividing
This is the one worth slowing down for, because the wrong method is so tempting and so plausible.
How many 2 cm cubes fit inside a box 7 cm by 5 cm by 3 cm?
The instinct is to divide the volumes. The box is 7 × 5 × 3 = 105 cm³. Each cube is 2 × 2 × 2 = 8 cm³. So 105 ÷ 8 is about 13.
That answer is wrong, and not slightly.
Working backwards
A question gives the volume and two dimensions and asks for the third.
Multiply the two you have to get the base area, then divide. A cuboid of 60 cm³ on a 5 × 4 base: the base is 20 cm², so the height is 60 ÷ 20 = 3 cm.
One division. The only difficulty is noticing the question has been turned round, which is why reading it twice is a rung of the routine.
Counting faces, edges and vertices
Do not count one at a time in a timed test. Use the pattern.
| Solid | Faces | Edges | Vertices |
|---|---|---|---|
| Prism, n-sided end | n + 2 | 3n | 2n |
| Pyramid, n-sided base | n + 1 | 2n | n + 1 |
A hexagonal prism: 8 faces, 18 edges, 12 vertices.
Then check it. On every flat-faced solid, faces + vertices − edges = 2. For the hexagonal prism: 8 + 12 − 18 = 2. That check takes three seconds and catches a miscount immediately.
Where do pupils lose marks?
Dividing volumes on a packing question.
Answering in cm² or cm rather than cm³.
Counting edges by eye and losing both time and accuracy.
Missing that a question is backwards, and multiplying when they should divide.
Try it yourself
For packing questions, work along each dimension separately. Never divide the volumes.
- What is the volume of a cuboid 5 cm by 4 cm by 3 cm?
- A cuboid has a volume of 60 cm³ and a base of 5 cm by 4 cm. What is its height?
- How many 2 cm cubes fit inside a box 7 cm by 5 cm by 3 cm?
- What answer do you get if you divide the volumes instead, and why is it wrong?
- How many faces, edges and vertices does a hexagonal prism have?
- 60 cm³. Five times four times three, and the unit is cubic centimetres because we are counting cubes.
- 3 cm. The base area is 20 cm², so 60 ÷ 20 = 3. Working backwards like this is common and is just a division once the base is found.
- 6. Along the 7 cm you fit 3 cubes with 1 cm wasted; along the 5 cm you fit 2 with 1 cm wasted; along the 3 cm you fit 1 with 1 cm wasted. So 3 × 2 × 1 = 6.
- 13, and it is wrong by more than double. The box holds 105 cm³ and each cube is 8 cm³, so the division suggests 13 — but the leftover space is in thin strips a 2 cm cube cannot occupy. Volume tells you about space; packing is about whether the cubes actually fit.
- 8 faces, 18 edges and 12 vertices. Use the pattern rather than counting: a prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices, so for six sides that is 8, 18 and 12.
How much practice does this type need at home?
Use real boxes. A cereal box and some dice, or sugar cubes, and the question how many fit? — then count them in.
That single exercise teaches the packing idea permanently, because your child watches the leftover strips appear and can see that nothing goes in them. No explanation matches it.
Free: a Maths workbook
Questions across the Maths question types, with the method printed at the top and full answers at the back. One workbook for the whole strand, not a sheet per question type.
Frequently Asked Questions
Why can't my child divide the volumes to find how many cubes fit?
Because leftover space is not usable space. A box 7 by 5 by 3 has a volume of 105 cm³ and a 2 cm cube has a volume of 8 cm³, so dividing suggests 13 cubes. Only 6 actually fit, because along each dimension there is a strip of 1 cm that no cube can occupy. Work along each dimension separately, divide, and round down each time.
How do I explain the difference simply?
Volume is about how much space there is. Packing is about whether the shapes go in. A suitcase might have room for another jumper by volume and no space in any actual gap. Children find that comparison convincing because they have met it, and it survives better than a rule about rounding down.
How does my child count faces and edges quickly?
Use the pattern rather than counting one by one, which is how a minute disappears. A prism with an n-sided end has n + 2 faces, 3n edges and 2n vertices. A pyramid with an n-sided base has n + 1 faces, 2n edges and n + 1 vertices. Then check with the rule that works on every flat-faced solid: faces plus vertices minus edges always equals two.
What does working backwards look like?
A question gives a volume and two of the three dimensions, and asks for the third. Multiply the two you have to get the base area, then divide the volume by it. A cuboid of 60 cm³ on a 5 by 4 base is 60 ÷ 20 = 3 cm tall. It is one division once the base is found, and the only difficulty is noticing that the question has been turned round.
Sources
- GL Assessment — 11+ familiarisation materials and question type descriptions Published 2025.
- Clever Clogs Academy — our own Year 4 and Year 5 lesson records, Winslow Published September 2025 to July 2026.
We are not affiliated with, endorsed by or connected to GL Assessment or Buckinghamshire Council. Test arrangements change; always check the council's own pages for the current year's dates.
We Teach This Method Every Week in Winslow
Groups of no more than six pupils with two qualified teachers, in person or online. Come and see a session before you decide.