Mathematics K–6 · Years 3–4
Layer count: volume in cubic centimetres by packing
Measurement and space
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
A rectangular prism packed with centimetre cubes has the same number of cubes in every layer, so its volume in cubic centimetres can be described and counted layer by layer, one layer's worth of cubes at a time.
What you need
- 100 centimetre cubes (1 cm edges) per pair, plain wooden cubes if possible; two colours help the layers stand out
- a small open box with inside measurements 4 cm by 3 cm by 5 cm made from card
- a 1 cm grid sheet to build on
- a recording table with columns layers, cubes in a layer, total, volume in cubic centimetres
How to do it
- Build a base of 12 cubes on the grid as 4 by 3. Record the number of cubes in the layer and the array pattern.
- Add a second layer, then a third, recording the total after each layer and writing the volume in cubic centimetres.
- Predict the total for five layers from the pattern in the table, then build it and check.
- Take the tower apart, then pack the 4 cm by 3 cm by 5 cm box with the same cubes, counting layers as you go, and compare the count with the total recorded for the five-layer tower.
- Rebuild the 36-cube prism with a different base (for example 6 by 2 or 9 by 4 with fewer layers) and check the total stays 36. Draw one prism on isometric dot paper showing the visible cubes.
What you should see
Each layer holds 12 cubes, so the totals run 12, 24, 36 and the prediction for five layers is 60, which the build confirms. The 4 by 3 by 5 box takes 5 layers of 12, 60 cubic centimetres. A 36-cube prism can be built as 4 by 3 by 3, 6 by 2 by 3, 9 by 4 by 1 or 6 by 6 by 1 among others, and every one counts to 36. A pair that counts only the visible faces of the drawing under-counts, and the physical prism shows why.
What changes
- What you change
- the number of layers
- What you measure
- the total number of cubes (volume in cubic centimetres)
- What you keep the same
- the same 4 by 3 base
- cubes packed with no gaps
- one colour per layer
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Only the cubes on the outside of the prism count.
- A tall thin prism always has more volume than a short wide one.
Safety card
Hazards
- small cubes are a choking hazard for younger siblings at home
Controls
- count cubes out and back in
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA2-3DS-02MAO-WM-01
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.
- curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/outcomes
- education.nsw.gov.au/content/dam/main-education/teaching-and-learning/curriculum/key-learning-areas/mathematics/media/documents/mathematics-s2-s3-teaching-measurement.pdf
- resolve.edu.au/v84-sequences/authentic-problems-10-000-centicubes
- education.nsw.gov.au/teaching-and-learning/curriculum/literacy-and-numeracy/teaching-and-learning-resources/numeracy/understanding-units-of-measurement