Mathematics K–6 · Years 1–2
Packing a box: volume with cubes in layers
Measurement and space
The idea
The volume of a box is the number of identical cubes that pack it without gaps, and the cubes sit in layers that each hold the same number.
What you need
- 30 wooden or plastic cubes with 2 cm edges
- an open-topped box made from card with inside measurements 8 cm by 6 cm by 4 cm (the adult makes it beforehand)
- a second box with inside measurements 6 cm by 6 cm by 6 cm
How to do it
- Estimate how many cubes will fill the 8 by 6 by 4 box. Write the estimate down.
- Pack the bottom layer, cubes touching. Count the cubes in one row and the number of rows, then the whole layer.
- Add the next layer. Count the cubes so far. Continue until the box is full and record the total.
- Empty the box and pack it a different way (rows running the other direction). Count again and compare.
- Pack the 6 by 6 by 6 box, recording layers and the total, and order the two boxes by volume.
What you should see
The 8 cm by 6 cm by 4 cm box takes 4 cubes by 3 cubes in the bottom layer (12 cubes) and 2 layers, 24 cubes in all. Packing the other way still gives 12 per layer and 24 in total. The 6 cm cube box takes 3 by 3 by 3, which is 27 cubes, so it holds more than the flatter box even though it looks smaller from above.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The box with the biggest top holds the most.
- Only the cubes you can see from the top count.
Safety card
Hazards
- none beyond ordinary classroom materials
Controls
- none needed
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 AuthorityMA1-3DS-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-es1-s1-teaching-measurement.pdf
- education.nsw.gov.au/teaching-and-learning/curriculum/literacy-and-numeracy/teaching-and-learning-resources/numeracy/understanding-units-of-measurement