Mathematics 7–10 · Year 7
Interlocking cube models: top, front and side views and isometric drawings
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 solid built from cubes can be represented by its top, front and side views and by an isometric drawing, each of which shows some features and hides others, and outline views alone can fail to fix how many cubes a model contains.
What you need
- 20 interlocking 2 cm cubes per pair
- Isometric dot paper and 1 cm square grid paper
- A card marked FRONT to stand each model on
- A folder standing upright as a screen between pairs
How to do it
- Build the five-cube model: a 2 by 2 square of cubes with one more cube on top of the front-left cube, standing on the FRONT card.
- Draw its top, front and right-side views as outlines on square grid paper, one grid square per cube face.
- Draw the model on isometric dot paper, keeping vertical edges vertical.
- Count the cubes (volume) and the exposed faces (surface area), and convert to cm³ and cm² using the 2 cm edge.
- Behind the screen build a model of 6 to 10 cubes, draw its three views and an isometric drawing, and give only the drawings to another pair to rebuild; compare the rebuilt model with the original.
- Build a 2 by 2 by 2 cube, then remove its bottom back-right cube, and draw the three outline views of both models.
What you should see
The five-cube model has a top view of 4 squares in a 2 by 2 square and front and side views of 3 squares in an L shape. Its volume is 5 cubes, 5 × 8 = 40 cm³, and it shows 20 faces, 20 × 4 = 80 cm² (the 2 by 2 base shows 16 faces; the top cube covers 1 and adds 5). The 2 by 2 by 2 cube and the same cube with its bottom back-right cube removed give identical outline views (a 2 by 2 square from the top, front and side) and even the same number of exposed faces, 24, although one has 8 cubes and the other 7. When a set of drawings does not fix the model, the rebuilding pair can make more than one model that matches it, and the class records which hidden cube made the difference. The learner knows it worked when every face count equals 6 × cubes − 2 × joins and each rebuilt model either matches the original or differs only by a cube the drawings could not show.
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 top view shows how many cubes there are.
- A model with fewer cubes always has less surface area.
- Three views always determine a model.
Safety card
Hazards
- small cubes on the floor are a slip hazard
Controls
- cubes kept in a tray and counted back at the end
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
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), Stage 4 Volume; page read 2026-09-22MA4-VOL-C-01
- Australian Curriculum v9AC9M7SP01
Sources
The pages the author read to write this activity.