The idea, step by step
Choose the drawing for the job
A floor plan looks down on the layout and can show usable floor area. A front elevation shows width and height. A side elevation shows depth and height. A net shows faces ready to fold. An angled sketch helps you imagine a solid, but lengths on the page may not be in their true proportion. State which view you are using.
For cube stacks, a plan can record the number of cubes at each occupied position. A front elevation shows the tallest stack in each left-to-right column; a side elevation shows the tallest stack along each front-to-back position.
Enough information matters
A front view hides everything behind its tallest visible columns. Several different solids may have the same front view. Use a second view or a height-labelled plan when you need a unique answer. If information is missing, describe what can and cannot be concluded rather than guessing hidden cubes.
Good diagrams include a direction, scale when needed and clear labels. For an original object, choose the representation that makes the decision easiest: a net for a container template, a plan for arranging desks, or an elevation for the height of a shelf.
A common trap
Adding cubes visible in each view as if they were different cubes.
Instead: The same cube can appear in several views. Reconstruct positions from the combined information rather than adding view totals.
See the thinking
Read a height-labelled plan
The plan gives back-row stack heights 1, 2, 1 and front-row heights 1, 0, 0. Find the total cubes and the front-view heights.
- Add every stack height: 1 + 2 + 1 + 1 = 5 cubes.
- For each left-to-right column, take the maximum over the two rows.
- The three maxima are 1, 2 and 1.
Recognise a hidden assumption
A front view shows two adjacent stacks, each two cubes high. Does this prove the solid contains exactly four cubes?
- At least four cubes are needed for those visible stacks.
- More cubes could be directly behind them and hidden from the front.
- A plan or another view is needed to determine all the stacks.
Check your understanding
Which drawing is most useful for deciding where tables fit in a classroom: a floor plan or a front elevation?
Show answer
A floor plan
It shows positions and horizontal space from above; a front elevation mainly shows height and width.
Your turn
6 questions · 11 marks · Work at your own pace.
Read the questions online
- Which representation is most useful for cutting out the faces of a box so they can be folded together?1 mark
- Use the labelled plan shown to find the total number of cubes.2 marks
- Use the plan shown. Draw the front elevation on square paper and state its heights, left to right.2 marks
- Use the plan shown. Draw the right-side elevation. When viewed from the right, show the front row then the back row from left to right. State the two heights.2 marks
- A front view of a rectangular building is 12 m wide and 5 m high. Can you find its volume from this information alone? Explain.2 marks
- A designer wants to show both room positions and the outside height of a house. Explain why two drawings may be clearer than one angled sketch.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Which representation is most useful for cutting out the faces of a box so they can be folded together?1 mark
It shows all faces and their joins.
A net - Use the labelled plan shown to find the total number of cubes.2 marks
Add all stack heights: 1 + 2 + 1 + 1 + 0 + 0 = 5.
5 cubes - Use the plan shown. Draw the front elevation on square paper and state its heights, left to right.2 marks
Take the greatest height in each left-to-right column across both rows.
1, 2, 1 - Use the plan shown. Draw the right-side elevation. When viewed from the right, show the front row then the back row from left to right. State the two heights.2 marks
Looking from the right makes the front row the left-hand column of this elevation.
The front row has maximum height 1; the back row has maximum height 2.
1, 2 - A front view of a rectangular building is 12 m wide and 5 m high. Can you find its volume from this information alone? Explain.2 marks
Front view supplies width and height only.
Volume also needs the distance from front to back.
No; the depth is missing. - A designer wants to show both room positions and the outside height of a house. Explain why two drawings may be clearer than one angled sketch.2 marks
Each view makes the relevant dimensions clear.
An angled sketch can hide features or distort apparent lengths.
Use a floor plan for room layout and an elevation for height.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 7 measurement and spatial representation: areas of triangles/parallelograms, prism volumes, circle circumference, nets and views. Precision is integrated into practical measurement; circle area is not introduced here.
Official curriculum source ↗