Understand the idea.
Choose the drawing for the job
Choose a drawing that exposes the information needed. A floor plan shows layout from above; a front elevation shows width and height; a side elevation shows depth and height. A net shows the surface faces ready to fold.
For stacks of cubes, a height-labelled plan records how many cubes stand at each position. A front elevation shows the tallest stack along each viewing line. Shorter stacks behind or in front of it can be hidden by that outline.
Enough information matters
One view often fits several different objects. A front outline does not reveal how many rows of cubes lie behind it. Use a second view or a height-labelled plan when the total or arrangement must be determined.
Keep the viewing direction clear and include dimensions or a scale when required. Do not add counts from different views: the same cube may appear in more than one. Combine the positional information to describe what is known and what remains hidden.
See the method in action.
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.
Worked solution
- 1
Add all occupied stack heights.
Each plan position contributes its entire stack once.
- 2
Find the tallest stack in each front-view column.
Looking from the front combines the back and front rows along each viewing line.
- 3
Record the total and the visible heights.
The front outline records maximum heights rather than adding depths together.
5 cubes; front-view heights 1, 2, 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?
Worked solution
- 1
Count the minimum visible arrangement.
Two adjacent two-high stacks can produce the stated front outline.
- 2
Consider positions hidden behind the stacks.
Additional stacks no taller than the visible outline could lie behind it without changing the front view.
- 3
State what the view establishes.
Four is a possible minimum; a plan or another view is needed to determine the actual total.
No. Four is a possible minimum, not a guaranteed total.
Try it yourself.
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 & reasoning
A floor plan
A floor plan shows the classroom from above, including table positions and the floor space between them. A front elevation does not show that depth layout.
Keep practising
6 worksheet questions · 11 marks
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: .
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 ↗