The idea, step by step
Assumptions change decisions
A model might assume constant wall thickness, a full tank or zero material waste. Decide whether each simplification is useful and identify its likely direction of effect where possible.
Do not guess a direction when the effect is uncertain. For example, irregular shape can increase or decrease an estimate depending on which dimensions were measured. Test an alternative model.
Report a defensible conclusion
A continuous-area price differs from buying whole packs or sheets. When the task requires a minimum amount, purchase enough whole units rather than rounding to the nearest integer automatically.
State the number, unit, relevant constraint and limitation. Quoting many decimals from rough measurements gives a false impression of certainty. Make any safety margin explicit rather than hiding it in the calculation.
| Quantity | Value |
|---|---|
| Paint needed | 5.2 L |
| Tin capacity | 2 L |
| Calculated tins | 2.6 |
| Whole tins to purchase | 3 |
| Paint purchased | 6 L |
A common trap
Rounding a material requirement down because ordinary rounding says to.
Instead: Minimum requirements may demand rounding upward to whole packs.
See the thinking
Buying paint
A job requires 5.2 L. Paint comes in 2 L tins. Find the minimum number.
- 5.2/2=2.6 tins.
- Whole tins require rounding up to 3.
- This buys 6 L, leaving about 0.8 L.
Walls matter
A closed cubic container has outside edge 20 cm. Its base, lid and four side walls are each 1 cm thick. Find its internal volume.
- Internal edge=20−2=18 cm.
- Inner volume 18³=5832 cm³.
- Outside volume 8000 cm³ overestimates by 2168 cm³.
Check your understanding
A job needs 17 tiles. Boxes hold 6 tiles. Find the minimum boxes.
Show answer
3
17/6≈2.83; buy 3 whole boxes.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Cable is sold in 2 m lengths. A job needs 7.1 m. Find the minimum number of lengths.2 marks
- A closed cubic container has outside edge 12 cm. Its base, lid and four side walls are each 1 cm thick. Find its capacity in cm³.2 marks
- Lengths measured to 0.1 m give a calculated area 17.382946 m². Explain a limitation of reporting every digit.3 marks
- Soil is delivered in 0.5 m³ units. A garden needs 3.6 m³. Find the minimum order and excess.2 marks
- A cylinder is filled to 90% of its internal height. What factor adjusts full capacity?2 marks
- A continuous-area model costs material at 19.80 dollars. Two whole sheets priced 12 dollars each are required. State actual purchase cost and explain.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Cable is sold in 2 m lengths. A job needs 7.1 m. Find the minimum number of lengths.2 marks
7.1/2=3.55, so buy 4.
4 - A closed cubic container has outside edge 12 cm. Its base, lid and four side walls are each 1 cm thick. Find its capacity in cm³.2 marks
Internal edge 10 cm.
10³=1000.
1000 cm³ - Lengths measured to 0.1 m give a calculated area 17.382946 m². Explain a limitation of reporting every digit.3 marks
The input measurements already have rounding uncertainty.
Report suitable rounding and state assumptions.
The digits imply unsupported precision. - Soil is delivered in 0.5 m³ units. A garden needs 3.6 m³. Find the minimum order and excess.2 marks
Buy 8 units rather than 7.2.
8×0.5=4.0.
4.0 m³; 0.4 m³ excess - A cylinder is filled to 90% of its internal height. What factor adjusts full capacity?2 marks
For fixed radius, volume is proportional to height.
0.9 - A continuous-area model costs material at 19.80 dollars. Two whole sheets priced 12 dollars each are required. State actual purchase cost and explain.3 marks
Two sheets cost 2×12=24.
The continuous model ignored whole-sheet constraints.
24 dollars
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Surface area of composite solids; volume of composite solids; proportion/scaling of objects; related length/area/volume factors; measurement error; the effect of rounding and repeated approximations; practical design models; evaluating assumptions and suitable precision.
Official curriculum source ↗