Evaluating assumptions and suitable precision | Year 10

01 / LEARN

Understand the idea.

Assumptions change decisions

Every model makes assumptions about the object or purchase. Ignoring wall thickness increases estimated internal capacity, while assuming a full tank can overstate usable storage. Identify the direction of an effect when the geometry supports it.

Some changes have no predictable direction without more information. An irregular shape can make a simple solid model too large or too small. Test another model rather than claiming that every simplification necessarily overestimates.

Report a defensible conclusion

A minimum purchase must satisfy the requirement using available whole units. Divide to see how many packs are needed, then choose the least integer that supplies enough. Ordinary nearest-integer rounding can leave a shortage.

Report the quantity, unit, purchasing constraint and any important limitation. Rough dimensions do not justify many decimal places. If a safety margin or waste allowance is used, include it explicitly so the recommendation can be assessed.

Meeting a minimum paint requirement
Quantity	Value
Paint needed	5.2 L
Tin capacity	2 L
Calculated tins	2.6
Whole tins to purchase	3
Paint purchased	6 L

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Buying paint

A job requires 5.2 L. Paint comes in 2 L tins. Find the minimum number.

Worked solution

1
Calculate the number of tin capacities required.
$\frac{5.2}{2} = 2.6$
Each tin supplies $2 L$ , but tins must be bought whole.
2
Choose the least sufficient whole number.
$n = 3, 2 (2) = 4 < 5.2 \leq 3 (2) = 6$
Two tins are insufficient and three meet the requirement.
3
Check the surplus.
$6 - 5.2 = 0.8 L$
Three tins supply $6 L$ , leaving $0.8 L$ beyond the modelled need.

Answer

3 tins

EXAMPLE 02

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.

Worked solution

1
Account for both walls along each dimension.
$l_{internal} = 20 - 1 - 1 = 18 cm$
Two opposite $1 cm$ walls reduce each outside edge; the base and lid likewise reduce the height.
2
Calculate the internal volume.
$V = 18^{3} = 5832 {cm}^{3}$
The enclosed space is a cube of edge $18 cm$ .
3
Compare with the outside-volume model.
$20^{3} - 18^{3} = 8000 - 5832 = 2168 {cm}^{3}$
Ignoring walls would overstate the internal volume by this amount.

Answer

5832 cm³

03 / YOUR TURN

Try it yourself.

Check your understanding

A job needs 17 tiles. Boxes hold 6 tiles. Find the minimum boxes.

Show answer & reasoning

Two boxes supply only $2 (6) = 12$ tiles, whereas three supply $3 (6) = 18$ . Since $12 < 17 \leq 18$ , the minimum is three boxes.

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

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
$\frac{7.1}{2} = 3.55$ , 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.
$10^{3} = 1000$ .
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.
$8 \times 0.5 = 4.0$ .
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 $2 \times 12 = 24$ .
The continuous model ignored whole-sheet constraints.
24 dollars

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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 ↗

In this lesson

Understand the idea.

Assumptions change decisions

Report a defensible conclusion

See the method in action.

Buying paint

Calculate the number of tin capacities required.

Choose the least sufficient whole number.

Check the surplus.

Walls matter

Account for both walls along each dimension.

Calculate the internal volume.

Compare with the outside-volume model.

Try it yourself.

Check your understanding

Keep practising