Practical measurement models | Year 11

01 / LEARN

Understand the idea.

Understand the idea

A practical measurement model connects a real task to quantities you can calculate. Painting starts with the area actually painted, not every visible rectangle. Windows may be excluded, while a second coat requires covering that same painted area again.

An allowance accounts for a stated effect such as cuts or waste. Calculate the basic requirement first, multiply by the allowance factor, and then convert it into a purchasable quantity. An allowance should have a reason; it cannot replace missing dimensions.

Choose and apply a method

Keep each stage separate: geometry gives area or volume, a coverage rate gives material, and package size gives a count. Check the direction of division using units. Dividing square metres by square metres per litre leaves litres.

When sufficient supplies are required, round the final package count up. Keep intermediate results unrounded so an early rounding choice does not alter the order. State the limits of the model, such as uniform depth, exact coverage or no waste beyond the supplied allowance.

\begin{aligned} required amount & = base amount \\ \times (1 + allowance rate) \end{aligned}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Paint order

A 6 m by 3 m wall has a 2 m $2$ window and needs two coats. Coverage is 8 m $2$ /L and tins hold 4 L. How many tins?

Worked solution

1
Remove the unpainted window.
$A_{net} = 6 \times 3 - 2 = 16 m^{2}$
The window does not need paint, so it is excluded from each coat.
2
Account for both coats.
$A_{coverage} = 2 \times 16 = 32 m^{2}$
Two coats cover the same net wall area twice.
3
Convert coverage area into litres.
$Q = \frac{32}{8} = 4 L$
Each litre covers 8 square metres under the supplied model.
4
Find the whole-tin order.
$N = \frac{4}{4} = 1 tin$
One 4 litre tin meets the exact requirement; no additional allowance is specified.

Answer

1 tin.

EXAMPLE 02

Paver allowance

A patio has area 23 m $2$ . A paver covers 0.25 m $2$ . Add 8% for cuts. How many whole pavers?

Worked solution

1
Find the basic number of pavers.
$N_{base} = \frac{23}{0.25} = 92$
Each paver supplies 0.25 square metres of coverage.
2
Apply the cutting allowance.
$N_{allowed} = 92 (1.08) = 99.36$
An 8% allowance means retaining the base count and adding 8% of it.
3
Order enough whole pavers.
$N = ⌈ 99.36 ⌉ = 100$
Pavers are purchased whole, and rounding down would not meet the modelled requirement.

Answer

100 pavers.

03 / YOUR TURN

Try it yourself.

Check your understanding

A job needs 5.2 L, sold in 2 L tins. How many tins?

Show answer & reasoning

3 tins.

Divide the requirement by the tin size: $5.2 \div 2 = 2.6$ . Two tins hold only $4 L$ , so three whole tins are required; they supply $6 L$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

A 5 m by 2.4 m wall has a 1.5 m $2$ window. Find one-coat paintable area.
2 marks
A 10.5 m $2$ wall needs two coats at 7 m $2$ /L. Find paint needed.
2 marks
A floor requires 48 tiles before an allowance. Add 12.5% for cuts. Find tile count.
2 marks
A 4 m by 1.5 m garden bed needs soil 0.2 m deep. Find soil volume.
2 marks
Soil is sold in 30 L bags. How many bags fill 1.2 m $3$ ?
2 marks
An irregular courtyard is modelled as one rectangle. Suggest a measurement that would test this assumption.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

A 5 m by 2.4 m wall has a 1.5 m $2$ window. Find one-coat paintable area.
2 marks
$5 \times 2.4 - 1.5 = 10.5$ .
10.5 m $2$ .
A 10.5 m $2$ wall needs two coats at 7 m $2$ /L. Find paint needed.
2 marks
$2 \times \frac{10.5}{7} = 3$ .
3 L.
A floor requires 48 tiles before an allowance. Add 12.5% for cuts. Find tile count.
2 marks
$48 \times 1.125 = 54$ .
54 tiles.
A 4 m by 1.5 m garden bed needs soil 0.2 m deep. Find soil volume.
2 marks
$4 \times 1.5 \times 0.2 = 1.2$ .
1.2 m $3$ .
Soil is sold in 30 L bags. How many bags fill 1.2 m $3$ ?
2 marks
Convert 1.2 m $3$ to 1200 L.
$\frac{1200}{30} = 40$ .
40 bags.
An irregular courtyard is modelled as one rectangle. Suggest a measurement that would test this assumption.
2 marks
Different widths show that one rectangle may be unsuitable; split the measured shape into simpler regions.
Measure the width at several positions.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

In this lesson

Understand the idea.

Understand the idea

Choose and apply a method

See the method in action.

Paint order

Remove the unpainted window.

Account for both coats.

Convert coverage area into litres.

Find the whole-tin order.

Paver allowance

Find the basic number of pavers.

Apply the cutting allowance.

Order enough whole pavers.

Try it yourself.

Check your understanding

Keep practising