Practical measurement models | Year 11

01 / LEARN

The idea, step by step

Understand the idea

A model replaces a real job with a manageable geometric description. A wall can be a rectangle, but windows reduce the painted area and two coats double the required coverage. State which effects are included.

An allowance represents a specified effect such as cutting waste. Calculate the basic quantity, apply the allowance in the correct order, then round to a purchasable package. An unexplained allowance cannot repair a wrong model.

Choose and apply a method

Record dimensions and assumptions, such as uniform soil depth or constant paint coverage. Subtract openings only when they really are excluded. Check whether an allowance applies to net area or purchased material.

The last step is a contextual recommendation. A calculation of 6.2 L does not mean ordering 1.55 four-litre tins: enough material requires two whole tins. State limitations such as uneven surfaces or variable coverage.

required amount = base amount \times (1 + allowance rate)

A common trap

Rounding package counts down because the remaining fraction seems small.

Instead: Round up after allowances when enough material must be supplied.

02 / WORKED EXAMPLES

See the thinking

Example 1

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?

Net area $= 18 - 2 = 16$ m $2$ .
Two coats need 32 m $2$ coverage.
Paint $= 32 / 8 = 4$ L, exactly one tin under this model.

1 tin.

Example 2

Paver allowance

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

Basic count $= 23 / 0.25 = 92$ .
Allowance gives $92 \times 1.08 = 99.36$ .
Round up to 100 pavers.

100 pavers.

Check your understanding

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

Show answer

3 tins.

$5.2 / 2 = 2.6$ ; three whole tins provide enough.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF 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
$2 \times 10.5 / 7 = 3$ .
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.
$1200 / 30 = 40$ .
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 ↗

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