Checking measurement results | Year 11

01 / LEARN

The idea, step by step

Understand the idea

A correct calculator calculation can still answer the wrong question. Check whether the quantity should be a length, area, volume or capacity, and whether the model uses the correct regions or exposed faces.

Estimate before a detailed calculation. A 5 m by 4 m room has area around 20 square metres, so 2000 square metres indicates a problem. For a circle, using $π \approx 3$ provides a quick check of size.

Choose and apply a method

Retain unrounded intermediate values, then round the final result as requested. For a purchase, round to the available package after allowances. A numerically close result can still under-order material.

Where possible, check independently: decompose an area in another way, substitute a calculated dimension back into a formula, or compare a solid with a bounding box. Explain assumptions limiting the conclusion.

A common trap

Rounding each intermediate quantity and checking only that the final number looks plausible.

Instead: Keep working precision and check units, model and final rounding separately.

02 / WORKED EXAMPLES

See the thinking

Example 1

Correct a unit error

A student calculates a 3 m by 40 cm board area as 120 m $2$ . Correct it.

40 cm is 0.4 m.
Use matching units: $3 \times 0.4 = 1.2$ m $2$ .
The estimate confirms 120 m $2$ is far too large.

1.2 m

2

Example 2

Check by substitution

A cylinder with radius 2 cm has volume $60 π$ cm $3$ . Check a proposed height of 15 cm.

Substitute: $π {(2)}^{2} (15) = 60 π$ cm $3$ .
This equals the supplied volume.

The height is correct.

Check your understanding

A 2 m by 30 cm rectangle is said to have area 60 m $2$ . Correct it.

Show answer

0.6 m $2$ .

30 cm is 0.3 m; $2 \times 0.3 = 0.6$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Correct the claim that a 4 m by 25 cm strip has area 100 m $2$ .
2 marks
A volume is 0.48 m $3$ . A student records 48 L. Correct it.
2 marks
A 10 m by 6 m floor is quoted as 600 m $2$ . Give an estimate and the exact area.
2 marks
For a closed cuboid 4 cm by 3 cm by 2 cm, a student gives 24 cm $2$ as surface area. Explain and correct.
2 marks
A calculation requires 11.2 tiles with no additional wastage. How many whole tiles must be ordered?
2 marks
A pond has radius 2 m. Estimate area with $π \approx 3$ , then give the calculator value to one decimal place.
2 marks

Read the worked solutions

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

Correct the claim that a 4 m by 25 cm strip has area 100 m $2$ .
2 marks
25 cm is 0.25 m; $4 \times 0.25 = 1$ .
1 m $2$ .
A volume is 0.48 m $3$ . A student records 48 L. Correct it.
2 marks
$0.48 \times 1000 = 480$ L.
480 L.
A 10 m by 6 m floor is quoted as 600 m $2$ . Give an estimate and the exact area.
2 marks
$10 \times 6 = 60$ ; 600 is ten times too large.
About 60 m $2$ ; exactly 60 m $2$ .
For a closed cuboid 4 cm by 3 cm by 2 cm, a student gives 24 cm $2$ as surface area. Explain and correct.
2 marks
$4 \times 3 \times 2 = 24$ calculates volume.
$S A = 2 (12 + 8 + 6) = 52$ cm $2$ .
24 cm $3$ is volume; surface area is 52 cm $2$ .
A calculation requires 11.2 tiles with no additional wastage. How many whole tiles must be ordered?
2 marks
Round up to provide enough tile area.
12 tiles.
A pond has radius 2 m. Estimate area with $π \approx 3$ , then give the calculator value to one decimal place.
2 marks
Estimate $3 \times 2^{2} = 12$ .
$4 π \approx 12.566$ , which rounds to 12.6.
Estimate 12 m $2$ ; calculator value 12.6 m $2$ .

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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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