Checking measurement results | Year 11

01 / LEARN

Understand the idea.

Understand the idea

A calculator checks arithmetic, but it does not decide whether you modelled the right quantity. Start a reasonableness check by asking whether the answer should measure a length, area, volume or capacity, then confirm that the unit matches.

Estimate the expected size before calculating precisely. A board a few metres long and less than a metre wide should have an area of a few square metres, not hundreds. A rough estimate can reveal a unit conversion error even when the multiplication is correct.

Choose and apply a method

Keep intermediate values unrounded and apply the requested rounding at the end. For materials, the final decision may require rounding up to a whole pack rather than to the nearest number. Check the purchasing requirement separately from the geometric calculation.

Use a second method when possible: split an area differently, compare a volume with an enclosing box, or substitute a proposed dimension into the original formula. Explain what the check confirms and which assumptions, such as exact dimensions or uniform shapes, still limit the result.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Correct a unit error

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

Worked solution

1
Convert the width to match the length unit.
$40 cm = 0.40 m$
A product of side lengths represents area in one square unit only when the length units match.
2
Calculate the area with consistent units.
$A = 3 (0.40) = 1.2 m^{2}$
Rectangle area is length times perpendicular width.
3
Check against a simple bound.
$0.40 < 1 ⟹ A < 3 (1) = 3 m^{2}$
The board is narrower than 1 metre, so 120 square metres is impossible for the stated dimensions.

Answer

1.2 m $2$ .

EXAMPLE 02

Check by substitution

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

Worked solution

1
Substitute the proposed height into the cylinder formula.
$V = π r^{2} h = π {(2)}^{2} (15)$
A proposed dimension is checked against the original volume relationship.
2
Evaluate the substituted expression.
$V = π \times 4 \times 15 = 60 π {cm}^{3}$
All supplied dimensions are in centimetres, so the resulting volume is in cubic centimetres.
3
Compare with the supplied volume.
$V_{calculated} = V_{given} = 60 π {cm}^{3}$
The values agree exactly, so the proposed 15 cm height is correct.

Answer

The height is correct.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

0.6 m $2$ .

Convert the width first: $30 cm = 0.30 m$ . Then $A = 2 (0.30) = 0.6 m^{2}$ . A width below 1 metre also shows that the area must be below $2 m^{2}$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet 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 $2$ .

Checking saved progress…

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.

Correct a unit error

Convert the width to match the length unit.

Calculate the area with consistent units.

Check against a simple bound.

Check by substitution

Substitute the proposed height into the cylinder formula.

Evaluate the substituted expression.

Compare with the supplied volume.

Try it yourself.

Check your understanding

Keep practising