Calculations in practical contexts using suitable digital tools | Year 9

01 / LEARN

The idea, step by step

Plan before pressing keys

Write the expression that represents the situation before entering numbers. Brackets protect a whole numerator, denominator or root input. Check that a root applies to the complete intended expression, not just its first term.

Estimate the scale first. A square with area nine hundred and fifty square metres has side between thirty and thirty-one metres because their squares are nine hundred and nine hundred and sixty-one. A calculator answer near three hundred must be an entry error.

Interpret the display

Keep unrounded calculator values for later steps. Record formula, substitution and final unit so another person can check the method. When buying enough material, a physical constraint may require rounding up rather than rounding to the nearest whole number.

Check a root result by squaring it, or substitute the answer back into the original formula. A small difference after rounding is expected; a large mismatch suggests a bracket, unit or formula error. A digital display supports your reasoning but does not replace it.

A common trap

$100 \div 2 \times π$ is the same as $100 \div (2 π)$ .

Instead: Multiplication and division proceed left to right unless brackets change the grouping. Group the complete denominator.

02 / WORKED EXAMPLES

See the thinking

Example 1

A garden side

A square garden has area $950 m^{2}$ . Find its side to two decimal places.

$s = \sqrt{950} m$ ; first expect $30 < s < 31$ .
Enter the root of the whole input: $s = 30.822070 \dots m$ .
Round the final measurement.

30.82 m

Example 2

A grouped denominator

A circular track has circumference $100 m$ . Use $r = C / (2 π)$ to find the radius to two decimal places.

$r = 100 / (2 π)$ .
Enter $100 \div (2 \times π)$ , grouping the whole denominator.
The display is $15.915494 \dots$ .

15.92 m

Check your understanding

A square has area $170 m^{2}$ . Is its side closer to $13$ or $17$ metres?

Show answer

$13 m$ .

$13^{2} = 169$ , so $\sqrt{170}$ is just above $13$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

A square court has area $625 m^{2}$ . Find its side and check.
2 marks
A square plot has area $730 m^{2}$ . Find its side to two decimal places.
2 marks
Use $r = C / (2 π)$ to find the radius for circumference $48 cm$ . Give two decimal places.
2 marks
A supplied formula is $D = \sqrt{a^{2} + b^{2}}$ . For $a = 8.4 cm$ and $b = 12.5 cm$ find $D$ to one decimal place.
2 marks
A square of area $50 m^{2}$ needs edging along all four sides. It is sold in whole metres. Find the least length to buy.
3 marks
A student reports $\sqrt{360} = 189.7$ . Explain a quick check and give the correct value to one decimal place.
3 marks

Read the worked solutions

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

A square court has area $625 m^{2}$ . Find its side and check.
2 marks
$\sqrt{625} = 25$ and $25^{2} = 625$ .
$25 m$ .
A square plot has area $730 m^{2}$ . Find its side to two decimal places.
2 marks
$s = \sqrt{730} = 27.018512 \dots m$ .
$27.02 m$ .
Use $r = C / (2 π)$ to find the radius for circumference $48 cm$ . Give two decimal places.
2 marks
$r = 48 / (2 π) = 7.639437 \dots cm$ .
$7.64 cm$ .
A supplied formula is $D = \sqrt{a^{2} + b^{2}}$ . For $a = 8.4 cm$ and $b = 12.5 cm$ find $D$ to one decimal place.
2 marks
$D = \sqrt{70.56 + 156.25} = \sqrt{226.81} = 15.060212 \dots cm$ .
$15.1 cm$ .
A square of area $50 m^{2}$ needs edging along all four sides. It is sold in whole metres. Find the least length to buy.
3 marks
Length $= 4 \sqrt{50} = 28.284271 \dots m$ .
Round up; twenty-eight metres is too short.
$29 m$ .
A student reports $\sqrt{360} = 189.7$ . Explain a quick check and give the correct value to one decimal place.
3 marks
$18^{2} = 324 < 360 < 361 = 19^{2}$ .
$\sqrt{360} = 18.973665 \dots$ .
The root is between $18$ and $19$ ; it rounds to $19.0$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 9 real-number classification and applications; root bounds and sensible digital approximation. Full surd manipulation is developed in Year 10.

Official curriculum source ↗

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