Mathematics 11–12 · Years 11–12

How much rain falls on the school roof: area from a scaled aerial photo and V = Ah

Ratios and rates: Ratios (Mathematics Standard 2, Year 12, including rainfall volume with V = Ah; Mathematics Standard 1, Year 12 covers only the measurements taken from the scaled plan); Applications of measurement: Practicalities of measurement (Mathematics Standard, Year 11)

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The idea

A depth of rain spread over a measured area is a volume, so 1 mm of rain on 1 square metre is 1 litre, and a roof's yearly catch follows from its scaled area and the local rainfall record.

What you need

A SIX Maps aerial view or site plan of one school roof with its scale
A trundle wheel for a ground check of one roof edge
A rain gauge reading to 0.2 mm (or the nearest Bureau of Meteorology station's daily rainfall from Climate Data Online)
The Bureau of Meteorology climate record for Sydney (Observatory Hill), station 066062, open from 1858 to 31 August 2020: mean annual rainfall 1213.4 mm over all years at the site, the figure the Bureau quotes in its Sydney annual climate statement, and a June mean of 133.1 mm

How to do it

Measure the roof's length and width on the aerial view, convert with the scale, and split an irregular roof into rectangles and triangles to find its plan area in square metres; check one roof edge with the trundle wheel, walking the ground directly under the gutter line rather than along the wall, because the eaves overhang the walls.
Record the rain gauge reading after a wet day and compute the volume that fell on the roof with V = Ah, converting to litres (1 m^3 = 1000 L).
Compute the average yearly and June volumes on the roof from the Bureau's Sydney means (or the means for your nearest station).
Compare the yearly volume with the capacity of a school rainwater tank and state what fraction a tank would catch if it filled only from this roof.
Explain why the real catch is less than V = Ah (first-flush diverters, evaporation, overflow).

What you should see

1 mm of rain on 1 m^2 is 0.001 m^3 = 1 L. A test roof of 150 m^2 receiving 25 mm in a day collects 3750 L. At the Sydney (Observatory Hill) mean of 1213.4 mm a year the same roof receives 182.0 kL a year on average, and 20.0 kL in an average June. The learner knows it worked when the scaled length of one roof edge matches the trundle-wheel length measured under the gutter line within a few per cent (a wall is shorter than the roof outline by the eaves overhang at each end) and the units are converted correctly from mm and m^2 to litres.

What changes

What you change: the rainfall depth
What you measure: the volume of water falling on the roof
What you keep the same: the same roof, with its plan area measured to the gutter line
the same rain gauge read at the same time each day
the map scale checked against one trundle-wheel measurement

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Rainfall in millimetres cannot be turned into litres without knowing the size of the gauge; the depth is the same on every square metre, so volume is depth times area.
A sloping roof catches more rain than its plan area; rain falling vertically sees only the plan area.

Safety card

Low riskLearners carry it out

Hazards

climbing to reach a roof or gutter

Controls

measure the roof only from the aerial view and the ground; never climb
place the rain gauge in an open area at ground level

Note

No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's grounds or excursion risk assessment (RiskAssess where the school uses it).

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Ratios and rates; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-05
Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 1 focus area Ratios and rates; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S1-05
Mathematics Standard 11–12 Syllabus (2024), Year 11 focus area Applications of measurement; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-11-05
Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

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