What’s that smell? The math of air quality

By Murray Bourne, 05 Nov 2008

This Air Contaminants Table from the U.S. Department of Labor Occupational Safety & Health Administration is interesting. Here's the first few entries:

TABLE Z-1. - LIMITS FOR AIR CONTAMINANTS

Substance        	ppm	 mg/m^3
		
Acetaldehyde		200	360
Acetic acid		10	25
Acetic anhydride	5	20
Acetone		1000	2400
Acetonitrile		40	70
Acetylene tetrabromide	1	14
Acrolein		0.1	0.25

"ppm" means "parts per million" and "mg/m^3" means "milligrams per cubic meter".

There are hundreds of airborne contaminants - what are you breathing right now?

The Air Contaminants Table could be the basis for an interesting applied math lesson. It could be part of a units topic (the meaning of concentration, mass per volume, parts per million, conversion between units, metric measure, etc).

First, students could find out more about the pollutants in their local area. Where do they come from? How bad is it? What can be done about it? If possible, get access to a 'real' air quality instrument (from the local council, or department of health, maybe?) and measure around the school and the local area.

They could plot the information using Excel and graph it. What are safe distances from the sources of pollution? What times of the day is it best — and worst? Posters of the results could be displayed as part of a community awareness event.

There's nothing like real, authentic data to make math more meaningful and interesting. And a key outcome is that students feel ownership for what they are discovering and learning - not like most textbook-based learning.

Aside: Singapore's air quality is generally good and certainly better than most cities in Asia. At least you can see the horizon on most days.

However, in my apartment, the fans are on almost all the time. When stopped, you can see a filthy black dust on them. Singapore is well known for having high concentrations of particulate matter (tiny particles in the 10μm range), mostly due to diesel use.

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