Today in Algebra II I went off the beaten track. I wanted to make logarithms useful to them. Yeah, I could talk about the Richter Scale, or pH scale, or decibels, but when it comes down to it, logarithms really only become intuitive, natural, and beautiful once you reach calculus. Plus, these examples seem like such cop outs. If the are only good for weird measuring systems, then they aren’t really worth teaching in math class (not that I would be opposed in, say, a chemistry or physics class).
When I was in North Carolina for a math teacher conference, I went to a talk on logarithms, and the speaker reminded me that one great use of logarithms is for displaying data (either on a log scale, or a semi-log plot).
So today, I talked about my students being science journalists and representing data (confession: I cribbed this idea from the NC conference too): namely, I wanted them to create a timeline of major events in the evolution of life, from the existence of prokaryotes (3,000,000,000 years ago) to the emergence of homo sapiens, to the advent of writing (6,000 years ago).
Plotting all the relevant moments on a standard timeline yields a major problem: the events that happened closer to now (e.g. emergence of homo sapiens, taming of fire, writing) all overlap on the timeline — because the scale (of now to 3,000,000,000) is so large. The difference between something happening 6,000 years ago and 15,000 years ago on a scale this large is negligible.
So I taught them how to plot on a logarithmic scale: the events all become spread out, but you lose the ease of pulling off the data immediately from the graph. It’s harder to interpret the data, but it all becomes visible.
I think they learned something from this activity. If I had planned it better, I would have asked them to each find their own set of data to plot on a log scale.