# Sig Figs

Well, the year is winding down here. Last week  I only taught one day; we left Wednesday for Washington DC for 4 days for the 8th grade end of year field trip.  A few pictures:

The last photo is at Arlington National Cemetery and was pretty thought-provoking for me on our coordinate plane system. Have to think some more about that one.

Anyway, I’m losing some teaching time for end-of-year tests, and tomorrow and possible Thursday as well I’m on team science fair, helping our science teacher and our students get ready. I needed something to teach at the end of the year that would be meaningful and hopefully interesting while our 8th graders are on their last legs. I settled on significant figures.

I’m already second guessing that, but even after one day I’m learning a ton, and my students are definitely learning something.

I introduced the topic with this question:

and asked students to predict the answer. Go ahead, try it. (Almost all of my students did 7.1*7.1*16*3.14, although a few tried to give me the answer in terms of pi).

Then I showed them Wolfram Alpha’s answer:

(If you didn’t calculate, the answer my students all got was 2532.5984)

Anyway, this was a pretty decent hook into the idea of significant figures. Problem was, it didn’t sink. I tried to get the class talking about precision, and the difference between measuring “about 5 inches” and “5.192 inches”. I think that, if I want to take that approach, I need to invest in more time working with and thinking about measurement (and this makes me think of Paul Lockhart’s book by that title, which I’m currently reading and thoroughly enjoying).

Anyway, I reversed course, and in my later classes I framed it differently. Instead of trying to justify this idea of “how precise is our answer really?” I framed it as “you know that weird thing where teachers ask you to round to random decimal places sometimes? here’s a rule that scientists use to figure out what to round to.”

Kids dug this, and I saw a huge increase in willingness to dive into problems and persevere.

Hypothesis:
1. This method was more effective because it was concretely connected to something my students understand (rounding) with a new twist (significant figures)
2. This method was more effective because it sat well with questions my students had asked (“why are we rounding to this place anyway”, and “do we haaave to write out all these decimals”)

I don’t know. I think there’s a lot of meaning in this idea of precision, but I’m not confident I can move kids there, especially at this stage in the year. My goals with this mini-unit are pretty humble — expose kids to sig figs, make them more confident going into high school science classes, and not have them hate math class the last two weeks of school. We’ll see how that goes.