Algebra II

Tech Post

This four day weekend I did a lot of relaxing and movie watching. I also have been working on three tech things, in addition to updating my slowly burgeoning online portfolio. Note: I store documents and host the banner picture on this great free site called boxstr. I highly recommend it.

1. I learned that my mac has iMovie, which I learned how to use in the most basic ways. But it’s simple, easy to use, and has a lot of things that makes me think that I could make a really funny short vignette for the classroom — setting up a math problem/puzzle for my kiddos. And the fact that it ties in so easily with iTunes, iPhoto, and the built in camera is just heaven.

(I already made a sample 3 minute video which consists of pictures of me and my friend Henny. It took about 40 minutes to learn how to do it, pick the song, and get all the photos to show up at the right time.)

2. I spent about 90 minutes researching rss aggregators. I want to have a place to put my math teacher blogs, and lets me read them all at once. My two criteria: (a) it must be web based so I can access my feeds anywhere, and (b) it must be pretty to look at. I’m so sick of rss aggregators looking like Outlook Express. My conclusion: netvibes wins. It’s not designed to be exclusively an rss aggregator, but it certainly does that, and does it well.

It’s customizable in all the right ways, too. So I’ve made it look pretty with no effort. Right now it only has 6 blogs, but when I have time, more!

3. I have been working on a project for my Algebra II kids. They are going to be making Smartboard videos of how to do certain problems, or addressing certain topics, from this year. The other Algebra II teacher and I are starting this now, and hopefully by Spring Break, each student will have created one video. Then hopefully students will be able to use these videos when studying for the final exam, to either refresh their memory on old topics, or in some cases, to learn them for the first time.

There are lots of logistical things which are going to be crazy about this, so I hope it goes smoothly.

The Origin of Life on Earth and Logarithms

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.

Logarithms

Logarithms. Confusing, unintuitive, blasted made-up things! I am teaching my Algebra II classes logs for the first time today, and since I didn’t have much time to do my planning last night (I went to the school dance concert, and by the time I got home, I was too tired to function), I made only a mediocre lesson plan.

I think if I had given myself more time to plan things out, I could have made an interesting lesson — one that made logs seem less like things that pop out of nowhere, and more like these concrete natural things that simply had to exist because them not existing would be even more horrifying.

Sort of like I tried to do when I introduced imaginary numbers.

I didn’t do a terrible job, but I know how confusing logs can be, so I wanted to do a bang up job. Instead I simply took the book’s presentation wholesale and translated that to Smartboard. Next year I’ll try to look what other teachers do.

Paper folding and exponential functions

I am teaching exponential functions in my Algebra II classes this week. And I just came back from this teaching conference, where one of the sessions included a few handouts of the types of problems that this one charter school uses. And lucky for me, one was on exponential growth and decay.

I wholesale retyped this activity-based lesson up and gave it to my students. I can’t say it was the “most awesome thing ever,” but I can say that it got students to think for themselves instead of being spoon fed everything. What it had students do is to:

Fold a piece of paper in half and record: (1) the number of folds made, (2) the number of regions the paper is divided into, and (3) the fractional area of each region. Then fold the paper again and record those numbers again. (So after 1 fold, there are 2 regions, each with fractional area 1/2; after 2 folds, there are 4 regions, each with fractional area 1/4; …).

What students discovered was exponential growth and decay. What was interesting i&s that when I had them try to come up with a function relating fold number to the number of regions (y=2^x), many of them couldn’t do it. They would try thinks like y=2x, or y=x^2, but it wasn’t until I reminded them that the number of regions (2, 4, 8, 16, 32, …) could be re-written as (2^1, 2^2, 2^3, 2^4, 2^5, …) that the majority of them could figure it out.

In any case, it took a good 20 – 30 minutes for them to finish the activity (which included some plotting, and some discussion of independent and dependent variables), but overall, I’d like to think they got more out of it than me simply explaining in words what an exponential function is.

Not that I have the time to come up with a bunch more of these, nor the classtime to implement them, but I think having one or two per chapter up my sleeve would be perfect.