Trying to find math inside everything else

Fish Populations and Proportions

One of the labs I did back at Banana Kelly was a fish population estimation lab. You may have seen something like it before elsewhere. The idea is to explore proportions and the mark and recapture technique of population estimation.

The gist is this: students have “lakes” filled with “fish” (boxes filled with lima beans). They use a sampling tool to collect a sample of fish and tag them all with stickers. Then they release the fish, mix them up, re-sample, and use proportions to determine the population of the lake. They do it a few times and average, then they count the actual population to see how close they were.

But I was at a BBQ the week before I did this lesson, and I was talking to my friend Rachel, who is a marine biologist. I mentioned the lab, and we talked about what they use tags for. One thing is to track populations over time, so they can determine the changes in populations since each different year has a different tag. I wondered if I could change the lab to include that.

(Rachel also dug up the video that I had students watch the night before. I’ve decide to have a little “flip” in my classroom by having students watch a video before we do a lab and start asking questions, which I can then address in the next class.)
So I thought about how I could change it. It actually took a lot of thinking, jotting things down on the white board, consulting with the living environment teacher to make sure I was on the right track. But I extended it, so now they would do at least 5 different calculations in the process, instead of spending all that time on just one proportion.

Now, students do the first part the same as before. Then, a random sample of fish “die” and are removed from the lake and put side, and a bunch of new fish are “born” by taking them from the bag of beans I had. Then when they took a sample of the new lake, they tagged the new fish (not already tagged) with a different color sticker. Now they had data from both years and could figure out the new population, and the difference from the old population.

Not every group got to the extension, but I think it improved the task overall.

The Materials

Fish Lab Instructions (formatted to fit in an INB)

The Lab Report

Math Needs to Be the Spark

At Twitter Math Camp I gave the following talk. The abstract from the program said:

When planning interdisciplinary projects, math teachers need to take the lead in order to create cohesive and authentic projects, and to ensure that the project doesn’t just become psuedocontext for their math goals. Uses two major interdisciplinary projects developed at my school as examples of how to bring all the subjects together, so math isn’t left out in the cold.

Here’s the talk:

After that I opened to questions. The one that I remember was asked by @JamiDanielle: “How can you get other teachers who might not be on board for these types of projects to join in?” And I think this process is actually how. If you go to a teacher with an idea and just dump on them to figure out how to connect it to their class, it’s not going to end well. It’s easier and less work to just not take part. But if you go to them with an idea already half-formed of how they can implement it, it is much easier to build off of that idea and will make teachers more willing to work together.

The Projects

High Line Field Guide v5 – This is the High Line field guide project mentioned in the video, and first mentioned in this blog post, “The Start of the New Year.”

Intersession Project Requirements – It would be difficult to post everything we did in the Intersession project, but the overview from the video and this packet of requirements for the product should be useful. Anyone interested in more can ask.

Scaling

Today’s Unshelved gave me an idea for a possible Living Environment-connected lesson I can do in the new year. Surprisingly, though most people think Math and Science go hand in hand, I have a much harder time connecting Living Environment to math than with ELA or History. (Maybe this XKCD comic explains why I have an easier time with Physics and Chemistry.)

During my statistics unit this past year I did a lesson on scaling and how area and volume scale proportionally to the square and cube of the length. I did it during the statistics unit because it was based on how improper scaling is used to mislead people. (My unit was based on the book “How to Lie with Statistics.”) Of course, where the lesson lies may change based on the curriculum overhaul I do this summer, but I imagine the basics will be the same.

I ran the lesson as a lab, with students building letters out of blocks and then scaling them upwards by factors of 2, 3, 4, and seeing what happens to the area of a trace and the volume (number of 1 cm^3 blocks needed). It was a fine lesson, but I wonder if I can’t improve it with a little more…wonder.

I want to see if I can find a good picture or video of a giant creature like mentioned in the Unshelved post and see if I can get students to wonder if it can exist. That sort of question can give purpose to the scaling exploration in the lab. If you read this and can offer assistance, great. Expect a post in the future based on what I find.