Category Archives: graphing

Motivating 1/x

We’re deep in a functions unit in FST (year two of a decelerated Algebra 2 course), and I love it. I love the concept of a relationship that takes inputs and produces outputs. I love visualizing functions with graphs. I love that functions feel natural and intuitive. I’m trying hard to share this enthusiasm with my students. They’re doing well with it so far, and it’s interesting to see how they think about functions.

Last class, I wanted to introduce f(x) = 1/x. I love this function. I love the discussions about division by zero and division by really large numbers and how the graph represents those ideas visually. My colleague shared a fun investigation with me, and I am so glad that I tried it out. At first I was hesitant because I know that I don’t explain directions well, but I focused on being very explicit and modelling each step. The kids investigated the breaking point of spaghetti. I wish I had some photos, but the students placed a dry spaghetti noodle over the edge of the table and hung a paper cup on the end of the noodle and added pennies one by one until the noodle snapped. The fun factor was definitely there- the kids enjoyed predicting when it would snap and liked watching the pennies crash to the floor.

Besides being fun, the activity modelled the function effectively. The kids recorded their data (length of spaghetti vs number of pennies), and I used Desmos to display some class data.

hyperbolaPenniesSpaghetti

Voilà, a hyperbola. The investigation gave the kids a good understanding of how the function behaves and why the graph looks the way it does. In retrospect, I should have done more of a “Noticing and Wondering” activity with the graph, but instead I just asked some questions like “What happened as the length of the spaghetti got longer?” and “What happened if the length of the spaghetti was really small?” which probably did too much of the thinking for them, but oh well.

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Filed under FST / Algebra 2, fun, graphing, group work

Desmos rocks my world

Last night I took the batteries out of my TI (83 plus!) graphing calculator to use in my bike lights. Sorry not sorry. Priorities.

In case you haven’t already discovered this fantastic resource, there is an online graphing calculator (and so much more) called desmos. Use it once and you will never want to use your old TI again. It’s easy to zoom in and out. It’s IN COLOR. If you are graphing multiple functions, you can make each one a different color. You can create sliders. And it is all FREE. Also be sure to check out all of the beautiful artwork while you’re there.

I won’t be ditching the TI for good because using it is a major part of my school’s current FST (aka the second half of Algebra 2) curriculum, which is fine. Students need to learn how to use TIs because right now they are the accepted technology for tests, both in the classroom and for standardized tests like the ACT and SAT.

Desmos is definitely worth incorporating into the classroom though. I used desmos with great success last summer when teaching summer school, and I think it’s great for doing investigations and creating visuals. That tiny, pixelated TI screen seems rather clunky and out-dated next to desmos, where students can really “see” the graphs and play around with them more easily. When I personally do math, I always use desmos if my laptop is with me. (Being significantly lighter than my laptop, the TI is more likely to be in my backpack on any given day.)

So I plan to use both desmos and the TIs in my classroom this fall. The TIs will be our go-to use-every-day type of calculator, but I’ll pull out the laptops as much as possible to use desmos for graphing investigations. I also hope the kids will come to appreciate desmos and start to use it at home or when they come to the math resource room during study hall. From summer school, I already have desmos investigations made up for quadratic functions and rational functions, but they were made hastily and need some improvement and some updating to more closely match my school’s FST curriculum. I’m excited! Now I just have to do some work and make these plans actually happen.

How do you incorporate desmos into your classroom?

Here are some examples I’ve found on the MTBoS:

Fawn’s Des-man which inspired the desmos team to create this awesome version of the project

Bob Lochel’s Desmos Filing Cabinet

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Filed under FST / Algebra 2, graphing, planning