Monday, May 16, 2011

Color Coding: For Sketching Piecewise

I tried a new (for me) approach for introducing piecewise functions in my Algebra 2 class, and it went over pretty well.  There is nothing really earth-shattering about this method, but it does involve color-coding -- and that is totally on my list of favorite things!

First of all, I am using only basic parent functions and their transformations that my students are already familiar with (linear, quadratic, and absolute value).  They do not need to plot points, because they already know how to sketch these graphs. I spent some time reviewing these before the lesson.

I start out with the idea of a restricted domain.  Students sketch the function, using the entire coordinate plane . . .

Then we worry about this "if" that comes after the function. Students color the restricted domain, and the corresponding portion of the x-axis.

Then they draw vertical lines to enclose the restricted area and shade it in completely.

And then they erase everything that is not in the restricted area.

We practiced these for a while before moving on to piecewise.

For piecewise, we shaded each restricted domain with a different color. Then shade in the corresponding restricted areas.

By the time we reached this point, most students could draw the graphs within the restricted areas without drawing the entire graph and erasing.

I've taught this lesson before, but pairing it with colored pencils was a first for me. I am pretty happy with the results, especially considering that a bunch of them are *DONE* and have started to shut down for summer.

Secret to motivating students this time of year, anyone?

Or, to get everyone to at least bring a pencil?


  1. I loved this post because I myself cannot teach graphing in Algebra 2 *WITHOUT* colored pencils! I had an old Russian mathematician professor who used colored chalk in a unit on graphing and you could physically see light bulbs going on over people's heads all over the room. Even the students who were already quite skilled with geometric interpretations of algebra latched on to this idea. I don't know why it has not been a staple for us in teaching students how to graph.

    I use colored pencils in teaching transformations of basic function graphs, but I really like your idea of using them to shade in the different areas of the domain in a piecewise-defined function. Something about the color-coding of the different parts of the domain makes a lot of sense. Piecewise-defined functions tend to really baffle students, but your idea makes it a lot clearer -- and connects the symbolic and geometric representations. Thank you!

    - Elizabeth (aka @cheesemonkeysf on Twitter)

  2. Hi Elizabeth! Thank you for commenting! I agree that colored pencils should be a staple in math class. I am curious, how do you use them for transformations? I'd love to hear more!


  3. I'm guessing if she wants to graph say 2|x-5|+1, she graphs |x| in one color, then |x-5| in a different color, then 2|x-5| in a different color, and so on.

    My Alg2 students are weirdly still motivated with only 7 class days to go...I wish I knew why! My best guess is that since the state canceled the August administration of their exam, they know there's not a second chance in a couple months.