Great Classroom Action

Brian Miller posts a smorgasbord of applied proportions activities, each of which poses students as crime scene investigators. He also gives purpose to the skills he wants to teach by fitting them inside a larger, more enticing question:

The basic premise is as follows: I show the Bone Collector clip first. I tell them we need to figure out the shoe size of the killer because we need to make sure that the killer is not in the room. Then I concede that I realize they are not trained investigators. Thus I tell them that over the next couple days we will be doing some investigator training, to get them ready to take on this case.

In some recently consulting, I was asked how to make to make trig identities less of a slog. I didn’t hesitate to send along Section 2 of Sam Shah’s worksheet. Section 2 really needs its own post. Briefly: watch how he sets students up for a major cognitive conflict as they all graph (seemingly) different trig functions only to compare and find out they’re exactly the same. “Okay, are you all graphed? On the count of three there will be the big reveal. One … TWO … REVEAL! Whoa. Really? REALLY? Yes, really.” (I don’t think I’ve seen anybody else pull off Sam’s worksheet persona, which is some kind of cross between “reality TV host” and “Vegas lounge act.”) The point of the worksheet isn’t practice. It isn’t instruction. It collects student hypotheses about a discrepant event which they’ll be working on “as we go through the next few days.” If math class were a movie, Sam’s worksheet would be the trailer.

Julie Reulbach encourages us to “save the math for last” in a very nice modeling activity. But questions like “what do we need here?” are modeling. They are math. Is it more accurate to say, “Save the computation for last?”

Never before had “test points” seemed so obvious to them. Test points were not just random points, they meant something. They told a story. The next day, when we finally got to the actually inequality lesson, foldable, and then homework, the students really understood the need for a test point. They also easily understood the horrific workbook word problem.

Bruce Ferrington asks students “What is my area?“:

My chief interest here is to look at how the kids are going to approach this question. I want to see if they can come up with any short-cuts that will speed up the calculations, so they don’t have to cover their entire body in 1cm grid paper and count out each square. Look what they did!

2013 Mar 22. Sam Shah wrote up his thinking behind the worksheet.

Featured Comment

Julie Reulbach:

Maybe, save the “procedures” for last? You know, the actual lesson with the steps and the summary of all of the rules they discovered but didn’t realize it.

I'm Dan and this is my blog. I'm a former high school teacher, former graduate student, and current head of teaching at Desmos. More here.


  1. Re: Sam’s worksheet

    I tell my students we all go by different names. You guys call me “Mr. Petersen,” some people call me “Dave,” others “David,” my mom calls me “son,” etc. Each of the names can reveal a different thing about me (and you), but at the core I’m still me. Sometimes I really WANT to be called “Mr. Petersen” because that’s what makes the most sense in that context. Other times it’s weird if my friends call me that. (This same analogy can be done with “looks.” Like how you dress up for a date, but slob around to clean the house. Still you inside, but different look and different uses for different places/times/functions.)

    Sometimes we want to use “1,” other times we need 1 to look like “2/2” (think common denominators), still other times it’s useful to have sin^2(x)/(1-cos^2 x). At the core, they’re all the same, but they look different and we call them different names.

  2. Seriously, calcdave, this is GENIUS. I need so many things like this in my teaching repertoire. I need moves like this which help kids analogize and remember why we’re doing what we’re doing in human (less abstract) terms… It’s similar to what Bowman talks about… making something “sticky” (calcdave, hold your tongue)… Now if I can only remember this post-spring-break, and then build it into my teaching… First you teach me to multiply matrices, and now this? Love you mucho.

  3. Thanks for the suggestion Dan. I spend much time tricking my students into “doing the math” while thinking that they are NOT “doing the math”. I would like to come up with a better “name” for it as we are going to start compiling our “Begin at the end” lessons in a combined document. I don’t know if I want to say save the computation for last because my students do simple computation all the way through the activity as well. Maybe, save the “procedures” for last? You know, the actual lesson with the steps and the summary of all of the rules they discovered but didn’t realize it. Suggestions are greatly appreciated! Thanks for the idea. I love our math community! :)

  4. Julie Reulbach:

    Maybe, save the “procedures” for last? You know, the actual lesson with the steps and the summary of all of the rules they discovered but didn’t realize it.

    Yup, that works for me.

  5. These are all awesome ideas! It’s a shame we can’t cram them all in one half semester. My personal favorite was the investigator idea because it’s something that you can build on first by giving students a goal and teach math in the mean time. The investigator’s sub-projects are also very malleable and short and easy to work with as a theme! Great post; bookmarked!