[3 Acts] Coffee followup

I just showed the video from my first ever 3 Acts lesson, and the results were awesome! The students were really into it, throughout the entire hour and a half class (the only day that is that long for the class), and they even commented throughout how interesting it was!

I was a little worried at the start when their first 10 questions had very little to do with the point of the video lesson that I had planned.  It verified my initial concern that the video was too long. It also had a bunch of irrelevant stuff, which prompted even more irrelevant question (“Mr. Newman, have you ever thought of a career as an actor?” jokingly mentioned). But with just a little nudging, we got onto the questions I wanted them to discuss, which in turn led to a wide variety of solutions that I had to “run” with.

Here are some of the questions they actually asked (in the format of a Think-Pair-Share):

Why is the lion king music there?

Why did you use the mug that had OUR class’s Popsicle sticks?

Did you wash the mug out before you drank from it?

Was that water you were heating up?

Was the mug hot when you touched it?

Did you record that this morning?

As you can see, none of these questions are ones I was prepared to turn into a math lesson, though I was willing to branch out a bit.  I had to ask them “What do you think I was wondering as I sat there waiting for my coffee?”  A little artificial, but not so artificial that they shut down the lesson.

One of them finally asked “How long before you can drink it?”  I made sure to listen to a few more questions as if that wasn’t the one I wanted before deciding with them to settle on that question.

From there we made guesses, and after the guesses we clarified the question (“How long from the time you put the thermometer in to when you could drink it?”), so of course we had to make new guesses so that everyone was on the same page.

Then we did a Think-Pair-Share on “What do we need to know for this problem?” and after writing them down, we eliminated a few as a class.  I gave them the first 5 data points that I measured and, finally, we jumped into group work–groups of 3 around a big (2′ x 3′) whiteboard.  This is where the lesson took off and my kids shined (shown?).

I had in mind that they would ask for the equation and I would give it to them and we’d talk about functions, variables, domain, range, graphs, etc.  But they had something else in mind.

Some groups tried an arithmetic sequence (and knew to call it that!).  Some tried that and then tried a geometric sequence (and knew it by name, too!).  Others tried graphing it.  Two of the five groups found the geometric sequence and turned it into an exponential equation right before my very eyes!  I was astonished! (I hadn’t taught them this and I, probably like most math teachers, don’t expect students to come to me with any math knowledge.)  What’s great is I think they just figured that out–they weren’t using “formulas” or anything (although a few asked “What’s the formula?” to which I gave a quizzical look).

By the time we came back together and had our “board meeting” (haha), I had 5 groups that started the problem 5 different ways.  I told them that they were NOT sharing “how they did the problem”.  Instead, each group has a story, a story that they just created, and they are to share their story with their friends and classmates.  I think they jumped on that idea a little better than “show how you got the answer”.  For one thing, I emphasized that I wanted to hear what mistakes they made because that is one of the things that sets their story apart from the other groups.

Students shared and they learned, and I think that even though we hardly talked about functions, THEY figured out the purpose of functions without my help, even though they wouldn’t call it that and don’t know that they did.  Infinitely more valuable.

Only at the very end did I show my function and we briefly compared what two of the groups found with my function.

Things I can fix for next time

Better summary.  We ended quickly because we ran out of time (yes, 1.5 hr class period…), and the students were working 100% of the time (except for one time when I looked over and saw a student on Facebook on her iPad). I need to return to students’ guesses and their other questions.  We’ll definitely do that Friday, but we have sequels to answer, and other questions cropping up… I think I could teach on this video and topic for a week straight and not run out of steam.  How do you guys teach these lessons and close them?

Better video. The video needs a few things.  For one thing, you can’t see the temperature (thermometer is too small), and the stopwatch is in the background, so it doesn’t lend itself very quickly to the natural question I wanted the students to examine.  Part of the problem is that I like using Linux, so I’m restricted to open-source video editing software. I’ve yet to find one where I can put text or something like a timer on the video.

Better discussion.  Perhaps this comes through practice (on the students’ part) of sharing what they did, and being engaged in each other’s work.  Many of the students didn’t seem interested, and I had to call on a few of them to (a) pay attention and (b) ask questions that I could see on their faces but didn’t want to ask for whatever reason. They all presented well, however, for a first time, and nobody showed signs of being intimidated to share their work, which was great.

Oooh, and I didn’t even show “the answer” (I totally forgot about it). I’ll need to remember to do that Friday. What’s great is I’m blogging about this during my planning period, and I teach this lesson to the next Precalculus class, so I’m excited to see where they take it and what they do with it.

Much thanks to Dan Meyer and others who have developed the 3 Acts lesson idea to the point that I can take them and use this format in my class.  If I have time, I’ll post pictures of the whiteboards with students’ work.

Edit: here are two of the whiteboards that weren’t erased to give you an idea of the variety of approaches they took.

photo 1

This group guessed the closest even though they approximated very, very roughly.

This group guessed the closest even though they approximated very, very roughly.


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