Watch this one minute clip and if you find yourself wondering, "Do Joulies really work?" ask yourself, "What would that kind of temperature graph look like?" and then click on through to the third act of the lesson plan to find out.
A few release notes:
- The Goods. My favorite part of the task is how much work the students have to do to translate the inventor's claims to mathematics. He says, "When coffee is poured into a travel mug with Joulies inside, the coffee cools down to a perfect temperature three times faster than normal. Then, when the coffee would normally cool off, the heat that was captured is released actually keeping your coffee pleasantly warm for twice as long." ¶ So students have to make an assumption about "perfect temperature." Is that a range? Is it a single temperature? Then they have to make an assumption about the initial temperature of the liquid and its final temperature. Then they have to create their initial graph. ¶ They get to decide and own all of that. We don't care. We care about their transformation of their initial graph and whether or not it fits the inventor's claims.
- Formative Assessment. Why did I close the first act video with this frame and not this frame?
- The Competition. Sometimes I wonder why we should bother with that level of precision, why we should analyze these videos on a frame-by-frame basis when our competition in the video-based math curriculum space is basically drooling all over itself.
- Citation. Marco Arment performed a similar experiment with Joulies. I got the idea to use rocks in the sequel from Jeff Ammons.
- Feedback From Pearson. They told me I should consider changing the domain of the temperature graph from six hours to one, because it's rare to drink the same cup of coffee for six hours, and to be a little kinder to ELL students by using "joulies / no joulies" rather than "joulies / plain." Other than that, they get what I'm trying to do here and they support it.
Criticism from Bowen Kerins is one of the big reasons why I bother posting this stuff. Here's his entire comment:
I think the one-hour timeframe is better than six hours. More importantly, though, you’re running across limitations of video technology by having to make this decision at all.
To me the “best” solution would be to let students decide what their axes limits should be, then see the graph populated. A tablet-PC environment could make this happen. A static video takes this decision out of the hands of students because you’re forced to select this in advance, or to set up a limited number of options. The same is true for the vertical axis — my first reaction to the presentation was “Why does the vertical start at zero degrees Fahrenheit??” And what led to the maximum being 160 degrees?
I’d want students making those choices as well, ideally in an environment where a quick change doesn’t cost them anything. Even when students are asked in advance to create the initial graph, leave the axes totally unlabeled and let them make all the decisions.
I also think this flexibility would lead to students coming to different conclusions about the effectiveness of the Joulies. A one-hour or thirty-minute graph makes it look like the Joulies are doing a pretty good job, while the six-hour graph makes it look like they do nothing most of the time. It could even lead to a cool “how to lie with data” conversation, or at least an important conversation about the nonlinearity of the graph (to meet 8.F.5). Often students think all graphs and functions are linear. The short-term graph of the “no Joulies” seems linear enough… then boom it ain’t!
I’m also a little confused by your student work example — the graphs show that the Joulies version stays in the “perfect” zone for more than twice as long (75 minutes versus 30). So I would not agree with the student’s assessment that they “stay perfect for almost exactly the same amount of time”. The six-hour versus one-hour makes a big difference here, I suppose.
Last, two nitpicks: the video talks of coffee but then presents tea (no big deal but why use tea and not coffee?). And please show me an actual eighth grader with the quality handwriting exhibited in the “student work” ;)