Exponential Decay
I really like the concept of NCTM's "Too Hot to Handle, Too Cold to Enjoy." However, I think I would take the video and run with it. The student worksheet is okay but leads the discussion a little too much. If we're trying to get at problem-solving skills and inquiry-based learning, then giving the kids a table completely undercuts the mission. In essence, you're saying solve the problem this way. After the initial investigation into water cooling, I think some hands-on extensions would be in order--an extension or "sequel" in Act 3 (Dan Meyer) terminology. Does the amount of water affect how quickly it cools? Does the type of container matter? As a class, decide on a question to investigate and set up the experiment. A Coleman camping stove and a couple of large pots would work. I'd rather do it in class and have students take measurements than simply video tape it at home: 1) Video editing isn't one of my strengths 2) student engagement with the experiment. Of course, you do risk students harming themselves or others with boiling water but these kids also take chemistry and handle sulfuric acid. Come on, I think we can do a hot water experiment.
If the class chose to measure how volume of water changes the cooling time, a discussion of transformations based on the amount of water might be appropriate. Can we create a way to predict how long it will take any amount of water to cool to room temperature (or any temperature we pick for that matter)?
Talking points:
I'm starting to post these thoughts to the MichEdMath.weebly.com website. Hopefully, by the end of the summer, I'll have a good repository of material to work with and, hopefully, I won't be the only one contributing.
I really like the concept of NCTM's "Too Hot to Handle, Too Cold to Enjoy." However, I think I would take the video and run with it. The student worksheet is okay but leads the discussion a little too much. If we're trying to get at problem-solving skills and inquiry-based learning, then giving the kids a table completely undercuts the mission. In essence, you're saying solve the problem this way. After the initial investigation into water cooling, I think some hands-on extensions would be in order--an extension or "sequel" in Act 3 (Dan Meyer) terminology. Does the amount of water affect how quickly it cools? Does the type of container matter? As a class, decide on a question to investigate and set up the experiment. A Coleman camping stove and a couple of large pots would work. I'd rather do it in class and have students take measurements than simply video tape it at home: 1) Video editing isn't one of my strengths 2) student engagement with the experiment. Of course, you do risk students harming themselves or others with boiling water but these kids also take chemistry and handle sulfuric acid. Come on, I think we can do a hot water experiment.
If the class chose to measure how volume of water changes the cooling time, a discussion of transformations based on the amount of water might be appropriate. Can we create a way to predict how long it will take any amount of water to cool to room temperature (or any temperature we pick for that matter)?
Talking points:
- Figuring out the type of function to model with based on the data (exponential, inverse, quadratic, inverse square, linear, etc) This leads to good discussions on the key features of graphs: i.e. the inverse function may work well for much of the data but does not allow for a y-intercept and the quadratic works excellent except for the fact that it comes back up after a time.
- Exponential modeling based on two points and regression.
- Taking asymptotes into account when doing modeling (room temperature being the asymptote means room temperature would need to be subtracted from all data points before getting a good regression fit)
- Solving exponential equations through graphing.
- Solving exponential equations with logarithms.
I'm starting to post these thoughts to the MichEdMath.weebly.com website. Hopefully, by the end of the summer, I'll have a good repository of material to work with and, hopefully, I won't be the only one contributing.
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