Cogitania

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Building a mathematical model

Dear Parents,

It has been so much FUN to observe your kids bending, sitting on the floor, problem solving and creating a REAL lab experiment. Here is the last session's summary. Please, share the data/results with your kids!

This week we started by discussing experimental strategies for addressing our questions and hypotheses about water flow from a reservoir through a tube. We came up with some interesting guesses for how flow rate could change if we only used a single tube length. From intuition and past experience, we think that there will be less flow as we decrease the height difference between the water surface in the reservoir and the tube exit.

But the students also came up with very important questions about the effect of the path of the tube between its entrance and exit. Specifically, if the tube is always extended, does the angle that it makes with the ground matter? We know, for example, that a block sliding down ramps of different grades (from the same height) would reach the bottom at different velocities. We then struggled with the physical reality that there is no way to keep both the tube length and height difference constant while changing the angle. How about if the tube was coiled up between entrance and exit? But how could we assign a single number to that condition? It was a good chance to think about the feedback loop between making hypotheses and designing experiments to test them.

The rest of the day was spent on measuring flow rates after changing the height difference, and making sure the tube remained extended. This way, we could at least record all of our variables (including angle) and hopefully sort things out later while we analyze our data. We practiced our engineering skills by improvising better and better ways to set up our experiment using the tools and equipment that we could find around the "laboratory". We got through 25 trials in an hour, as compared to 12 in the last session.

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We will analyze our results together next session to see if we can start building a mathematical model of the system, but I am sending out the data collected in case anyone wanted to get a head start. Also next session we will have to address the outstanding issue of whether tube path matters. At that point we should be in a good position to understand the nature of the driving force for the flow!

Have the most memorable Thanksgiving ever!
warmly,
Joanna