How Long Until Mr. Cloud’s Out of Water?

Today in geometry, I had an empty 2.5 gallon container of water. I raised the question “How long did it take for me to drain the container?”

The first step was for the students to decide what was a reasonable guess:

9.3 Running Water Problem_1

Once it was time to get to mathematical business, they quickly asked for some measurements. We’ve just started with calculating volume, so they decided for length, width, and height:

9.3 Running Water Problem_4

9.3 Running Water Problem_3

9.3 Running Water Problem_2

There was a quick conversation about the water level at the start of the draining, and a quick conversation about the accuracy of our calculations since the container isn’t a perfect rectangular prism.

Finally, someone asked how fast the water drains out of the container. I couldn’t answer that question for them, but I could give them this:

9.3 Running Water Problem_7

9.3 Running Water Problem_8

9.3 Running Water Problem_6

It took me 13 seconds to fill up the smaller container. My students were content at this time and went about their calculations. Most of the calculations were along these lines:

9.3 Running Water Problem_9

9.3 Running Water Problem_10

Seemed reasonable. Most people were in this ballpark. So we got our answer:

9.3 Running Water Problem_11

This confounded them. They weren’t right. They looked to me for answers. No calculation errors were found. They concluded that the flow rate wasn’t constant and that the amount of water in the container helped determine how fast the water comes out. Huge insight!! Now if only we offered physics!

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