Mr. Cloud Makes Dinner Part 2

So yesterday’s and today’s lesson in geometry started with this picture:

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_1

The question asked of them was “Will the pot of sauce overflow when the meatballs are added?” My students were quick to break that question down to “how many meatballs will make the pot overflow?” They’ve gotten to the point that they ask for measurements very quickly:

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_2

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_3

They had their dimensions. Then they asked for the sauce level:

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_4

They knew that we’ve been working with volume, but we had not discussed cylinders yet (they were at least calling the pot a cylinder). They asked about how to do the volume of a cylinder and that turned into a 30 minute lesson involing some basic calculus ideas. The bell rang and they didn’t get their answer.

Today’s lesson started with a review of the homework from the previous night. Once they felt grounded with cylinders, we brought back up the measurements. They calculated their volume of the pot. They quickly realized that the meatballs are spheres. On went a lesson about the volume of a sphere. Once they were okay with that, we got some measurments:

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_5

I didn’t give them every meatball’s diameter, but they decided that 4.5 cm was a “good enough” estimate (they actually found a use for an average). Then came their work:

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_6

Mr. Cloud Makes Dinner Part II Meatballs in the Sauce_7

The general consensus was that 11 would be okay but meatball #12 would be too many. Tomorrow we get to see if they were right!

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