So yesterday’s and today’s lesson in geometry started with this picture:
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:
They had their dimensions. Then they asked for the sauce level:
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:
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:
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!