Reflection:
In some ways, the money here is the last question from the sheet they completed as partners. I memorized these formulas many years ago but they’re irrelevant when you’re trying to figure out the connection between a pile of green waste — let’s say rotty greens from the kitchen — which weighs two pounds and a composter that holds six cubic feet of material. How do you know? How do you account for the fact that a mass of greens will weigh less than a mass of shredded carrots? And if you’re trying to plan a composter, what do you do?

Student responses:
In plain English, write down 3-5 ways you can explain the volume of an object.
DW: How much it can hold The space inside an object!
VG: The space an object takes up.

In math teacher language, write down the best definition you can think of to explain the volume of an object.
IP: The space within an object which matter consumes.
JH: It can be measured in ml or liters.
VG: The measurement of a three dimensional geometric space.

In borderline inappropriate language, write down the definition of volume.
MC: What in it.
AR: The bottom times the side times the middle equals the inside.

Basically, how does one calculate the volume of an object?
TC: Length x Width x Depth
AH: There are different equations for different types of shapes
VG: Cut an object into slices and then add up all those slices.
BC: Multiply all the sides!

Why is it easier to calculate the volume of a rectangular object like a box as opposed to something round like a cylinder?
DW: With a cylinder you have to know the area of a circle.
VG: You have to know the area of the base for any object but it’s easier when it’s a rectangle.

Write down the formula for calculating the volume of a round object.
V=r2hPiXr2Xdepth where V is the volume of the object, r is the radius of the circular base, and h is the height of the object.

How would you calculate the volume of two different size objects attached to each other?
Break into two parts and then add ‘em up!

How does one write the volume of an object in cubic feet?
Eight cubic feet cu ft ft3

The “footprint” of your composter is measured in square feet. The composter’s capacity is measured in cubic feet. Why?
The footprint is the space it takes up looking down (2D)
The composter is measured in how much it holds (3D)

On the back, write down three strategies for converting weight into volume. We have to do this for our composter. How should we do it?

Opening reflection:

“There’s no difference between small decisions and big decisions when it comes to morality.” True or false? Defend your position.

Circle is a struggle these mornings. I’m gaining some traction by calling/texting every child who is late and/or absent. I’m gaining more traction by grading the short writing reflections that we use to start our conversations. It’s a tough balance, though, trying to get engagement because it’s worth thinking about these questions while simultaneously managing what has evolved into a disciplinary matter.

Either way, we got where I hoped we’d get pretty quickly: one brilliant person arguing that there are just decisions and small decisions all pave the road for big decisions and another brilliant person arguing that we cannot compare things like murder and what you eat for breakfast. Can we draw a moral equivalence between all actions? Or is it enough to drive towards an awareness about how all of your small decisions flow into your larger decisions?