In middle school we only get 47 minutes, which is not enough time for the 3-act lessons I had gotten used to (coming from 90 minute blocks!). After a 5 minute warm-up, and 5 minutes of going over HW, that leaves no time for a lesson. But today I think I was able to get all three acts in, so I wanted to share my success!

We’re doing volume of cylinders, cones, and spheres in 8th grade math right now.

**Act 1**

Me: Spring break is next week, and here’s my Spring Break plans.

Students: You’re going to the beach?

Me: Nope, I’m going to build a sandbox for Benji (my 2-year-old). What do you think is the most expensive part of the sandbox?

Students (in unison, surprisingly): The Sand!

Me: Right, so forget the wood for now because I have enough scrap wood that I can probably build the frame without buying any wood. My wife and I are trying to decide between a 6’x6′ and an 8’x8′ sandbox.

Student: 8’x8′ cause it’s bigger, duh!

Another Student: But that would cost more!

Me: What do you need to know to find out how much more it would cost?

Student: How much all the sand costs.

Me: Right. You don’t buy “one sandbox worth of sand” at Lowes. It comes in bags.

Eventually they get to needing (1) how much is in a bag (0.5 cubic feet worth of sand), (2) how deep is the sand in the sandbox (6 inches), (3) how much each bag costs ($4.25 is what I found at the local Lowes).

We did the comparison together because we were so short on time. If we had a block period, then I would have let them struggle instead, but I wanted them to get to calculating volume of cylinders in context instead. The work I write on the board looks something like this:

**6’x6′**x0.5′

18 cubic feet

36 bags

$153 is the total cost for a 6’x6′

**8’x8′**x0.5′

32 cubic feet

64 bags

$272 is the total cost for an 8’x8′

We have a brief discussion answering “why is $272 nearly double $153 but 8′ isn’t nearly double 6′?” Unfortunately I pointed this out to them and had to start the discussion but it’s something that I feel is important enough for me to “artificially” bring up.

**Act 2**

Now I want you to get one large (4’x2′) whiteboard for your table, one marker, and make a cost comparison between a 6′ diameter circular sand box and an 8′ diameter circular sandbox. Go!

The students did a really good job (we’ve been practicing finding the volume of cylinders).

Here’s some of their work (I’m sharing the more legible ones)

**Act 3**

As students finished, I gave them this challenge problem:

“Suppose the silo at our farm is filled with sand. How many 8’x8′ rectangular sandboxes could we fill with all that sand?”

I draw a picture of a silo (hemisphere sitting on a cylinder) with cylindrical height of 20′ and overall diameter of 10′. As you can see from the pictures above, some students did pretty well at that problem, too!

**Analysis**

The students were really interested in my spring break plans. The “builders” of the class liked the idea of figuring out how to get ready to build a project, even if it was just buying sand. The “caretakers” of the class like that I was doing something for my 2-year-old. Get enough of the students on board and they all really take to it, and I was fortunately that this happened here. Here’s the google slides I used for the lesson.

How would you improve it? Alter it? Thanks for any and all feedback!