# Monthly Archives: April 2017

## [3 Act Lesson] Sandboxes: Volume of Cylinders (& Spheres)

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!