## Tuesday, November 15, 2016

### The Capacity of Water-Carrying Structures (Day 61)

Learning Module 6 of the Illinois State text is "The Capacity of Water-Carrying Structures." (As usual, I'm referring to the eighth grade text.) This project is the first one of the second trimester.

Yesterday was the first day of our "everyday is like Wednesday" schedule for parent conferences. So we squeezed in all of our classes into the shortened Common Planning schedule. This is not unlike what full middle schools do on their Common Planning Days, shorten every period -- so each period was only 50 minutes long instead of 80.

This would have worked out perfectly had it not been for Monday coding. On a regular Monday, the coding teacher sees the seventh graders during the first part of first block, and then the eighth graders during the last part of second block. That's because in between he sees the combo K-1 class -- and it's awkward for him to change his elementary schedule just because middle school has shorter classes.

And so he ended up coding with 7th grade, then K-1, and then 6th grade during 3rd period. As it turned out, 4th period is usually IXL with 8th grade, so he just did coding with them then instead.

This meant that I had 2nd period with 8th grade with nothing to do -- nothing, that is, except begin the STEM project. So we actually began "Capacity" yesterday.

What exactly is "Capacity," anyway? In this project, students are to discover that the most efficient pipe shape is a cylinder. By efficient, of course, I mean that it has the largest volume given a fixed lateral area.

Notice that this is really just the Isoperimetric Theorem that I mentioned back in April. Of all plane figures with the same perimeter, the circle has the largest area. Multiplying both sides of this inequality by the constant height, we conclude that of all prisms with the same lateral area, the cylinder has the largest volume. (Of course, of all solids with the same surface, rather than lateral, area, the sphere has the largest volume. But a pipe can't be a sphere -- pipes must actually go places, and so they are actually prisms.)

Of course, in this project, the students are to discover this for themselves. Yesterday, the students created four "pipes," each out of a half-sheet of paper. One is a cylinder, one a rectangular prism, one a triangle prism, and the fourth is of their choosing. Then today, the goal is to pour sand down the pipes and measure how fast they fall, in hopes they'll see that the cylinder is the fastest.

Unfortunately, when we return to the project today there are a few problems. Some of the tubes the students constructed yesterday got lost -- and I haven't been able to find the scissors all week. I had to ask the English teacher yesterday for scissors, and I don't want to ask her again for them today. In the end, I have one group perform the experiment with just three tubes. But then this group, who tries the cylinder first, has trouble figuring out how to control the stopwatch. In the end, they time it wrong, so that it appears that the cylinder is the slowest instead of the fastest! Notice that all of the problems with the project ultimately go back to materials -- from losing the scissors to losing the tubes to not knowing how to stop the watch.

Today the seventh graders work on the project "Traveling Around," where they learn how to read topographic maps, and the sixth graders work on "Walk This Way," where they try to keep track of human movement. There;s more confusion with the schedule today -- after nutrition I want to have IXL with the sixth graders. But then the other middle school teachers say that it's better to rotate the last class of the day, and I find myself with seventh grade instead. So I just have them continue working on "Traveling Around." Some of the groups draw their own topographic maps, but there's not enough time for them to try making their own relief maps (with depth).

The "Day in the Life" poster whose monthly posting day is the 15th is Kathy Howe:

https://mathyesyoucan.wordpress.com/

Howe hasn't made her November 15th post yet, but I do see something interesting in her October 15th post, despite that date being a Saturday:

https://mathyesyoucan.wordpress.com/2016/10/16/october-15-blessed-saturday/

Howe writes:

It’s 6:00 and the sixth-grade tests are finished [being graded -- dw].

Ah ha -- so Howe is a fellow middle school teacher! (It turns out that she teaches in Texas.) I'm always especially interested in middle school bloggers, so let's look at this post in more detail:

Notice that I haven't really taught decimals yet this year, but this certainly gives me something to look out for whenever we do reach decimals.

Howe writes about her seventh grade class as part of the reflection questions:

We’re starting new units in both of my classes next week.  I’m going to teach fraction, decimal, and percent equivalence in sixth grade.  I’m teaching rates, ratios, and proportions in seventh.  In the sixth grade class, I’m not doing a lot to change the delivery of the material from last year.  But in seventh, I’m pushing to have a lot more real-world applications and student-centered lessons.  Because this topic is so easy to connect to the real world, I have a lot of different options for 3-act tasks [King (of MTBoS) Dan Meyer's lessons -- dw] and authentic assessments.  The sixth graders will do this same topic soon, so they will benefit from these applications as well.  I’m realizing that sometimes you need to teach skills and it is ok if they are not saturated with context.  When the context is genuine, then you apply it like crazy, and use the skills that you learned before in the new context.

Notice that in my class we already covered unit rates in both sixth and seventh grades -- this is what I taught at the start of the year.

Howe even writes about a trip to the doctor she made that Saturday morning:

As I’m filling out my paperwork, a woman sits down with a Saxon math book and a grade book in hand.  The woman on the other side asks if she is a teacher.  It turns out that there are four of us who are teachers, all sitting together in the waiting room.  Lucky for us this clinic offers Saturday appointments!

Ah yes, we've discussed the Saxon texts several times here on the blog -- in fact, I purchased the Saxon Algebra 1/2 text just last month. Yes, there do exist schools actually use the Saxon texts, and recall that Texas was never a Common Core state.