Tuesday, November 29, 2016

Student Journals: Volumes of Pyramids, Cones, and Spheres (Days 65-66)

Today the eighth graders return to the Student Journals. As I promised on the blog last week, they are now working on the following standard:

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Today I cover cylinders, and tomorrow I'll do cylinders. We're now in the geometry standards -- and as you can tell from the title of this blog, geometry is my favorite subject to teach.

There are a few issues with this lesson. As the readers of this blog already know, the volume of a cylinder is:

V = pi r^2 h

The problem here is how to handle the number pi here. Some texts have their students leave the answers in terms of pi, while others have the students use 3.14 instead. This can make a difference in the answers, for example:

Find the volume of a cylinder with radius 1 and height 10, to the nearest hundredth.

Let's try this one -- since pi to the nearest hundredth, we obtain:

V = pi r^2 h
V = (3.14)(1^2)(10)
V = 31.4 cubic units

But the correct answer is 31.42 cubic units -- since pi is more accurately 3.14159, the answer of 10pi is actually closer to 31.4159, which rounds to 31.42. We lose the digit 2 when we round before we perform the multiplication.

The Illinois State text doesn't make it clear which convention is to be used -- the students are merely instructed to find the volume, with no mention of rounding at all. But there is one question where the volume is given and the students are supposed to find the radius. It goes something like this:

Find the radius of a cylinder with volume 6280 cubic units and height 20.

Notice that if we use pi = 3.14, we obtain the exact equation r^2 = 100, which is clearly intended. So the Illinois State text expects students to use 3.14 for pi.

The expectation that students round pi to 3.14 before using it is made more explicit on IXL. The instructions given on that website are:

Use pi = 3.14, and round your answer to the nearest hundredth.

So IXL would not accept 31.42 as the answer to the above question, even though 10pi is much closer to 31.42 than 31.4.

I want to keep my class consistent with Illinois State and IXL, and so I tell my students to substitute in 3.14 for pi, just as they substitute in values of h and r. In particular, I don't have my students use the pi key on the calculator.

But then there's another problem. You see, most of the calculators in the class are Casio fx-300ES, and on these calculators, decimals are automatically converted to fractions. So instead of 31.4, the Casio displays 157/5. As awkward as 31.4 is, 157/5 is even worse. It sends the wrong message, as it makes numbers like 10pi appear rational, after we made a big deal about irrationality. And I can't figure out how to turn off the fractions, except by pressing the scientific notation mode -- and I don't want the students to see 3.140000000 01 either. We did cover scientific notation earlier, but it was taught briefly and in pieces.

By the way, the calculator also displays some irrationals exactly, including some square roots like sqrt(2), and even pi itself and its multiples. So 10pi displays exactly as 10pi, if the students were to use the pi key to perform the calculation.

At this point, I could have the students just keep their answers in terms of pi using the Casio, or even by hand and dispense with the calculator completely. But this approach doesn't satisfy Illinois State or IXL, where students need to multiply by 3.14. And finding the volume of a cylinder with radius 14 and height 16, using 3.14 as pi, is very cumbersome to do by hand -- even more so if we replace "cylinder" with "cone" and force the students to divide by 3.

Finally, I keep bringing up IXL, but I'm sure whether the students will even get to use IXL for this lesson before this week's test. Eighth graders are scheduled for IXL on Mondays and Thursdays, but the Monday lesson is right after coding. I couldn't have had the eighth graders find volume on IXL yesterday, since they didn't learn about volume until today. And on Thursdays by Bruin Corps member may be present, and then I'll switch to science for both the main class period and IXL time (when they'll use another online program for science instead).

I was considering purchasing some cheap four-function calculators for $1 each to avoid the Casio fraction problem. But I don't want to buy them and then end up doing science instead of IXL anyway.

I had a new eighth grade student enroll today. Fortunately, she's seen 

Meanwhile, yesterday the seventh grade class got in trouble. The coding teacher walked in and asked the class to quiet down. They didn't, and so he just walked right back out. This forced me to take out the seventh grade Student Journals and begin the lesson on scale drawings -- and if they weren't quiet for the coding teacher, of course they weren't quiet for me either. I was so upset with them that I declared one of the pages to be a quiz, and then collected it. Naturally most of the students scored 0 out of 7, since they were too busy talking to learn it.

As it turned out, the seventh grade talking continued into English class. My colleague sent the biggest offenders to the office -- the administrators called their parents and suspended them after getting in trouble for the third time. Well, at least the history teacher got a quiet seventh grade class.

Meanwhile, all three of us middle school teachers agreed to start giving out packets of worksheets, which are a combination of homework and classwork. I could tell you how the packets work -- or better yet, I can sing it to you:


1st Verse:
Your folks came up to us and said,
"Hey teachers, you can't hack it!
You make the claim you give our kids
Much work, but you can't back it."
So we got together and said,
"Let's stop all this racket!
We'll staple all our good worksheets
To make a ten-page packet."

2nd Verse:
Don't leave your packet behind,
Make sure that you backpack it.
Or if it starts to rain then
Hide it underneath your jacket.
Keep it in a folder so that
You can always track it,
Make sure that you never ever
Leave your ten-page packet.

3rd Verse:
When it's homework time then
Take it out and just attack it.
When there's extra time in class
Then you need to unpack it.
When it's time to turn it in
Make sure that you don't lack it.
To each and every teacher just
Turn in your ten-page packet.

By the way, you may be wondering where I'm getting the worksheets to fill these packets. Actually, I'm getting them from the texts I've purchased from the library -- Saxon 65 and Algebra 1/2 for sixth and eighth graders respectively, along with the old McDougal Littell seventh grade text!

For "Day in the Life," there is no teacher whose daily posting day is the 29th. So instead, let's go back to our old standby, Fawn Nguyen:

Nguyen writes a special Thanksgiving post in which she makes a big announcement:

On Sunday, I wrote a longer-than-usual email to my siblings about my intentions to begin gathering facts and etching memories for a bucket-list item of writing a book. I told them it could take anywhere between 3 to 10 years, meaning I have no clue.

So apparently Nguyen's upcoming book will be an autobiography. I look forward to reading it -- more to see what she has to say about her teaching career than her "fish cabin" story. Well, I guess I'll have to check the bookstores and Amazon between 2019 and 2026.

If I'm reading Nguyen's blog, I might as well check out our other old standby, Sarah Carter:

Carter's physical science class is still working on chemistry. As you can see, she and two students used pipe cleaners to create three molecules -- H2O, NH3, and CH4. No, my own class is not working on chemistry yet, but we might get there soon.

This is a two-day post. Tomorrow we will continue working on the Student Journals in all grades, so it should be a normal day -- at least as normal as a middle school Wednesday can be.

My next post will be Thursday, December 1st.

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