Tag: volume

Apocalypse soon

On By Luther M. SilerIn TeachingLeave a comment

It hasn’t started yet, but apparently the thunderstorms currently headed my way are going to bring flash floods, hail measured in inches, and several dozen tornadoes. So, great! We were all surprised by the two fog delays we got last week; apparently I get to look forward to flood delays tomorrow morning, because if 2026 has shown me anything at all, it’s that when it is possible for there to be fuckery, it is an absolute certainty that fuckery there will be.

The trend of rough-as-fuck days continues; I had to do an office referral today for a kid who wouldn’t stop using the word “jigaboo” in class, and amended the referral a bit later when I discovered he’d also written “KKK” on his desk. It was also one of those days where everyone is having the same comprehension issue and I absolutely cannot figure out what is causing it. We are working on simple volume and surface area formulas; today, specifically, volume and surface area of spheres. The relevant formulas:

I generally will teach them how to calculate both formulas (not especially tricky) and then point out that since 4π and 4/3 π are always going to be the same number, you can actually shortcut the formula and use 12.56r2 for surface area and 4.19r3 for volume. The volume formula is a little bit of an estimate, but they’re both perfectly cromulent for what we’re doing.

For the first time since I’ve been doing this, this year’s kids showed a marked preference for the fuller version of the formula, and a lot of them simply could not wrap their heads around the shortcut formula. I was getting a ton of them who were multiplying 4.19 by the radius cubed and then insisting that they needed to divide by 3 afterwards. I would point at the formula they were using and ask them where that formula told them to divide and it wasn’t helping.

“Literally just multiply 4.19 by the radius three times. So if the radius is 7, you’ll calculate 4.19x7x7x7.”

“Okay. So when do I divide?”

“You don’t have to divide. Dividing by three is already worked into the 4.19.” And then I’d demonstrate how I got that number, for, like, the fourteenth time. And then they’d do a sample problem and still divide by three.

I had one of them write the volume formula as (1πr3)/3– so the whole thing as a big fraction, but replacing the four with a one for some reason. I pointed out that they had that wrong and told them that they needed to use four and not one, and then walked them through a problem.

“Okay. So when do you multiply by one?”

<head explodes>

“You don’t. First, it’s not in the formula. Second, multiplying by one would give you the same answer anyway, remember? So there would be no reason to put that in there.”

“Oh, okay.” <Does a problem.> “So, now I multiply by one?”

I change tactics. “Point to the one in the formula.”

They point at the one in the formula that they wrote down and still haven’t fixed.

“Have you noticed that you’re pointing at the one that only exists in your formula, the one I told you was wrong? Look at the formula at the board. Is there a 1 in there anywhere?”

“No. So where does it go?”

…

For six straight hours. I’m going back to selling furniture, God damn it.

In which I am successful and I don’t like it

On By Luther M. SilerIn Teaching3 Comments

Objectively speaking, today was a good day. Unfortunately, I apparently have no idea how to react to good news, so my brain is melting and I’m looking around for ways to mistrust what I should be treating as evidence that I have some idea how to do my job.

My first two classes of the day are seventh graders, and they are working on volume this week. We started with cubes and rectangular solids, moved on to triangular solids, and then started working on cylinders today. Now, in some ways, all of these are fairly simple– there is a reason that “follow the formula” is literally one of my classroom rules, and I allow calculator use any time that the calculation is not the point, and in this case I don’t want an inability to multiply fluently interfering with understanding what three pieces of information you need to calculate the volume of a prism.

Cubes and rectangles and triangles went fine, but in sixteen years I’ve never had a class of math kids that didn’t struggle with cylinders. Once pi comes into the mix, and especially once not only pi is in the mix but radius squared becomes a thing, they start having trouble. They get over it, but kids always need to be monitored carefully while they’re doing cylinder volume for the first time. They screw it up. I’m used to it. It’s okay.

Nope. Both classes sailed through the assignment I gave them, and from watching the class I could tell that damn near all of them understood what they were doing. Just like they’ve sailed through basically every assignment I’ve given them this week. They just aren’t having trouble with this, in a way that I haven’t seen with my previous math classes. And how did I react, to evidence that my students have learned what I have tried to teach them, a fact that in a sane world would make a math teacher happy?

Tomorrow’s assignment is going to include a mix of shapes, because I’m paranoid that what I actually have is an age cohort that has learned to push buttons in the right order but can’t actually figure out which formula they should use if I don’t hand it directly to them. I’m still going to make sure they have access to the formulas they need; I don’t need them to have anything memorized yet– but it’s not going to be a situation where they can use the same formula every time. And we will see if they crater or if they finish this assignment with the same ease that they’ve completed everything else I’ve thrown at them this week.

“But Luther,” you may be thinking, “you used an image related to graphing equations up there! That doesn’t have anything to do with volume! Why would you choose such a misleading graphic?”

Because my 8th graders pulled the exact same shit with working on slope and graphing linear equations this week. Now, I’ve talked about teaching slope on here before— be sure to read the comments, which feature the single most entertaining fight I ever got into in my comments section in the entire history of the blog, including the utterly priceless “you’re lucky you’re Canadian” final comment– and it is something that middle school kids tend to struggle with. The whole thing is weird, really; they’re just getting used to one letter being in their math, and now there are two, and somehow there’s not one right answer but a whole bunch of right answers, and you’re telling me that this equation and this line are the same thing, somehow? Okay, boomer. Sure.

Thing is, my kids have got this this year. In a way that previous groups never have. And part of the reason is definitely that because of the way that the scope and sequence was set up this year I was able to take my time and go piece by piece with it in a way that I haven’t in previous years, but it’s still stunning how well they seem to have absorbed this particular material.

So, again, I don’t trust it a bit, and I expect to go into work tomorrow and discover that they now think you use your feet to add numbers. We shall see. One way or another, Winter Break is six teaching days away, and that means they will forget everything I’ve ever told them in six teaching days plus one minute. But for now? It’s nice to feel like I know what I’m doing.