Tag: math

Okay, fine, I’ll do the math

On By Luther M. SilerIn Geek, idiocy, TeachingLeave a comment

I have removed the Second Skin from my new tattoo, and the itching is absolutely maddening, so I’m going to distract myself with math. Because that’s why you come here, right? As a reminder, this is the original image, and the question is the ratio of the inner square to the outer square:

The first thing we’re going to do is draw the two diagonals of the inner square. These are, by definition, perpendicular to each other, and they are also equal to the circumference of the circle. Let us define the radius of the circle as x:

What we have now is four right triangles inscribed inside the circle. Pythagoras tells us that the sum of the squares of the two legs are equal to the square of the hypotenuse, which is the line on the left of the square there. Therefore, defining the hypotenuse as Y, we get:

x2 + x2 = y2
2x2 = y2

Take the square roots of each side, and we get:

√(2x2) = √(y2)

And therefore:

√(2x2) = y

Which means that all four sides of the inner circle are equal to √(2x2), thusly:

To get the area of the inner square, all we have to do is multiply √(2x2) by √(2x2), which, conveniently, just gets rid of the square root symbols. The area of the inner circle is 2x2.

Now, we need to realize that since the radius of the circle is x, the diameter of the circle is 2x, and that the diameter of the circle also equals the width and the height of the outside square. So that outer square is 2x high and 2x wide:

Therefore, all we have to do to get the area of the outside square is multiply 2x by 2x, which gives us 4x2. Which, conveniently, is exactly twice the area of the inner square, which was 2x2.

The outside square is therefore twice the size of the inner square, and the ratio of the inner square to the outer square is 1:2.

Or, y’know, you could just rotate the fuckin’ inside square, which makes it visually obvious.

New tattoo!

On By Luther M. SilerIn art, Teaching2 Comments

It has been, I think, sixteen or seventeen years since my last tattoo. I know my wife was with me; I’m less certain that we were actually married at the time. And while you very well might be looking at that and wondering what the hell I was thinking, I’ve been thinking about this exact design for my next tattoo (that’s my right wrist) for most of that time, and only just now decided to pull the trigger on it.

It is, oh, I dunno, sometime during the first Obama administration, and I am at a training with a bunch of other teachers from my school, none of whom are math teachers. We are presented with three pieces of construction paper, held together in the center by a brass paper fastener, in this shape: a large square, with a circle inscribed in the square, and a second square inscribed inside the circle.

“Figure out what the ratio of the inner square to the outer square is,” they tell us. “You can do whatever you like to come up with the answer.”

My entire group looks at me.

Sigh. Okay, fine, I’ll math this shit. To be entirely honest, I do not, at this time, remember exactly how I got the answer, but there was a lot of Pythagoras involved, and I think at least one place where I solved a set of equations with two variables. It took a few minutes. I’ve considered reconstructing the math, but I think the story is kind of better if I don’t. The ratio is 1:2. In other words, the outer square is twice the size of the inner square.

Anyway, they give us a few minutes, and then ask if anyone wants to share their answer. My group volunteers me to explain my answer, having heard my explanation and apparently accepting none of it. So I attempt to explain my logic to this group, again, none of whom are math people. It takes a few minutes and I may have killed at least one of them. The presenters, now with wide grins on their faces, because they are a step ahead of me and I have walked into their trap, ask if anyone else solved the problem in a different way. A large man on the other side of the room raises his hand. They call on him. He looks like a not-insignificant portion of the people who know him call him Coach, possibly including people he has never actually coached.

He asks if he can use their prop. They say yes, and their grins get larger.

He demonstrates a solution in about a second, by rotating the inner square exactly forty-five degrees to the left.

“S’ half,” he says, and sits the fuck back down.

I start swearing. There’s a moment of disbelief and then the whole room, including me, starts laughing.

Perhaps you have trouble picturing what he’s done. Let me draw this real quick:

I think it is probably immediately clear to everyone looking at this, with the inner square rotated, that the inner square is half of the outer square.

A few days later, I found a second construction-paper shape similar to this one in my classroom, also held together by a brass paper fastener. I kept it in my classroom for years. I don’t think I have it any longer, but I had it for a really long time, across multiple classrooms in multiple schools.

This tattoo is my permanent reminder that sometimes shit does not have to be complicated, which is something I have been fairly accused of in my life, more than once.

In which my numbers are off

On By Luther M. SilerIn Teaching1 Comment

Okay. I got grades caught up today, and only a quarter of them are failing! Still too many although I’ve certainly seen worse. I’m going to try and do a catch-up day tomorrow; we’ll see how that goes.

All that said, I’ve been grading for three hours, and I would like some time for recreation tonight, so this is all y’all get for tonight. Something cool should be happening tomorrow though so you may eagerly anticipate that if you like.

One more day and a three day weekend.

“Good morning. Half of you are failing already.”

On By Luther M. SilerIn Teaching1 Comment

Guess how many classes I had to say that to today?

Okay, not in those words, but I did tell one of my classes that two different adults had described their time with them as a “shitshow” yesterday, and yes, I used that exact word.

I’m tired.

Math-people, Pt. 2

On By Luther M. SilerIn TeachingLeave a comment

Okay, maybe that wasn’t as complicated as I thought it was going to be:

Basically all I did was add the “Is the number a fraction?” step there, and we’ll have to review converting fractions to decimals a bit, but it’ll do and they need to remember how to do that anyway.

In the meantime, I actually called out sick today; my Mounjaro (I assume) got on top of me hard in the last couple of days and I spent less of last night sleeping than I generally like to do, in favor of activities that generally aren’t meant to be described in polite company. So I slept most of the day away once it passed. I may have to have a review day for my kids on Friday already, though, which feels awfully early, although if I remember right we probably had about one a month last year anyway so maybe not. We’ll see how the next couple of days go, assuming I can drag my ass out of bed.

Math humans!

On By Luther M. SilerIn Teaching2 Comments

Look at this flowchart:

I am not a digital artist, as you can probably tell, and I put this together in Sheets, which is certainly really far from the best way to do it, but it gets the job done. Here’s the question: how do I best include the existence of fractions? Fractions are always rational, but depending on what the fraction is, it can be any of the rational number sub-categories as well. I could just include an instruction after the first question to convert fractions to decimals, but 1) that feels inelegant, and 2) it sort of introduces another source of error, but that source is there anyway, I suppose– a kid that doesn’t recognize 1/3 as a repeating decimal is probably also not going to realize that 12/4 is a natural number.

Can you figure out a way to work fractions into this without adding a ton of qualifiers and disclaimers or extra questions? One or two is fine but I don’t want this to get much messier than it already is.

Hmm.

In which the machinery of government moves … quickly?

On By Luther M. SilerIn TeachingLeave a comment

Holy shit, y’all. I applied for my high school math licensure literally yesterday and I got an email today that my addition had been approved and my license was updated. This from, remember, sending them test results from a test that took forty days to get official score results on, and in what is almost certainly their busiest time of the year.

I’ve talked my fair amount of shit about the IDOE during my time working here, but they’re absolutely on point with getting licenses up to date. Damn.

And, yes, that’s seven different content areas I’m licensed for. I really should get my science licensure just for the hell of it.

Adding to the level of today’s miraculousness, of three meetings I was expected to attend today, two ended early– one by forty-five minutes, and that was the one I was fully expecting to eat every single second of its allotted time– and the third took within a minute of precisely the time it was planned for. Tomorrow is going to be a crazy-long day because it’s parent-teacher night, and I have to dress like a grown-up and everything, but Wednesday should be pretty chill and then on Thursday the children arrive.

We are still missing two math teachers– a department that should be five people is only three– so I got another overage approved today. It went fine last year, so unless this group of kids is markedly more evil than last year’s– cross your fingers– I should be able to manage it just fine. I would always rather have an overage and soak up the enormous amount of extra money you get paid for it than be constantly getting phone calls to cover random classes during my prep period anyway.

That said, because I’ll be at work for twelve hours tomorrow, expect a video update at best. I will be in full no-brain-only-sleep mode by the time I get home, especially since I got no meaningful sleep at all last night and am kind of running on fumes already.

Here we go here we go here we go.

In which I knew that already

On By Luther M. SilerIn idiocyLeave a comment

I passed my Math test, officially, with exactly the same score I had “unofficially” on July 1st. Delayed fully 40 days for no Goddamn reason at all. Remember, kids, ETS is the devil.

That’s all I’ve got for today, as we have family in town and we will have more family in town tomorrow. Must sleep.