# Real or Fake #7: Jumping off a mountain into a plane

Here at thegeometryteacher, we’ve been calling out potentially fake messaging since 2011. We’ll we’ve come across another video that just makes you wonder.

It’s either awesome extreme play…

… or awesome filmmaking.

What do you think?

I do think it is more likely to be real than the snow jump luge or the sky-dive trampoline.

If you are interested, check out Real or Fake #’s 1-6.

# Fun with The Magic Octagon

So, we are wrapping up our unit in Geometry on rigid transformations, which means it is that wonderful time of year when I show the students Dan Meyer’s The Magic Octagon!

Seriously… have you seen this? (Go through it like a student. Pause it to make your first prediction.)

Isn’t that cool? Not sure whether you predicted correctly or not (I did not the first time), but I’ve used this video with 6 or so geometry classes and the results are somewhat predictable. 85-90% of the class guesses 10:00. Most of the remaining voters choose 7ish:00 and get called crazy.

Then they see the answer and they JUST… CAN’T… BELIEVE IT!

“Wait… wait. How does one side go clockwise and the other side go counterclockwise?

“No. Run the video again. What did I miss?

That would be a 10-out-of-10 on the perplexity scale, when, like 85-90% of the class gets the math problem wrong and that suddenly becomes a motivator!

Then as they start trying to figure it out, they start making lots of hand gestures, which is surprisingly helpful to them and

Then they don’t want you to move on. They want two more minutes to talk about it. Then a classmate starts explaining it. Not all of them get it the first time, but some of the demand to have it explained again.

Then they move on to the second rotation and they feel so confident. You ask for explanations. They give them… quickly. Quickly because they can’t wait to see the answer. And then they did.

And those who got it right cheered! Quite loudly.

Then a boy stopped us and offered a sequel.

“If the front side arrow is pointed at 5:00, would the other arrow point at 5:00, too?”

He turned the tables enough close to the end of the hour that we left with that question unanswered.

And I fully expect a couple students to have something to say about it tomorrow.

# Kids, I’ll tell you why you need math…

So I was at Kroger and I was thirsty.

I went to the cooler to pick out a 20 oz. Coke. \$1.69. Reasonable. About what you’ll pay most places, at least around these parts.

But I had some more shopping to do. So, I kept walking. Gathering the items on my list.

Then I saw some 2-liter Cokes. (Remind me. Which is a bigger amount of Coke? 2 Liters? or 20 ounces?)

The 2-Liter Coke was priced at “2/\$3.00”. (Which, I’m pretty sure is less than \$1.69.)

(Oh! And you don’t have to buy 2 to get that price. Kroger is awesome like that.)

I get pricing a little bit. I worked concessions at a college football stadium for a while (true story, by the way). I know the shtick. It’s upselling.

“For an extra quarter, you get almost double the pop!”

But this isn’t like that.

You have to buy 4 twenty-ouncers to fill a 2-liter. 4! You include the 10-cent bottle deposit here in the great state of Michigan, and that’s over \$7.00!

2-Liter? \$1.50

This isn’t even close.

Kids, THAT’S why you learn math.

# Okay… I solved it, but how’s that math?

Its on these warm, spring days that some learners tend to start checking out. They recognize our typical reviewing and recirculating attempts to help students recapture some learning before the last tests and exams. But some of them learned the content the first time. Essentially, this time of year can bring with it a lot of down time for our students who learn the fastest.

That’s when I like to pull out my old college textbooks. I spoke before of the power of ungraded bonus problems. If interesting and placed properly, they can provide powerful opportunities for thinking simply for the sake of thinking. I like to give them a window into math that “doesn’t look like math.” After all, most of the content that K-12 mathematics includes has some commonalities that students get used to. They’ve gotten used to “what math looks like.”

Today, four groups got a problem that I adapted from one of my undergrad courses that I took at WMU with Dr. Ping Zhang who, along with Dr. Gary Chartrand co-authored this book which was the textbook for the course I took.

The problem is adapted from Example 1.1 from Chapter 1. It asks the students to create a schedule for 7 committees that share ten people. Now, the purpose of the problem in the book is to give a simple example of how a graph can be used to visualize a complex situation. Often the way a problem is mathematically modeled can change the intensity of the solution process.

Figure 1.1 from Page 1

The reason I like to give this problem (and problems detached from the K-12 curriculum in general) is that in May, to curious students, these problems tend to hit the perplexity button just in the right spot. In fact, all the students looked at the handout at first and were unimpressed. Until I asked them to read it… then, they seemed to just want to see what the answer looked like. As one student put it, “It seems really easy at first, then you get into it and it’s actually harder than we thought.”

Graph theory is about creating visual representations. I didn’t want to ruin their experience by pigeon-holing them into trying to represent this they way I knew they could. And given the time, that didn’t stop this group from creating a similar idea. Not with a graph, but they did use crayons.

To hear Kailey explain: “We just gave each person their own color. Then we knew we could have two committees meet at the same time if they didn’t have any colors in common.” That isn’t different thinking, really. Just a different representation.

I enjoy the conversations that come out it. No grade. Just doing math for the sake of thinking about something that’s interesting. It’s especially interesting to students like Katie who said, “Okay… I solved it, but how’s that math?”

Reference

Introduction to Graph Theory (2005) Chartrand, G., and Zhang, P., New York: McGraw Hill

# (not) Explaining “Half”

“If you can’t explain it to a 6-year-old, you don’t understand it yourself.” – Albert Einstein

“I’ve drank half my water”

My daughter isn’t a 6-year-old… yet. I get a couple more months before Dr. Einstein’s quote applies. Regardless, today I found myself at the breakfast table trying to make sense of one of those topics that exists in the intersection of math and common language.

It’s good to make mathematics common place, but the problem with making technically-specific terms commonplace is that it often leads to the usage of the word becoming a bit less technical. ELA teachers will tell you that this has happened with the word “literally.” (For more on “literally”, this post will literally blow your mind.)

In that same spirit, today’s breakfast was abuzz with the word “half”. My daughter is comfortable with the word “half.” She will often take a couple of gulps from her cup leaving ~5 ounces in a 6-ounce cup. Then she’ll say, “I drank half my water.” To her that means that she has consumed a some portion of her water, more than “just a little”, and less than “all” or even “a lot”. It seems the developing spectrum looks something like this:

Water Drinking Spectrum

It’s clear that spectra like this make clear the need for fractions, but that’s a discussion for another time.

Well, today, she asked about what “half” means. Which was a question that I should be qualified to answer, but you wouldn’t know it from how the conversation went.

Her: “Dad, what does ‘half’ mean?”

Me: “Well, it’s like broken into two pieces that are the same size.”

Her: “No, like, I drank half my water”

[See? My explanation didn’t work because I was thinking the two pieces were the water in the cup and the empty space. She only sees water. That’s only one piece.]

Me: “That means that the amount of water that you have already drank is the same as the amount of water you have left.”

Sage: “I don’t get it.”

Me: [holding up clear cylindrical glass that is “about half-full”] “See? This glass has water up to here [I point at the water line], and then the rest of the glass is empty. It’s like there’s the same amount of water and empty.”

Sage: “Um… Maybe we should talk about this when I’m older.” [Sage continues eating oatmeal and the topic changes]

Good thing she’s only five. I have a few months to prepare for Dr. Einstein’s test of whether or not I really understand the idea of “half.”