The Grand March in the Quad: Linear vs. Angular Velocity, Part II

trigferrisfinale
So my students had done a magnificent job the previous day. And I hadn’t done too badly my own self. The original Sammy problem is, I submit, a masterpiece that integrates three different concepts without tipping its hand.

But the students’ skepticism came through loud and clear. They understood the math. They grasped the significance of the radius to the speed. But ain’t no way they bought the notion that Sammy was going faster than the bird.

I mulled this over the evening, and went back to youtube looking for videos. The Grand March? Too much time to wait for a very small demo.

But wait. What if I did my own Grand March? And in the words of the great Oracle Jones of the noted Western mockumentary The Hallelujah Trail:


THERE, now I see it!”

Alas, no whiskey to be found.

But I had the idea. And it all depended on George.
George, seen here in my algebra 2 class last year, is a top student and a fantastic young man. He also possesses a battery-operated wheelchair.

The next morning, before class, I went looking for him.George1

“George. I have a really cool idea, I think, but I need your help. Can you set your wheelchair to a particular speed?”

“Sure.” George doesn’t even ask why. He’s used to me.

“Okay, and this is a weird question–but can you, like, tip over? Do I have to worry if you go round and round on a 3-foot radius circle that it will….tilt?”

He’s kind, and doesn’t mock me.

“Ms. K, it weighs a lot. It can’t tilt over.”

“Phew. I was having nightmares.”

So before class started, I got some chalk from an old-school colleague and using a tape measure, marked out a circle around the courtyard drain, with a 3′ radius.

When the bell rang, I was ready.

“So. Yesterday I noticed skepticism about the bird’s speed. You understand the evidence, but you trust your lyin’ eyes more. I came up with a way to illustrate the proof so you won’t have to take math’s word for it.”

Then for the first time in my over five years as a teacher, I took my kids outside. Very unnerving. (Yes. I’m a big weenie.)

So the basic idea: George sets a speed and follows my traced circle at a very slow pace. The rest of the kids line up on opposite sides of the quad, and one by one they join in with George. Two kids go in on each of George’s rotation, one from each side.

The class was skeptical, but game.(In fact, this trigonometry class could not have been a better guinea pig for my first time teaching the subject. Every day, they jumped right in.)

On the first day, I just did proof of concept. I wasn’t sure how to get everyone to link together, so everyone held the edge of a tape measure.

The kids did a great job and the activity just exceeded my wildest expectations—and best of all, took less than 20 minutes from start to finish. I took pictures, and showed them to anyone walking by, including the entire admin team. This is my favorite shot from the first day:

FWDay113stdnts

The end of the tail really captures the movement. Austin the Action Figure!

We went back in and worked basic problems on angular and linear velocity for the rest of the day.

Then I realized that I really missed an opportunity. I was so worried my idea wouldn’t work that I didn’t take advantage of the obvious real-life problem at hand. What was our Grand March angular and linear velocity? How fast was George going? What about the speed of those at the end of the chain?

So the next day, we went out and did it again. But the kids had some changes. Nuff of those idiotic tape measures, Ms. Kerr. We are all comfortable with our sexuality, and will link arms. Football players and all.

Note–some of these pictures are taken by me with my tablet, which has a pretty low quality camera for a Samsung; other stills were taken from video that two of my students filmed.

trigferrislinkingarms trigferrislinkingarms2
trigferris5 trigferris8
trigferris9a trigferris10a
trigferris13 trigferris14
ferristrig14a trigferris15

I knew we’d added as many kids as we could when I saw Alexis nearly getting creamed by the quad wall.

trigferris17

So I yelled at them all to go full speed for the last half for the grand finale, the picture at the top. Here they are a couple seconds later.

trigferrisfinale2

You can see the “whip” effect in many of the pictures. It would work even better if we weren’t running into the quad wall towards the end.

The kids had a blast. Between the two days, almost all the kids participated in a “grand march”.

Then everyone went in and learned how fast they’d been going. I measured a bunch of them shoulder to shoulder and took an average of 36″, or 3 feet for every two students.

FWLinearVelocity

*****************************************************************************

This lesson was a stunning success, and not just because of the fun and games. I had created memories and math that students would remember—and they did, all the way through to the final. I couldn’t wait to try it again with my two trig classes in the spring semester.

But while part 1, the Ferris wheel problem, went just as well both times, the outside activity was just a bit flat. Our German exchange student, Simon, was my TA this semester after having taken my trig class last fall (he’s the first one next to George, above). He played the anchor position, since I didn’t have George, and did it very well.

trigferrissemsd trigferrissem2e
trigferrissem2a trigferrissem2b

If you notice, two students in the last picture, above, have dropped out later:

trigferrissem2c

This despite the fact that Simon was holding the same pace that George was (we had timers to confirm).

It wasn’t a disaster, and we had plenty of time to do it again. In both my spring classes, I had kids drop out, which simply hadn’t occurred the first time last fall. They seemed to have fun, but there wasn’t the same joy I saw in the fall. Simon agreed that the spring students didn’t seem to be as absolutely thrilled.

However, I had one of the best “told you so” comments in my third block class. I was explaining that the first student had to move very, very slowly—around 18 seconds per cycle–so that everyone could keep up.

“Um, keep up? Eighteen seconds around?” Braxton said. “That’s not going to be a problem.”

“Okay, everyone remember he said that!” I ordered. Which made a nice little teaching point when we got back to the room after the grand march.

Still, I wish I could have made the spring classes as absolutely perfect as the fall one was.

When I finally got around to writing this up, I suddenly had a revelation. Look at the top picture again. At least 10 of the 17 students in that picture are athletes—4 of them in two sports. I suddenly remembered all the students towards the end of the whip bouncing on their toes, warming up, waiting for the line to come around.

I mentally riffed through all my students in the two classes this time round, and yep–far fewer athletes. And here their trig teacher is demanding physical activity.

While I was always calling kids randomly, I had a much higher shot at getting an athlete in my fall class.

So same activity, same lack of warning–but not the same level of absolute ready-to-go spirit I had in the fall. I’m going to have to think about how to get them prepared to enjoy themselves, get some guidelines, maybe warn them ahead of time.

But even with less absolute magic, the kids understood and enjoyed the lesson.

I just need more space! Maybe I’ll try the football field in the fall.

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