Pythagoras and Pele; Gooooooooooooaaaaaaaa… (to be continued)

…ooooaaaaalllll!

There’s about a hundred different ways you could use the following artifacts to construct a lesson around Pythagorean’s Theorem. So I’ll just toss out all the artifacts and let you, esteemed teacher, take it from there. I’d love to get feedback and suggestions on how to implement these materials in the comments below.

Artifacts

Use any combination of the following.

This video from This Old House in which two small girls assist with the construction of a pint-sized soccer net: How to Build a Soccer Goal | Video | Family Projects | This Old House.

The screen shot of the girl holding up one of the 5 most beautiful right triangles I have ever seen.  (note: before math geeks go berserk, I know it’s technically not a right triangle with the extra bit off to the side, but still.)

This is the strangest x-axis I have ever seen (update: not really that strange at all)

Update 1: Anonymous points out that it says log scale right under the graph. Yep. That’s it right there. I’ve said it before and I’ll say it again: I need an editor. Thanks anon. So it’s actually not strange, but rather perfectly logical. It’s also Friday. Oh well. Still, there’s got to be something we can do with this. Give students the x-axis demarcations and ask them to provide the scale? Linearize the data? Or turn the linear data into a log scale? Regress the data linearly and logarithmically?

And here I was getting all uptight about the Tour de France stage profile x-axes.

(from thetransportpolitic.com)

Pythagoras and the Pyrenees ; Performance Enhancing Math

This image and its ilk bothers me to no end. This is a profile of the 9th stage of the Tour de France*.

(image adapted from letour.fr)

So I had this simple little post in mind about the Tour de France and biking and elevation and distance and it would wrap up neatly into a little Pythagorean Theorem lesson. I start looking around for nice little diagrams much like this one, showing the distance and elevation. The idea was going to be simply, “find the absolute distance the bikers travel in this particular stage.”

But it turns out these diagrams are a sham. An absolute sham. You see, the x-axis already does represent the absolute distance. Take this stage, for example. Above is the “cross section” of the stage. And here’s the actual route.

Note the exact same distance peddled. So x-axis is in actual distance peddled, not simply the horizontal distance traveled, as any proper diagramer should do. I suppose it’s more helpful for the bikers to know the absolute distance they have to travel, but it’s …. it’s….. it’s… just wrong. In retrospect, I did sort of think these slopes seemed a tad steep….

So we have a new task.

‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 2)

Our celebration of Groundhog Day and Groundhog Day continues with our second question about Phil and his time spent in Punsutawney.

Artifact

This scene from Groundhog Day.

Guiding Questions

  • How long has Bill Murray (“Phil”) been practicing throwing cards into a hat?
  • Has Phil spent more time throwing cards into a hat than you’ve spent in Math class this year? Your entire high school career?
  • How good can you get at throwing cards into a hat after practicing for, say, 5 minutes? Can you make three in a row?

Solution

Rita: It would take a year to get good at this.

Phil: No. Six months. Four to five hours a day and you’d be an expert.

6 months = about 180 days.

180 days x 4 hours/day = 720 hours.

180 days x 5 hours/day = 900 hours.

Depending on the length of your school calendar and class periods, students are probably in Math class for about 200 hours/year. So that would be a “no” on Math-in-a-year vs. Phil-with-a-hat. But a “possibly” to Math-in-a-high-school-career vs. Phil-with-a-hat.

‘Groundhog Day’ “I’m a god” scene solution

Here’s my attempt at a solution to the previous post on Groundhog Day.

In order for Bill Murray (“Phil”) to convince Rita and allow for Rita’s peppering of questions, we have to assume that Phil knows everyone in the restaurantIt’s tough to get a beat on the number of people in the restaurant, but it’s a lot. I’ll start counting, but then we may have to fudge the numbers a little bit.

‘Groundhog Day:’ How long has Bill Murray been in Punxsutawney? (Part 1)

Happy Groundhog Day everyone! Brief synopsis of Groundhog Day in case you didn’t know: Bill Murray is trapped in the same, repeating day in perpetuity.

How long Murray has been trapped is a question that has plagued mankind since the early 1990’s. It’s never directly addressed in the movie, it’s just hinted that it’s a long, long time. Probably months, possibly years.

Artifact

Let’s take this scene, for example.

How many days do you think it took Bill Murray to adequately retrieve and retain enough information to convince Rita that he is, in fact, a god?

Guiding Questions

  • How many people did Bill Murray discuss?
  • How many people are in the restaurant?
  • How many times would it take to know all that stuff about them?
  • How many times through would it take to get the timing on that crash of the tray dropping?

Suggested Activities

Some of these questions can be observed from the video. Some of these questions probably have to be estimated. But then, some could be investigated by your students. Think of all those “getting to know you” activities you put at the start of the year. Couldn’t we recreate something like that with this scene? Couldn’t we investigate “how many conversations does it take before you know enough details to describe the person well?”

Or couldn’t we investigate how many times before we could know exactly when an event will occur (the tray dropping)? I mean, don’t we do that in rewatching movies all the time?

Is there anything cooler than a math tattoo? (A: yes, pretty much everything)

As I mentioned last time, the Pythagorean Theorem is a difficult concept to have students discover intuitively. So we’re focusing on it specifically this week. If you have any activities or ideas, please let me know. Or tweet it to me.

Here’s one sent in by Kevin.

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A math nerd (Let’s say her name is Tara) decides that she is going to get a tattoo, and she draws up the following design for the artist to put on her back:

The colored ink costs $3 per square centimeter.  Outlining in black is free if the color costs $150 or more.   If the color is less than $150, then black outlining costs 50 cents per cm.

Tara wants those squares to form a right triangle like above, where the vertical leg is 5 cm long, and the horizontal leg is 7 cm long.

How much will the tattoo cost Tara?   Make sure to write out all of your calculations.