pythagorean’s theorem – emergent math

Pythagoras and Plants ; Aunt Bitty’s Gardens

Posted by Geoff in geometry, pythagorean's theorem, tasks

Continuing from last week, we have another potential Pythagorean’s Theorem Project/Problem. This one was sent in by Steve.

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AUNT BITTY’S GARDENS

Launch: My Aunt Bitty has a business creating “designer gardens”. These are beautiful little triangular gardens that fit into a particular space–usually the corner of a yard. You tell her your space, and she tells you just how to put in the rocks and plants to make it beautiful.

She is making models of different sized gardens that she wants to sell–and she has a problem.

Pythagoras and Pele; Gooooooooooooaaaaaaaa… (to be continued)

Posted by Geoff in area, geometry, proportion, pythagorean's theorem, tasks

…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.)

Pythagoras and the Pyrenees ; Performance Enhancing Math

Posted by Geoff in pythagorean's theorem, tasks

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.

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

Posted by Geoff in area, geometry, pythagorean's theorem, tasks

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.

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

The Problem With Pythagoras

Posted by Geoff in pythagorean's theorem

And I’m not talking about the fact that he was a math cult leader. The Pythagorean Theorem is a tough one to teach in a “student-driven” or “discovery” fashion. It’s not very intuitive. It’s not like a high school student will be walking along one day, see a ladder propped up against a building and go,

Aha! A²+B²=C²!

This is ironic considering how widely used it and its parent, the Law of Cosines may be applied. So under the suggestion of a colleague, we’ll be looking at Pythagorean Theorem explicitly for the next couple posts. If you have any awesome ideas or stuff that your students have enjoyed in the past, please comment below or email me.