You may be asking yourself what a Pythagorean Triple is but it is 3 numbers that fit the a^2 + b^2 = c^2 pattern. Today, December 16, 2020, is just such a day! 12/16/20 fits this pattern. Are there other days coming up that fit this pattern? Will we be alive when another happens?

Teaching adults how to identify this pattern 3-4-5 supports a deeper understanding of this theorem, in addition, to teaching them the formula. Do you have other ways of teaching the Pythagorean Theorem?

I would love to hear them!

Happy Pythagorean Triple Day!

Brooke

## Comments

I teach them 3 4 5, but I wish I had made a realization that today was the day of one. I also teach 5 -12 -13 as it is the other pretty one. I always have them discover the 3, 4, 5 with blocks. they use unit blocks and make a 3 - 4 right angle and then complete the triangle with 5 that they discover. Then we create squares with more blocks - creating the classic pythagorean picture. then I have them take the 3 square blocks and the 4 square blocks and place them one on one on the 5 square blocks and they see they equal one another. Just by doing that it creates a picture. Then we grow our triangles and shrink them. Haven't figured out what I can use to do this online except by making a video of me doing it but I would rather they do it.

The most fun I've ever had noodling around with pythagorean triples was in an exploration of families of triples at the NYC Community of Adult Math Instructors (CAMI) math teachers circle. Here are the notes and materials and some of the thinking that came out of our observations.

http://nyccami.org/keep-it-in-the-family-with-pythagorean-triples/

yours in productive struggle,

Mark

I tried a new lesson last winter that went pretty well and avoided memorizing the Pythagorean formula until students had explored making triangles that were or weren't right triangles.

I started by showing students an image of a triangle with a few measurements and asked them to write everything they knew about the figure. When it was time to discuss as a group, I tried not to add too much and mostly just took notes on what they said.

I then gave them a bunch of squares and asked them to choose three that would make a triangle with the negative space between. Once they could create a triangle, I asked them to find right triangles. They used protractors to check if there was a 90 degree angle.

I then asked them to see if they could find all combinations of three squares that would produce a right triangle.

They eventually used the formula as a way to find other combinations or check combinations that were very close to having a 90 degree angle, _____, for example.

Here's the draft lesson below and here are the handouts and here are some photos from the class.

Write everything you know about this figure. 20 min.

Write everything you know about this figure.What else can you tell us?Make sure everyone is measuring from the right part of the ruler. ( “ means inches, the missing edge is 5 inches long)90 angles - 10 min.

Door frame is a good example. (Return to this later to check to see if it is 90 degrees.)

What do you notice? What do you wonder? - 15 min.

Can you make triangles with any three squares? Can you make right triangles with any three squares?Making triangles with squares - 20 min.

Pythagorean theorem - 10 min.

In a right triangle, the combined areas of squares of the legs are equal to the square of the hypotenuse.Sorry, I meant to add 8, 9, 12 as an example of a triangle that looked like it would be a right triangle. It produced an angle that was so close to 90 degrees that you couldn't tell the difference with a protractor. It makes me wonder about triples that are more Pythagorean than others. This one is about as close as you can get.