Saturday, August 29, 2015

Spending a Week with Pythagoras

Standards dealing with the Pythagorean Theorem fall in our eighth grade course of study. If I don't cover those standards with my eighth grade Algebra 1 students, they will miss learning and using the Pythagorean Theorem. And high school teachers will come after me. :)

I always cover the Pythagorean Theorem with my Algebra 1 students, but this year I decided to follow the lead of a blogger friend who also teaches Algebra 1 to eighth graders and start the year with it (after discussing square roots and real numbers). I covered the material in fewer days than I will with my Pre-Algebra students, because, after all, we still have a lot of Algebra 1 standards to get to.

We started the unit with a visual proof of the theorem. It's a proof out of a book I've used since teaching high school geometry another lifetime ago, Visualized Geometry (I just looked it up; the book was published in 1990!). A right triangle has squares drawn off each side, the squares from the legs are cut and arranged to cover the square off the hypotenuse. After some productive struggle with getting the pieces to "fit," students readily see that "a^2 + b^2 = c^2." (I didn't get any good pictures of the final product. And as we were disposing of all the pieces, a student in the last period of the day said, "We should have glued that in our INBs!" Brilliant! Why didn't I think of that? I made a note of it for next time.)

I have to cover the Pythagorean Theorem, its converse, applications of the Pythagorean Theorem, and using the Pythagorean Theorem to find the distance between points in the coordinate plane. Students had 3 videos dealing with these topics.

In class I tried several new activities this year. I was very pleased with the work students were able to do with the content.

To practice using the Pythagorean Theorem, I used this activity from Equation Freak. It was SO much better than a page of "find the missing side" problems. Students got great practice with visualization and finding lengths of sides in a diagram that will help them in future math classes. And they had one, final goal. We did not get completely finished with the activity in class, but I gave students the option to finish it at home. A good number of students brought it in completed the next day!

"Pythagorean Stack" by Equation Freak
We practiced applications of the Pythagorean Theorem using task cards I've had for a few years from Live Love Math. I added QR codes to the back so students could check their work as they went.

Pythagorean Applications
To find distance on the coordinate plane, I used Rockstar Math Teacher's "Pythagorean Zoo" activity. I have not done a lot with Socrative, but the activity went smoothly, and the kids enjoyed it. The funniest comment all day was, "Mrs. Gibbs! Are you ruining the zoo with MATH?!?"

"Pythagorean Zoo" by Rockstar Math Teacher
I was confident my students understood and could use the Pythagorean Theorem, so the day before the test I was able to do a few activities I had not had time for earlier in the week. We did a couple of problems with the converse of the theorem. In hindsight, these problems should have been done earlier in the week, after they had seen the converse in a video. Many students did not remember seeing anything like that, and I had to point them to their notes. I should have reinforced the topic right after they had watched the video.

We looked at the Pythagorean Theorem in 3D. This problem led to some great class discussions and was also good for their visualization skills. Having taught Geometry in that former life, I know how important those skills are!

We finished the unit with another lesson I snagged from Equation Freak. We watched a clip from The Wizard of Oz and "corrected the scarecrow." Like Jan, I had a few students who had never seen the movie. The activity was a great exercise in using precise mathematical vocabulary.

"Correct the Scarecrow"
I received another funny comment with this activity: "Now you're ruining The Wizard of Oz with math!" But I'm hoping students will begin to see we can find math EVERYwhere.

I have more pictures than normal because I'm participating in #teach180 on Twitter. I'm trying to tweet a picture of something going on in my classroom every day. Some are blogging every day, but I know better than to try a daily blog post. :) The highlight of my day for the last couple of weeks has been scrolling through the pictures posted with the hashtag. I've already gotten (and used!) a couple of ideas from others' posts.

I'm also trying to focus my blog this year on what we do in class. I make the videos, my students watch the videos, but the real magic happens in the 51 minutes I have with my students.

As I've said before, none of these meaningful, engaging, beneficial activities would have been possible in my traditional classroom. Or the unit would have taken twice as long as it did. I have much more fun in my flipped classroom, and I know my students do, too.

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