## Thursday, September 28, 2017

### Lesson 3-1: Angles and Their Measures (Day 31)

This is what Theoni Pappas writes on page 271 of her Magic of Mathematics:

-- "Madre was a midget," [Terri summarized]. "His wife and the trapeze artist sawed off some of his cane, one day when he wasn't using it. When he went to use his cane, it was too short for him. Madre thought that he was growing taller, which aggravated his precarious heart problem. He couldn't get to his medicine in time. How does that sound Mr. Mason?"
-- "That's it!"

OK, and so the girl Terri solves the mystery after all. Since there is still room left on this page, Pappas gives us three logic stumpers for us to try out:

(1) It was Tuesday and Tom and Jerry were at the same job. When it came time for Tom to go home, Jerry wouldn't let him go home. WHY?

(2) Eric walked into a bar, and asked the bartender for a glass of water. The bartender looked at Eric for a moment, then pulled out a gun and pointed it at Eric. Eric was startled for a moment, and then said thank you and walked out of the bar without having drunk the water. WHAT IS THE SCENARIO?

(3) When Mary came home she walked into the kitchen. She suddenly let out a scream when she discovered her dead husband on the floor. Along side was water from a bowl that had been on the table and was now tipped over on the floor. The window over the kitchen table was ajar. WHAT HAD HAPPENED?

Pappas provides the answers in the back of the book. Once again, I think I'll just post the answers right here on the blog -- tomorrow, of course!

By the way, I can keep going on with riddles like these forever. Here is a link to a riddles website:

http://www.briddles.com/

As for the riddle dated yesterday, maybe Madre was the rider of this elevator:

http://www.briddles.com/2011/07/famous-elevator-puzzle.html

And here's the riddle dated today:

http://www.briddles.com/2011/07/cross-river-puzzle.html

Two boys wish to cross a river. The only way to get to the other side is by boat, but that boat can only take one boy at a time. The boat cannot return on its own, there are no ropes or similar tricks, yet both boys manage to cross using the boat.

But now here's my own riddle -- why is that these riddles are posted yesterday and today, yet they link to a URL containing /2011/07/ (as in July 2011)? I'll never know the answer to that one.

Anyway, it may be a good idea for math teachers to give these riddles and logic puzzles in class -- particularly Geometry teachers.

Lesson 3-1 of the U of Chicago text is called "Angles and Their Measures." I didn't write much about this lesson two years ago due to a subbing day, so instead we'll go back three years.

This is what I wrote three years ago about today's lesson:

I don't have much to say about the book's treatment of angles. This text is unusual in that it includes a zero angle -- an angle measured zero degrees. Then again, in Common Core we may need to discuss the rotation of zero degrees -- the identity function.

The key to angle measure is what this text calls the Angle Measure Postulate -- so this is the second major postulate included on this blog. Many texts call this the Protractor Postulate -- since protractors measure angles the same way that rulers measure length for the Ruler Postulate. The last part of the postulate, the Angle Addition Property, is often called the Angle Addition Postulate. Notice that unlike the Segment Addition Postulate -- which this text calls the Betweenness Theorem -- the text makes no attempt to prove the Angle Addition Postulate the same way. Notice that Dr. Franklin Mason's Protractor Postulate -- in his Section 1-6, has angle measures going up to 360 rather than 180.

So let me include a few more things in this post. First, here's another relevant video from Square One TV -- the "Angle Dance":

By the way, last year I taught angles to my seventh grade class, and I showed them the "Angle Dance," so let me also reblog what I wrote last year about angles. From my January 10th post:

9:45 -- My sixth graders leave and my seventh graders arrive. In this class, the students are learning about angles, as well as how to draw a triangle given its three angles. I start out by telling the class about a movie I watched over the weekend, Hidden Figures, whose main theme is that black girls can do math, too. I'm offering extra credit points to anyone who watches the movie, brings me the ticket stub, and answers five questions about the movie. I'm hoping that my students -- especially the black female students -- will watch the movie.

Halfway during class, I give the students a "music break" and I sing a song from Square One TV that's appropriate for this lesson, "Angle Dance."

I offer the students a participation point for dancing along with the song. Several students take me up on my offer, including two black girls -- the target demographic of Hidden Figures.