Magical Triangle Theorem

Today, we had an exercise in hype and entertainment, and it didn’t even feel like work.

First period, I taught this:

Figure 1: INSTANT engagement for students.

Figure 1: INSTANT engagement for students.

The prescribed curriculum has me teach this way:

  • Angles 1 and 2 are supplementary angles, Angle 2 = 40°
  • Angles 2 and 10 are alternate interior angles, Angle 10 = 40°
  • Angles 8, 9, and 10 make a straight angle, Angle 8 = 60°
  • Angles 8 and 11 are alternate interior angles, Angle 11 = 60°
Oooo. Ahhh.

Oooo. Ahhh.

Instead, we did this:

Photo Nov 20, 9 49 25 AM

Pass out a ton of triangles, all different shapes. Students cut them out and label the angles. Colored paper helps. Shading the angle helps also for students who have a hard time identifying the vertex.

First, tear off angle A and align its vertex onto the vertex of the straight angle, then the angle side on the side of the straight angle.

Do the same thing with angle B.

Students now have a little gap, as you can see here:

Photo Nov 20, 9 48 54 AM2

Now, the next part is very important, so I’ll explain it step by step:

1.) Clap your hands loudly and jump on a desk. Sweep your hand over the class and declare, “Magic has arrived!” in a triumphant tone.

2.) You likely have the students’ attention now.

3.) In the same majestic voice, announce, “At this point… every page in the class has a different triangle* with angles labeled differently. All of us have a gap between the two angles.
With my magic powers… I predict… (roll your Rs; it really sets the mood)  that your one remaining angle will fit perfectly between the other two… go!”

4.) Students fit the third angle between the first two, then exclaim with wonder and throw roses at your feet. Third period gave a standing ovation and asked how long I was in town. One girl is bringing her parents to the matinee tomorrow.

Spoiler: It’s the Triangle Sum Theorem.

5.) Explain that they can perform the same trick at home, and you’ll give away your secret right now: The sum of all the angles in any triangle is always 180°, just like the straight line upon which they are perched.

See? Wasn’t that better than this?

Figure 2: Reading an owner's manual about magic.

Figure 2: Reading an owner’s manual about magic.

To be fair, we went actually tackled the above problem after the magic show, but–and you can quote me on this–it’s way easier to hold students’ focus when there is magic involved.

On that note, the book I’ve been promoting for several months finally arrived today from Amazon.

It’s also notable that CUE’s keynote speaker for this year teaches it the other way.

~Matt “Criss Angel” Vaudrey

*There were only 12 different triangles, but I didn’t tell them how to label the angles, so the odds are one in 144 that two students had the same situation.

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5 responses to “Magical Triangle Theorem

  1. Pingback: Sum it Up, Angle Edition: Part 2 | Math Butler

  2. Pingback: dy/dan » Blog Archive » [Fake World] Limited Theories of Engagement

  3. Thank you for posting this! I love tlap but as a first year teacher have struggled to make activities as engaging as I’d like them to be. The curriculum gives students too many prompts, which isn’t doing them any favors. I really love the things you do in class and you have really inspired me as an educator as well as introduced me to other amazing educators. So thanks for having such an amazing blog!

  4. Clever and simple in its approach, powerful in its delivery, what a great activity to get them interested and to move forward. My kids would always know how to do this when we walked through it, but failed to apply it on their own. They were capable of doing it when prompted, but couldn’t apply on their own, and I bet this may be an approach that would really connect with them.

  5. I love doing that activity so basic yet very convincing. I’ve never been quite that dramatic though. Maybe I’ll give it a go next year .

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