Tuesday, April 2, 2013

Triangle Challenge: The Ambiguous Case Explored using Pipe Cleaners

I have always had trouble with teaching the Ambiguous Case.  It seemed that whatever I did, the explanation was not good enough.  The kids came out of my class with their heads exploding with all the things they had to remember.  A couple colleagues and I created a hands-on activity that really explores the heart of the ambiguous case and the Law of Sines SSA example.  After going through this lesson, I really feel like the students had a grasp on the ambiguous case conceptually.  My work is not finished, because I have to now finish the procedural process and we should be good..  The first video is the explanation of the original challenge.  The second and third videos where students explain their partial and full answers.

Triangle Challenge Rules and Guidelines   SMARTBoard Notebook Lesson      PDF Lesson
1.  Use one pipe cleaner that is 8 inches long (light colored) and put it as side two

2.  Angle A is exactly 30 degrees.
3.  Side one is a second pipe cleaner (darker color) and starts at 12 inches long.  It can be shortened by 1 inch increments.
4.  Create as many triangles as you can using the above restrictions.
5.  Hint:  There are more than 10 solutions.

The Challenge

A Student's Partial Solution

A Student's Full Solution

An interesting Solution

PIPE CLEANERS ARE A MUST FOR PRECALCULUS CLASS! See another blog post using pipe cleaners click here.

CLICK HERE FOR THE SMARTBOARD LESSON  (use must have notebook software to view this)


Happy Ambiguous Case Days ahead!!


Tonya Roberts said...

What an awesome way to teach. Hands on teaching actually engages the students and increases the chances of them being able to follow along with the lesson. I also like the way you complimented the students for their work. Most teachers walk around the class room looking to make sure the work is being done, but you actually verbalized that they did well. Positive reinforcement helps confidence levels and makes children want to do better.

Angela Custodio said...

Thank you very much for this! I was actually making lesson materials for practically the same activity (except mine made use of different materials) for my sophomores and was pleasantly surprised to find your blog. I would like to incorporate some of the elements of this activity for mine, if it would be okay. Being a relatively new teacher, I've been told that teaching the Ambiguous Case to students has always been a bit of a challenge but I feel exposing them to this hands-on approach will help them make more meaningful learning out of the lesson. Thank you for affirming that. Good job, Dave! :D