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)

CLICK HERE FOR THE PDF LESSON 

Happy Ambiguous Case Days ahead!!
Best,
Dave

Using Pipe Cleaners for Transformations of Graphs in High School Math Class

I keep trying to find activities for my kinesthetic learners. This activity helped students to actually "DO" the math. There were some definite ahah moments for some of my students. I took out some pipe cleaners and handed them out to my pre-calculus class. Pipe cleaners are great for teaching transformations of graphs. Students had to physically move the graph up, down, left or right. We predicted shifts and we found multiple answers to graphs. See below.


1. Either have your student make their own scale on a piece of paper or hand out a scale for your students.
2. With the paper scale in hand, ask them to make a certain graph. I asked my students to make a y = sin x graph. They proceeded to bend the pipe cleaner into a sign wave. The graph could be a parabola, or cubic or even a line.
3. Then I asked them to shift the graph up. Explain what the new equation would be.
For my class I then had them shift the graph to the left until it turned out to be the same graph as the original. They shifted it over one period. we found our new equation to be y = sin(x-2π)
4. Have them shift it left or right and predict the new equation
5. Have them move the pipe cleaner into a certain location and then ask for an equation.

6. Ask them to reflect the pipe cleaner over an axis or the origin.

Here are some of the things we graphed and explored in my pre-calculus class.

Find 5 other graphs that are equivalent to y = sin(x+2π)including at least 1 cosine graph.
Find 3 other graphs including at least 2 sine graphs equivalent to y = cos(x)

Graph y = cos(x-π)+1
Graph y = -sin(x+2π)

Give it a try and let me know how it goes.

All the Best,

Dave