Finishing Up the Similar Triangles Project

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Objective

SWBAT to plan and write essays about the role that the Mathematical Practices have played in their exploration of similarity, the properties of right triangles, and the trigonometric ratios.

Big Idea

It's time for students to synthesize what they've learned about the trigonometric ratios, precision, similarity, and patterns. Today's work period gives students a chance to clarify their thinking and to put it in writing.

Circle Up: What do you need to do today?

10 minutes

How can you know if your theoretical values are accurate?

10 minutes

To review the big idea of the Similar Triangles Project, I post a photograph of the chart that we used in the previous class, and I ask for volunteers to walk us through the process of testing the viability of each answer.

If I'm teaching two different sections, I might have one section check the results of the other, cultivating a friendly little rivalry between the two classes.  I might also post the work of last year's class for comparison to ours.  We have a spirited discussion about how everything worked out, and this is a nice opportunity to students to share their conceptions and to surface their misconptions of what we've done so far.

I also have some notes prepared on today's Prezi.  I might use these, I might not: they're here if I realize they'll be useful.  On each slide, there are questions to guide conversations about each of the SLTs for this project, as well as the "Fascinating Chart". There are also a few basic example problems for finding unknown measurements in a right triangle; if I realize that students are ahead, or if they ask for reminders of how they originally learned to use the trig ratios, I might share some of these.

Work Time: The Similar Triangles Project

50 minutes

Closing: Group Question

5 minutes
Here is the prompt:
  • List all of the properties you know about similar triangles.
  • How certain are you that your theoretical values are accurate? Why?

Now that students have had the chance to work on their projects, I pose this pair of questions and ask them to confer with their colored rectangle groups as they answer.  I collect their responses as they leave.