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# Finishing Up the Similar Triangles Project

Lesson 5 of 9

## 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.

*75 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.

#### Resources

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#### Closing: Group Question

*5 min*

- 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.

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- UNIT 1: Statistics: Data in One Variable
- UNIT 2: Statistics: Bivariate Data
- UNIT 3: Statistics: Modeling With Exponential Functions
- UNIT 4: Statistics: Using Probability to Make Decisions
- UNIT 5: Trigonometry: Triangles
- UNIT 6: Trigonometry: Circles
- UNIT 7: Trigonometry: The Unit Circle
- UNIT 8: Trigonometry: Periodic Functions

- LESSON 1: Intro to Trigonometry / What is Similarity?
- LESSON 2: Course Structures and the Similar Triangles Project, Part 1
- LESSON 3: The Similar Triangles Project, Part 2: Empirical and Theoretical Data
- LESSON 4: Definitions of the Trig Ratios and a Fascinating Chart
- LESSON 5: Finishing Up the Similar Triangles Project
- LESSON 6: Solving Right Triangle Trig Problems
- LESSON 7: Constructing an Equilateral Triangle
- LESSON 8: Constructing Special Triangles on Geogebra
- LESSON 9: Using Special Right Triangles and Spotting Some Patterns