Reflection: Classroom Setup Converse of the Pythagorean Theorem and Special Right Triangles Investigation - Section 3: Special Right Triangles Investigation


I decided to include a “You will be successful if…” slide into my PowerPoint because I wanted to explicitly communicate my expectations for how my students would work through this task—this slide included a reference to one of the math practice standards, attending to precision.  By being transparent and clear, I was able to show students how they could meet my standards while sending the message that I would hold them accountable to working this way. 

I have also learned from prior teaching experiences that some students will have memorized tricks and shortcuts for special right triangles in the past; in order to appropriately challenge all of my students, I needed the students who had been exposed to these ideas not to share what they had seen or memorized, but rather, to instead create an opportunity for their peers to make sense of patterns and deeply understand the relationship between the sides of these triangles.  Specifically telling these students they could not share the “rule” tended to lead to deeper wondering and conversation around why the patterns made sense and how they could actually see the pattern in the structure of their work.     

  Communicating High Expectations
  Classroom Setup: Communicating High Expectations
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Converse of the Pythagorean Theorem and Special Right Triangles Investigation

Unit 11: The Pythagorean Theorem
Lesson 2 of 6

Objective: Students will be able to apply the Pythagorean Theorem to derive shortcuts for 30-60-90 triangles and 45-45-90 triangles.

Big Idea: By using linguini noodles, students will see how the Pythagorean Theorem and its converse work. Then, in a small group investigation, students will discover the special right triangles shortcuts and justify their reasoning.

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  70 minutes
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