Reflection: Coherence Using Special Right Triangles and Spotting Some Patterns - Section 4: Guided Lecture Notes: Trig Ratios for Special Triangles


An important element in this section of the lesson is that I say the word "memorize," but today's class is really a lesson on the nature of memorization.  If we simply try to force ourselves to memorize information, it's hard.  I tell my students that it's actually physically difficult for our brains to memorize disparate facts.  "Our brains are all about connections," I say.  "If we can spot the patterns, if we can make connections, then all of this will be easier."  I also like add, "You're welcome.  I'm providing you with a user's guide for your brain."

We spend some time exploring the connections between the trigonometric ratios, which takes us back to SLT Triangles 2: I understand the relationships between different trigonometric ratios.  I'll remind students of how we checked our work during the similar triangles project, by looking at tangent as the quotient sine/cosine. We discuss what it means for sine and cosine (literally, "complementary sine") to complement each other.  

We also look at the nifty pattern illustrated in pattern chart 2, and I note to students that one of the hallmarks of advanced algebra - and to being well-skilled in abstract and quantitative reasoning (MP2) - is being able to consider unexpected representations of expressions.  For example, no one would default to saying "√(4)/2" when they could simply say "2", but by taking a moment to rewrite it this way, we can uncover this interesting pattern.

  Coherence: Considering Memorization
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Using Special Right Triangles and Spotting Some Patterns

Unit 5: Trigonometry: Triangles
Lesson 9 of 9

Objective: SWBAT use special right triangles to determine geometrically the sine, cosine, and tangent of 30, 45, and 60 degrees.

Big Idea: What does it really mean to memorize something? To recognize the underlying structures and patterns, and to use them to make sense of and remember, conceptually, what is happening.

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