## Reflection: Connection to Prior Knowledge Law of Sines - Section 1: Activate Prior Knowledge

I have often heard colleagues lament the fact that even our most advanced students have trouble performing arithmetic with fractions. This year teaching Common Core Geometry has really highlighted the importance of students having fluency with fractions.

Having to perform arithmetic with actual numerical fractions is one thing, but in the new Geometry course, there is such an emphasis on deriving and proving formulas and identities in the abstract that students must truly understand the structural aspect of performing operations with fractions. When I refer to the structural aspect I'm talking about looking at expressions structurally rather than computationally. For example, in the problem 2/3 + 5/8, students focus on the computational aspect when they figure that the common denominator is 8x3 = 24. By contrast, in a problem like q/ab + p/bc, students should look at the structure and realize that the common denominator would be abc, rather than ab^2c.

In this lesson, we realize that when we have a/b divided by c, it's the same as a/b times 1/c, and by generalizing, we realize that the c (viewed as a structural object) appears in the denominator: a/bc.

So again, it become less about computation and more about viewing expressions as being composed of objects that can be manipulated according to rules.

Number Sense: Fractions
Connection to Prior Knowledge: Number Sense: Fractions

# Law of Sines

Unit 7: Right Triangles and Trigonometry
Lesson 6 of 6

## Big Idea: Looking for a sine? In this lesson, students will prove the law of sines and use it to solve problems.

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110 minutes

### Anthony Carruthers

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