## Reflection: Modeling Law of Cosines - Section 2: An Approach to Deriving Formulas

Although this lesson was specifically on deriving the Law of Cosines, the larger goal, as I see it, was to teach students a heuristic for deriving formulas in general. I wanted my students to understand that formulas are essentially functions with an output variable and usually multiple input variables.

Keeping this in mind caused me to really emphasize the idea of using the output variable and input variables as a way of guiding the derivation process.  I chose to explicitly model the heuristic for deriving a formula (deriving the SAS area formula as an example) in the hope that students would apply this heuristic to derive the Law of Cosines formula and adopt it as a heuristic to use when deriving formulas in general.

To facilitate this, I designed the lesson handout in way that would continually prompt students to engage in the type of thinking prescribed by the heuristic.

Teaching Heuristics
Modeling: Teaching Heuristics

# Law of Cosines

Unit 7: Right Triangles and Trigonometry
Lesson 5 of 6

## Big Idea: Deriver's...start your engines!...In this lesson, we'll be doing some heavy duty mathematics to derive the Law of Cosines.

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135 minutes

### Anthony Carruthers

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