Hyperbolas

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Objective

SWBAT write the equation of a hyperbola and graph hyperbolas.

Big Idea

Students identify and make use of the structure of an equation as they learn to graph hyperbolas.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Precalculus and Calculus

Standards

HSA-SSE.A.2

Use the structure of an expression to identify ways to rewrite it. For example, see x4 â y4 as (x2)2 â (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 â y2)(x2 + y2).

HSG-GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP7

Look for and make use of structure.

Warm-up: Review Homework

5 minutes

I know that conic sections are very difficult for my students so I want to be sure to give plenty of time to review homework in class and for students to help each other. When student first enter class today, I give 5 minutes to review last nights’ Homework in their teams. After five minutes I ask each team to text in the question they had the most difficulty understanding as a team. I will then go over the most difficult question as determined by the class.

Introduction: Modeling Hyperbolas

20 minutes

My students can always use more practice on decoding mathematical language and applying formulas. To start class off today I model how I would go about figuring out hyperbolas with only the provided information on the Student Handout - Hyperbolas Summary. I give every student the Handout. Then, I work through some problems from the Hyperbolas PowerPoint. I over-emphasize any opportunity to demonstrate skills related to Mathematical Practice 7: identify and make use of structure in mathematics.

Since I am giving students the Summary, during today's lesson students will spend less time identifying the structure, but they will gain valuable practice! The Hyperbolas Video Narrative provides more detail on how I will use the presentation in front of the class.

Application: Hyperbolas

15 minutes

I want students to get started on Student Worksheet - Hyperbolas in class and complete the rest for homework. These problems are not routine for students. Each varies from the examples that I modeled subtly, so I predict many students will need the support from their team.

My goal is for students to persevere in breaking down the problems: (a) identifying what they know, (b) figuring out what they need to learn, and (c) making a plan to get there. (Do I see another opportunity for improvement on a mathematical practice? Yes I do! Mathematical Practice 1: Make sense of problems and persevere in solving them).