## MP7.MP4 - Section 2: Introduction: Modeling Hyperbolas

# Hyperbolas

Lesson 10 of 13

## 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.

*40 minutes*

#### Warm-up: Review Homework

*5 min*

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.

#### Resources

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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.

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#### Application: Hyperbolas

*15 min*

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**).

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Students should complete the Student Worksheet - Hyperbolas for homework tonight. It will be Homework #5 for the Conic Sections unit.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Cutting Conics
- LESSON 2: Name that Conic
- LESSON 3: Human Conics: Circles and Ellipses
- LESSON 4: Circles and Completing the Square (Day 1 of 2)
- LESSON 5: Circles and Completing the Square (Day 2 of 2)
- LESSON 6: Ellipses
- LESSON 7: Human Conics: Parabolas
- LESSON 8: Parabolas
- LESSON 9: Parabola Problem Partner Critiques
- LESSON 10: Hyperbolas
- LESSON 11: Non-Linear Systems of Equations
- LESSON 12: Conic Sections Test Review
- LESSON 13: Conic Sections Unit Test