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# Non-Linear Systems of Equations

Lesson 11 of 13

## Objective: SWBAT solve a system of non-linear equations both algebraically and graphically.

*50 minutes*

Students will answer three clicker questions on (Flipchart - p.2-4) where they will need to match the equation of a hyperbola to the correct graph or they will find the equation of the hyperbola when given the vertices and the length of the conjugate axis.

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**Preparation:** To access the video linked below you will need an account on the SAS curriculum pathways website. (Just follow the video link below and you can create a free account from that page.)

**Narrative:**

** **Before students begin their work today, I am going to help them to activate their prior knowledge of solving systems of equations by showing them a quick video. I like how this video describes solving systems of equations in such a concise way. It also gives students a great side-by-side graphical and algebraic view of each solution as it proceeds.

In order to keep students engaged throughout the video, I will pause the video at the 2:22 mark and have students complete a Think-Pair-Share answering the question “Is it possible for a system to have more than one solution, but not infinitely many? Draw a sketch of two graphs to justify your answer.” Then, I will show the remainder of the video.

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#### 4-way Models

*27 min*

My goal for this section of the lesson is for students to complete one **4-way Problem** where they model a solution in three different ways. There are four different problems (A-D) to choose from on the Student worksheets 4-way models handout. I sequenced them so that A is the easiest and D is the most difficult.

I am going to place 1 copy of each problem at every table (teams of 3 per table). The students can work together to choose which problem each of them will work on. I place two restrictions on the activity: (a)two people at the same table cannot work on the same problem and (b) calculators should not be used. Team members can assist each other. But, each student will be responsible for solving one of the four problems. As I monitor the classroom, I will encourage students to explain how they know that all four representations model the same solution.

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#### Closure: Clicker Quiz

*10 min*

At the end of the period, students will take a 5 question clicker quiz independently. This will help me to know which students may need extra assistance. There are three questions in the Flipchart that students should solve graphically and two that students should solve algebraically.

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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