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# The Three Musketeers: Simplifying the Quadratic Formula

Lesson 9 of 13

## Objective: SWBAT use the completing the square method to transform a quadratic equation. SWBAT solve quadratic equations using completing the square and the quadratic formula. SWBAT recognize and write complex solutions to quadratic equations.

## Big Idea: Just like the Three Musketeers, the three pieces of the quadratic formula stick together, and work together to find solutions!

*90 minutes*

#### Entry Ticket

*15 min*

To start class, students work on the **Entry Ticket: The Three Musketeers: Simplifying the Quadratic Formula**. I have students factor and complete the square to one quadratic and then try to solve a second that does not easily factor. The reason for this is to both re-activate prior knowledge, but perhaps more importantly lay the groundwork for the reason why the quadratic formula is a useful tool and not just another isolated equation that students need to know because we tell them they do.

During the **Entry Ticket **I expect students to be conversing with each other, and I make my way around the class checking in for student understanding.

After students complete the **Entry Ticket**, I turn to the agenda board and highlight the learning and language objectives, agenda and homework for the class. I ask students if they have anything else they want to include on the agenda to provide an opportunity to give students increased agency and ownership for their own learning. If, in the case a student brings up an inappropriate idea for the agenda I ask the class for their input on whether or not that should be included – we use the class objectives and essential question as a decision making guide as to whether or not the proposed agenda item is relevant or not.

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**Explaining and Using the Quadratic Formula**

In this sub-section I go through the **Class Notes: The Three Musketeers - Simplifying the Quadratic Formula** and explain the quadratic formula as being comprised of three main parts: 1. –b, the discriminant and 3. 2a. Two of the three parts are relatively easy to compute and chunking the formula into three parts makes it easier for many students to work with, and also understand.

During the slide we go through an example with students taking notes and then students complete a think-pair-share on a practice problem using the quadratic formula.

During the class notes, we discuss both real and complex solutions to quadratic equations.** **

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To practice solving quadratic equations with real and complex solutions, students work in groups on the **Collaborative Work: The Quadratic Formula. **I provide students with the **Reference Sheet: Quadratic Formula to Solve Quadratic Equations **as a way to differentiate instruction and provide organizational support for students. Often I go through a problem together and ask students to take detailed notes so they have a good model/exemplar problem which they can use as a reference.

During this time it is my role to facilitate and provide differentiated support to the groups. I want to be sure all students are able to work with, and struggle, with the practice problems. My goal is not for every student to be experts at using the quadratic formula by the end of this class, but I do want every student to make improvements in their understanding and comfort level applying the quadratic formula for both real and complex solutions.

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#### Exit Ticket and Homework

*15 min*

To close this lesson, students complete the E**xit Ticket: The Three Musketeers Simplifying the Quadratic Formula** that has them practice using both the completing the square method and the quadratic formula to solve quadratic equations. The reason for having students show their work using both methods is to help them make the connections and commonalities of what they are doing, just in two different ways. I expect students to complete at least the first problem before the end of class, and often times assign the remaining problems for the night's homework.

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Introduction to Quadratic Functions
- LESSON 2: Interpreting and Graphing Quadratic Functions
- LESSON 3: Rate of Change & Comparing Representations of Quadratic Functions
- LESSON 4: Rearranging and Graphing Quadratics
- LESSON 5: Graphing Functions: Lines, Quadratics, Square and Cube Roots (and Absolute Values)
- LESSON 6: Building Quadratic Functions: f(x), kf(x) and f(kx)
- LESSON 7: Factoring and Completing the Square to Find Zeros
- LESSON 8: Forming Quadratics: Math Assessment Project Classroom Challenge
- LESSON 9: The Three Musketeers: Simplifying the Quadratic Formula
- LESSON 10: Quadratic Quandaries: Modeling with Quadratic Functions
- LESSON 11: Performance Task: Pulling It Together with Quadratics
- LESSON 12: Study Session for Unit Test on Quadratics
- LESSON 13: Unit Assessment: Quadratic Functions and Equations