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# Quadratic Formula

Lesson 10 of 12

## Objective: Students will be able to solve quadratic equations with the quadratic formula

*50 minutes*

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. To stretch student's thinking this lesson’s Warm Up- Quadratic Formula, asks students to solve a quadratic equations using two different methods.

I also use this time to correct and record the previous day's Homework.

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#### Quadratic Formula

*37 min*

This lesson reviews an Algebra 1 standard, the quadratic formula, using the Algebra 2 extension of complex numbers.

We begin by reviewing the methods students currently have to solve quadratic equations which frames the day's lesson. Please watch the Video Narrative for more information about this introduction. At this point, I give the students the general form of a quadratic: ax^{2} + bx + c = 0 and have them complete the square with a, b, and c (**Math Practice 7). **This puts the quadratic formula in perspective so students don’t think it’s just some magical formula that somehow works. Once they have had an opportunity to work on it, we will build it as a class to ensure that all students are on the same page. We then solve several equations, with real and complex solutions, using the quadratic formula.

The final goal for this lesson is to solve an area problem. *My contractor sent me a $3000 bill for fencing, priced at $15 per foot for a rectangular field that covers 1600* *ft ^{2}. He said he hopes I’ll be happy with the project but forgot to tell me the dimensions of the fence he is building. He’s out of cell phone range on another building site, how can I figure out what dimensions he’s planning to install? *My goal for this problem is to give the students an opportunity to work on something that seems challenging at first (

**Math Practice 1**) but is quite doable as they make start to look at the given information. One scaffolding measure that may be useful is reminding the students to draw a diagram. Another place students may struggle is figuring out the variable dimensions of each side of the rectangle so asking questions like "What would the length be if we call the width x?" or "What portion of the perimeter is just one length and one width?". For the remainder of the class, we will discuss the solution and steps to the solution.

Detailed presentation notes can be downloaded in the PowerPoint.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to solve a quadratic equation using the quadratic formula.

#### Resources

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This Assignment gives the students an opportunity to practice using the quadratic formula as well as solve several quadratic area problems (**Math Practice 4**).

This worksheet was created with Kuta Software which is an amazing resource for any mathematics teacher.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: The Real Number System
- LESSON 2: Simplifying Square Roots
- LESSON 3: Imaginary Numbers Day 1 of 2
- LESSON 4: Imaginary Numbers Day 2 of 2
- LESSON 5: Complex Numbers Day 1 of 2
- LESSON 6: Complex Numbers Day 2 of 2
- LESSON 7: Completing the Square Day 1 of 2
- LESSON 8: Completing the Square Day 2 of 2
- LESSON 9: Real and Complex Number System Quiz
- LESSON 10: Quadratic Formula
- LESSON 11: Complex Numbers and Quadratic Equations Review
- LESSON 12: Complex Numbers and Quadratic Equations Test