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# Completing the Square Day 2 of 2

Lesson 8 of 12

## Objective: Students will be able to complete the square to solve a quadratic equation with both real and complex roots.

## Big Idea: Compare and contrast the effectiveness of multiple methods of solving quadratic equations.

*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. The Video Narrative specifically explains this lesson’s Warm Up- Complete the Square Day 2, which asks students to determine whether a quadratic equation has been solved properly.

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

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#### Complete the Square

*37 min*

In the previous lesson, Complete the Square Day 1, we were introduced to completing the square as a method of solving quadratic equations. In this lesson, we will extend this concept into quadratics with a leading coefficient that is not 1. This lesson consists of a Guided Practice. Like the previous lesson, we will associate these with the graphic solution (**Math Practice 5**). This lesson is very straight forward but I feel that this is an algebraic skill that they need to master.

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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 by completing the square.

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This Assignment is intended to help students master completing the square. I have also asked students to describe how they know whether a quadratic equation is going to have real or complex solutions (**Math Practice 7**). There are a variety of possible solutions here including look at a graph or stating whether it is factorable.

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