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# Radical Equations Day 1

Lesson 5 of 8

## Objective: Students will be able to solve radical equations.

## Big Idea: Multiple representations and problem solving are the key features of this radical equation lesson.

*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. This lesson’s Warm Up- Radical Equations Day 1, asks students to use a square root model to determine the depth of water in which a tsunami is traveling. This model was used in a previous lesson and introduce's today's concepts.

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

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#### Radical Equations

*37 min*

This lesson begins by looking at the warm up as a class. I ask for a volunteer to share their steps and solution. I then ask if anyone did the problem in a different way, a useful strategy for highlighting student thinking as well as multiple methods of solution (**Math Practice 3**).

The next portion of the lesson consists of a Guided Practice that looks at using both graphing and algebraic manipulation to solve increasingly complex radical equations. I planned the problems carefully to build upon each other both graphically and algebraically. I have included a graph paper handout as it can be difficult to solve an equation using a freehand graph. I am not allowing my students to use a graphing calculator during this lesson as I want to reinforce the skill of graphing radical equations using transformations.

For each problem, the students will graph it and then solve it algebraically. Please see my Video Narrative for more information.

The final activity is a modeling problem. *To estimate the maximum safe speed when traveling around a curve, the formula, V = √(2.5r), is used where V is the maximum velocity and r is the radius of the curve. A new semi-circular exit ramp is being planned on I-84. How much land will need to be prepared for this exit if the velocity on the ramp can be no less then 40mph.* I have the students work with their partner on this problem (**Math Practice 4**). I may pause the class part of the way through to ask for ideas on how to proceed with this problem. This scaffolding measure will help students who may be struggling to make sense of the problem (**Math Practice 1**). This problem might be added to the homework depending on the remaining time.

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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 radical equation.

#### Resources

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This assignment ensures that students are capable of independently solving the radical equations seen in the lesson. I have also included problems that ask students to first write two radical equations that equal ten and then write two more radical equations with no solution. These tasks help students deepening their structural knowledge of radical equations (**Math Practice 7**). I may also ask students to finish the modeling problem from the lesson.

This worksheet was created with Kuta Software which is an excellent resource for a mathematics teacher.

#### Resources

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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: Modeling the Speed of Tsunamis with Square Roots
- LESSON 2: Transformations on Quadratic Functions Day 1 of 2
- LESSON 3: Transformation of Quadratic Functions Day 2 of 2
- LESSON 4: Square Root Functions
- LESSON 5: Radical Equations Day 1
- LESSON 6: Radical Equations Day 2
- LESSON 7: Radical Functions and Equations Review
- LESSON 8: Radical Function Test