##
* *Reflection: Complex Tasks
Radical Equations Day 2 - Section 1: Warm Up and Homework Review

Solving an equation, even a polynomial, rational, or radical equation, is a straight forward skill with a black and white answer. One method of increasing the complexity of this type of problem is demonstrated in today’s warm up. Rather than asking the students to solve some equations, I asked them to identify a particular characteristic out of one of them, in this case an equation with no solution. I didn’t tell them what method to use which is important for an open ended question like this. Their responses were really good. Some students, like in Warm Up 4, knew that the root couldn’t be negative but picked the wrong one because they didn’t simplify the equations. Warm Up 3 was interesting because they got the right answer but used the wrong explanation. Around 50% of the students identified the correct response and gave an adequate reason. Warm Up 2 typified a certain number of students who knew the correct response but didn’t explain it well. Warm Up 1 was one that wrote a strong explanation. To bring the rest of the kids up to the level I want, I identified those with really great responses and had them share out.

*Complex Tasks: Taking Solving Equations To The Next Level*

# Radical Equations Day 2

Lesson 6 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- Polynomial Review Day 2, asks students to determine which of three radical equations has an extraneous solution.

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

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#### Radical Equations

*37 min*

This lesson is a Guided Practice lesson meant to build both student skill with radical equations and student understanding of extraneous solutions.

I begin with a problem similar to the ones from the previous lesson. We then extend to new types of radical equations. I have carefully selected to problems and order to build student skill and understanding. I add problems as necessary. Please watch my Video Narrative on maximizing student thinking during this lesson.

Please see the PowerPoint for detailed presentation notes.

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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. The final problem asks students to create a radical equation with an extraneous solution. This gives them an opportunity to use what they know about the structure of a radical equation (**Math Practice 7**).

This assignment 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