# Roots

Lesson 7 of 19

## Objective: SWBAT graph radical functions and identify key features.

*50 minutes*

#### Set the Stage

*10 min*

I begin this lesson with a real-world function on my board and explain why I choose to do so in my video. I ask my students to graph the function , which should be a review of lessons from previous classes. **(MP1) **I have included a graph for the teacher on the resource.

While they're working I walk around observing who is working with ease and who might be struggling. For the struggling students I usually suggest creating a table of several points or factoring to find the roots. Reminding them of these strategies they already know helps build their confidence for the main part of the lesson. I do not specifically require my students to use their graphing calculators for this part of the lesson, but encourage them to do so in preparation for the next activity.

After a few minutes or when everyone is done I ask for volunteers to share their graphs with the class and explain how they created them. I anticipate at least a few of the volunteers will include key features in their explanation, like intercepts and changes in slope. **(MP3) **If not, I ask questions like "What parts of this graph might be particularly interesting to the builders of the roller coaster and why?" and "Where does the ride slow down to climb a slope? How do you know?"** (MP4) **When we've thoroughly discussed the graph and how it relates to the roller coaster function, I let my students know they'll be practicing more graphing today.

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#### Put It Into Action

*30 min*

For this section of the lesson I have my students work independently to graph and describe key features of several real-world problems using their graphing calculators. I explain that I don't just want them to list the features, but also to describe what they represent in terms of the problem. I distribute the graphing worksheet and ask if there are any questions then tell my students they have about 20 minutes to complete the assignment. **(MP1, MP2)** While they're working I walk around offering encouragement and assistance as necessary. Some students will struggle with the descriptions because they are still uncomfortable writing about mathematics. For them I suggest that they just write what they are thinking and worry about editing it after they've gotten the basics written. I also suggest that they write as though they are explaining it to a fourth grader of someone else who might not understand as well as they do. When everyone is finished or after about 20 minutes I tell my students that today they will be checking their own papers as I go through the answers. I remind them of my standard condition for this kind of self-check - I expect them to challenge any answers I give that don't make sense, that they disagree with, or that are incomplete. I always throw at least one or two of these kinds of answers into the activity so that my students stay alert and so that they understand that neither I nor the textbook are infallible.

#### Resources

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#### Wrap It Up

*10 min*

I close this lesson by giving my students a real world function then asking them to create a sketch labeled with key points and descriptions. I have included a graph for teacher use, but just give my students the function in words and symbols. This gives them additional practice at relating mathematics to real-world situations and gives me additional insight into which students might need additional support. **(MP2) **It also brings the lesson back to where we started the day, graphing a real-world function and making sense of the key features.

#### Resources

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Keys
- LESSON 2: BrainPower!
- LESSON 3: Sketchbook
- LESSON 4: Reign Over the Domain
- LESSON 5: Change!
- LESSON 6: Estimate!
- LESSON 7: Roots
- LESSON 8: Pieces
- LESSON 9: Zero to Hero
- LESSON 10: Happy Endings
- LESSON 11: Logs; but not for building
- LESSON 12: Power to the Mathematician
- LESSON 13: Write That!
- LESSON 14: And Write That!
- LESSON 15: Compare and Contrast
- LESSON 16: The Choice is Yours
- LESSON 17: Retrospective
- LESSON 18: Self-Assessment
- LESSON 19: No Surprises Testing