##
* *Reflection: Accountability
Roots - Section 2: Put It Into Action

One of the"incorrect" answers I gave for the self-check was for problem #3. I used square root instead of cube root because I thought it was a mistake a student might make and because if you use a standard window you can't really tell the two graphs apart. When I sketched the graph on the board I used a standard window and was happy to hear my students immediately complain that the window didn't fit the function well. Instead of just changing it I challenged them to figure out what settings I should use. This led to some interesting discussion among the students because some wanted to use the key features as I'd labeled them and others wanted to use what they felt were the "correct" features. I invited both groups to post their results on the board and let them figure out that my answer really was wrong.

*Right about wrong answers*

*Accountability: Right about wrong answers*

# 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