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# Compare and Contrast

Lesson 15 of 19

## Objective: SWBAT compare properties of two functions each represented in different ways.

## Big Idea: Can you really tease out the important features of a function? Try your hand at this compare/contrast lesson working with graphs, tables, functions and verbal descriptions.

*55 minutes*

#### Set the Stage

*5 min*

I begin class with a function like f(x)=x^2-4 on board and ask my students for summary of any key features they see and different ways to represent the function to show other key features. **(MP7) **I expect them to be able to comment on the zeros, x and y-intercepts, max/min points, end behavior, and symmetry, as well as suggesting that we could factor the equation, could graph it, and could write it in table form because these are what we've been studying in this unit. If they are really on top of it today, someone will suggest that we need a verbal description of a real-world problem this function might represent to give more meaning to the key features. I then ask my students to pair-share which representations give the best information about which key features and why. After a few moments I randomly select students to share what they discussed then tell them that today they will be comparing a variety of functions represented in different ways, so they can test their opinions about what works best and why.

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#### Put It Into Action

*45 min*

For this activity I tell my students that they will be working with their back partner to compare two different functions given different representations. I explain that they will be looking for things like which has steeper rate of change, how their end behavior is similar/different, or which has higher maximum or lower minimum point. I distribute the Compare and Contrast handout, ask if there are any questions, then tell my students they have about 20 minutes to complete this assignment. **(MP1, MP2) **Some students will struggle with two different representations and for them I suggest that they try looking at one function at a time, listing the key features for that function before moving to the second function. I also recommend that they choose the representation that makes the most sense to them and convert the other function into that same form. When everyone is done or after about 25 minutes I ask for volunteers to share their work with the class. I state my expectation that each team will share at least one problem and have a meaningful critique of the others. **(MP3) **

#### Resources

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#### Wrap It Up

*5 min*

I close this lesson by having my students write summary of the lesson for an "absent" classmate, a strategy I explain further in my video. These summaries help my students pull together what they've learned today and give me some insight into which students might need additional support.

#### 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