##
* *Reflection: Developing a Conceptual Understanding
Estimate! - Section 3: Wrap It Up

Some of my students are still intimidated by graphs that aren't linear or quadratic so this lesson helps build their confidence about working with graphs of functions in general. It was interesting to see which students actually used a slope formula to estimate a line between the points at (1, ?) and (2, ?) and which students just took a guess about what worked. I even had one student who put equations in his calculator several times and used the table option to get points. His Tips for a missing student show that he really does understand this lesson, as did the fact that he won the competition handily.

# Estimate!

Lesson 6 of 19

## Objective: SWBAT estimate the rate of change of a function from a graph.

## Big Idea: Just like estimating the number of jelly beans in a jar, your students estimate the rate of change for graphs with the best estimate winning the prize!

*55 minutes*

#### Set the Stage

*5 min*

I begin this lesson by asking my students if they've ever participated in a "guestimating" event like trying to estimate the number of jelly beans in a jar. This leads to a general discussion of what it means to estimate after which I put a graph of the function f(x) = x^3 on the board and ask my students to independently estimate the rate of change for the domain from x=1 to x=2. **(MP1)** When they've had a few minutes to work, I randomly select students to post their responses on the board, four at a time, until all students have posted. I then have the class critique the answers with a focus on which ones fit the graph the best. **(MP3) **As we work through these critiques I ask for volunteers to explain how they determined their answers. I'm anticipating some students might say that they look at the slope between two points because that should be familiar from earlier classes. I hope that someone also suggests using the axes to estimate points if they aren't given. If these aren't mentioned I might ask a leading question like "How can you find points to work with if none are labeled on the graph?"

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#### Put It Into Action

*45 min*

Instead of just having my students work independently as they practice estimating rates of change, I create a classroom friendly competition which encourages student engagement. I tell my students that they will each need a white board, marker, and eraser to write and share answers. I distribute the Estimate handout (except for the final page with all the equations and rates of change!) and review the rules of the game.

- Each student should make their best estimate for the rate of change for each graph, for the section between x=1 and x=2, writing it on their whiteboard.
- When a reasonable time has passed (anywhere from 30 seconds to 2 minutes) I will call time at which point everyone must display their whiteboard simultaneously.
- The student(s) with the best estimate wins a point for the problem. Ties each win a point.
- Students may challenge any decision but must support their challenge claim mathematically.

I ask if there are any questions, then begin the game, with each student working to estimate each rate of change. ** (MP1)**

#### Resources

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#### Wrap It Up

*5 min*

I close this lesson by giving each student a notecard and asking them to write three strategies/tips, that they would give to an absent classmate, for estimating rate of change accurately. **(MP2, MP6)**

If you needed to provide your class with more specific directions, you might have your students answer the following questions:

- What is one important thing you would share with an absent classmate about today's lesson and why do you think it's important?
- Describe one strategy you used to estimate the rate of change for a data table.
- Describe one strategy you used to estimate the rate of change for an equation.

#### 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