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# Constructing Linear and Exponential Functions

Lesson 3 of 10

## Objective: SWBAT construct linear and exponential functions. SWBAT interpret the parameters of linear and exponential functions in terms of context.

To start class, students work on the **Entry Ticket: Constructing Linear and Exponential Functions. **For today's Entry Ticket, I give students the task of identifying a number of functions in different representations as linear or exponential. The activity provides additional practice on previously learned concepts in this unit, specifically interpreting characteristics of exponential functions and distinguishing between linear and exponential functions.

I word the third task of the assignment (create a different representation for as many scenarios as possible) with the term "as many as possible" because many students will not complete an alternate representation for all of the scenarios in the time allotted.

**Differentiation**: One way to easily differentiate this assignment is to assign each group, pair, or individual student one of the scenarios to create a different representation. Students can record their work on white boards and present a brief presentation as a way to review the Entry Ticket.

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As a class, we then review the **Class Notes: Constructing Linear and Exponential Functions**. During this time I review how to construct linear and exponential functions from varying representations (table, graph and set of input-output pairs). I provide students with Explicit Instruction on how to approach and complete these types of problems. I encourage my students to be active and take **Two-Column **notes during this section of class. When opportunities avail themselves, I try to decrease the level of support and have students increase participation in constructing the functions.

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Students then work in small groups completing a number of problems similar to those reviewed in the active note-taking section of class.

The intent of guided practice is to decrease support and to encourage students to work together to deepen their collective and individual understanding of the day's skills and concepts.

I like to have each group complete all of the **Collaborative Work: Constructing Linear and Exponential Functions. **As an extension I also assign each group a "focus" problem that they are expected to put their work on one of the white boards and also present their work to the class at the conclusion of the section.

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For the next session I have students complete the **Construct Your Own Exponential Function** in small groups. The task asks students to write a scenario that can be modeled by an exponential function. Then, students construct the function and create at least one other representation to model the scenario.

This exercise gives students a nice balance of focus and flexibility in how they show their understanding of the day's objectives. It also provides nice opportunities to engage in MP3 as students work together and navigate various points of view toward a common group goal.

#### Resources

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For today's **Exit Ticket: Recap and Review on Constructing Linear and Exponential Functions** students complete a written response that asks them to identify the most important lessons learned today. This open ended recap develops the important skill of summarizing. Students can utilize their notes, group work, and other artifacts from class to identify the 2-3 most important points from class (from their perspective).

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For homework students are asked to complete the **Homework: Constructing Linear and Exponential Functions** on constructing linear and exponential functions.

The homework provides practice with newer concepts (namely creating exponential functions and distinguishing linear from exponential functions), but also gives needed practice with linear functions. My students struggle with applying the concept of slope. Their difficulty becomes greater the longer and longer we get from teaching the unit on linear functions.

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Rewriting Radical and Rational Exponents (Plus Exponents Review)
- LESSON 2: Creating and Interpreting Exponential Functions
- LESSON 3: Constructing Linear and Exponential Functions
- LESSON 4: Comparing and Contrasting Linear and Exponential Functions
- LESSON 5: Pizza, Hot Chocolate and Newton's Law of Cooling: Adding Constants to Exponential Functions
- LESSON 6: The Luckiest Man in the World: Graphing Exponential and Linear Functions
- LESSON 7: Formative Assessment: Modeling Population Growth (A Math Assessment Project Classroom Challenge)
- LESSON 8: Marketing Exponential Functions: A Group Performance Assessment Task
- LESSON 9: Review Lesson on Exponential Functions
- LESSON 10: Writing in Math Classroom, Part 3: Comparing and Contrasting Arithmetic and Geometric Sequences