Name: Breanna Andristbreesportfolio.weebly.com/uploads/7/6/3/0/7630806/mth_lesson_3…  · Web view: You are a college football star that is being recruited by several professional

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Name: Breanna AndristGrade Level: Algebra 1Lesson Title: Lesson 7.2 Exponential Models (day 3)

Content Big Idea and Learning Targets Content Big Idea:

o Explore patterns of exponential models using tables and graphs and compare both linear and exponential models.

Learning Targets: o By the end of this lesson, students should be able to complete the following:

Complete a table of values given a particular real-world situation Graph the table of values creating an exponential function Write an exponential equation based on the starting value and constant

multiplier of the table data Compare and contrast several exponential and linear models

Why are these important?o Students will be exposed to exponential models throughout their life and they

need to be able to interpret data and equations in order to compare and contrast various situations. Although technology makes exploring exponential models easier, students need to have a basic understanding of how equations are created and what the information means.

How do the targets and big ideas relate to your discipline and to your specific students?o Students are able to work with a partner on many of the tasks in the lesson and

they will also have opportunities to demonstrate work and understanding in front of their peers. Because my students are social and like to talk through problems, this lesson allows them opportunities to engage with each other several times over the course of the period. This lesson also connects to students’ prior learning experiences of general exponential equations. This lesson was designed to spark student interest by focusing on how exponential models are related to football, which many of the students have expressed is a recreational hobby.

State Standards Addressed:o A1.7.C: Express arithmetic and geometric sequences in both explicit and

recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.

o A1.1.E: Solve problems that can be represented by exponential functions and equations.

o A1.7.A Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.

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Academic Language Key vocabulary:

o Constant Multiplier : In a sequence that grows or decrease exponentially, the number each term is multiplied by to get the next term. The value of (1 + r) in the exponential equation y = A(1 + r)x or the value b in the general form y=abx.

Assessment of Student Learning How will you assess student learning?

o Formative Assessment: Students will be asked several questions throughout the lesson to informally assess their understanding of learned concepts (how to graph exponential equations, how to write an exponential equation, and how to use the equation and graph to analyze a particular situation. In addition to class discussions, teacher will also walk around room to observe student work as a means of informal assessment. Formative assessment will be done using the Touch Down worksheet, which is to be completed individually. After students individually complete the worksheet, they are then paired up with other students to complete a group poster and presentation. Although the final product is showcased as a group, students are individually assessed prior to assigning groups.

o Student Voice: Students will have opportunities to express their understanding of exponential equations and models prior to starting the lesson. The introduction activity and warm-up are designed to assess whether students understand exponential models after two days of instruction.

o Accommodations/Modifications: Teacher will walk around the room during the lesson to help assist students who continue to struggle with concepts.

Instruction and Engagement to Support Student Learning (Lesson Breakdown) Supplies/Materials :

o Attached Worksheets (Warm-up and Touch Down or Fumble Worksheet)o Class football field poster

Warm-Up (see attached warm-up): o This warm-up is designed to assess prior days understanding identifying starting

value (y-intercept), constant multiplier, writing an exponential equation, and graphing the table values to visually see the exponential curve.

o Explain that the warm-up helps transition to the lesson target of being able to compare exponential equations and tables in order to determine what equation creates the highest output in regards to football salaries.

Introduction Example (student football throwing): o This introduction is designed to have students actively engage in the idea behind

the lesson project.o Two students will be asked to stand on opposite ends of the classroom with one

student holding a mini football. Student A throws the football to student B and the class observes the distance between the two students. A penalty is called and student A gets to move ½ the distance to the goal (1/2 way to student B).

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Another throw is observed and again student A gets to move 1/2 the distance to the goal because of a penalty.

o Following the student visual demonstration, a football field poster (see picture below) is displayed in the front of the room and teacher models the movement on the poster.

o Questions for the students: What do you notice about the distance between each of the movements? If the player keeps moving ½ the distance of the goal, would the player

actually ever reach the end zone? Given the starting position on the field and thinking about moving ½ the

distance of the goal with each movement, what would an exponential equation be for the situation?

What do each of the numbers and variables represent? Worksheet: Touch Down or Fumble (see attached)

o This lesson is designed to be an extension of the lessons from the prior two days. This lesson will also serve as a formative assessment for student understanding of exponential models.

o Pass out worksheets and explain to students that they are all college football stars that are being recruited by professional football teams. Each team is offering a different salary and it is the students’ job to decide what offer will make them the most money (offers include both linear and exponential models).

o Students will work individually to complete lesson worksheet and when they have completed the worksheet, teacher will evaluate work and assign a partner to each students and a particular professional team. The partners will then be asked to create a poster that includes: team name, salary offer, table of values that represents weeks played and salary, equation for data in the table, and student names (see picture on following page of actual poster created).

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o After groups complete their posters, they will present their posters to the class and then there will be a class discussion about all of the offers.

o Prior to starting the class presentations, ask students what the learning targets have been over the past few days. In addition, ask students to rate their overall understanding of exponential models by holding up their hands and displaying one to five fingers (one = still do not understand, five = great understanding)

o Questions for the class after presentations How can you tell the difference between linear and exponential models? Looking at the exponential models, what offer paid the most money at the

end of five weeks? What do you notice about the constant multiplier of that equation

compared to the other equations? Closing the Lesson

o Ask students what they have learned over the last few days and what activities helped with their ability to reach the learning targets.

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Warm-Up Lesson 7.2

NAME: ______________________________ PERIOD: _____________

x 0 1 2 3 4 5y 3 12 48 192 768 3072

Starting Value: _____________________ Constant Multiplier: ____________

Exponential Equation for the Data: _______________________________

Warm-Up Lesson 7.2

NAME: ______________________________ PERIOD: _____________

x 0 1 2 3 4 5y 3 12 48 192 768 3072

Starting Value: _____________________ Constant Multiplier: ____________

Exponential Equation for the Data: _______________________________

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Lesson 7.2: Touch Down or Fumble?

NAME: ___________________________________ PERIOD: __________

Objectives: Explore exponential growth patterns Compare exponential and linear growth models Create a table, graph, and write equations for exponential or linear models

Situation: You are a college football star that is being recruited by several professional football teams. Each of these teams is offering you different salary schedules and you are having a hard time deciding what offer is best. Your job is to sit down and create a table of values for each of the teams to help guide your decision making.

Team #1 (Falcons)Offer: $1000 first week, $1000 every week after

Week 1 2 3 4 5 6Total Salary

Team #2 (Eagles)Offer: $200 first week, total triples every week

Week 1 2 3 4 5 6Total Salary

Team #3 (Bears)Offer: $500 first week, total doubles every week

Week 1 2 3 4 5 6Total Salary

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Team #4 (Tigers)Offer: $100 first week, total multiplies by four every week

Week 1 2 3 4 5 6Total Salary

Team #5 (Lions)Offer: $10 first week, total multiplies by 10 every week

Week 1 2 3 4 5 6Total Salary

Group Assignment:

In your groups, you will be creating a poster with the following information: Table of values for your offer Graph showing weeks (x) and total income (y) An exponential or linear equation for your data

o y = abx

o a = starting valueo b = constant multiplier

Assigned Team: _______________________

Graph:

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Exponential / Linear Equation: _____________________________