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Louisiana State UniversityClassroom InteractionsThis lesson is a two-day 5E Lesson. There are two complete 5E Lesson Plans for each day below.

Day 1LESSON TITLE: Exponential Decay and Growth as Seen In A Town’s Crisis

Use an appropriate title to connect concept topics with real-world applications

Standards Louisiana State Standards for Science and Math;

Science must include appropriate PE, SEP, DCI, and CCC. Math must include appropriate Math Standards and Practices

Key Concepts Concepts include both tangible objects and abstract ideas. Identify the key concepts, knowledge, and skills that describe what the students will need to understand. Use the

concept map you created for reference. A2: F-IF.C.8b Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions.

Standards for Mathematical Practice- Make sense of problems and persevere in solving them.- Reason abstractly and quantitatively- Model with mathematics- Use appropriate tools strategically - Attend to precision- Look for and make use of structure

- Exponential Decay- Exponential Growth- Compound Interest

Big IdeaBig ideas are important, enduring, and transferable beyond the scope of core concepts,

principles, theories and process.

Essential QuestionsEssential questions are thought provoking questions used to engage students’ interest

and to facilitate inquiry throughout the learning cycle of the instructional plan. Essential questions stimulate discussion and thinking over time.

Using exponential functions to model real world situations. - What are some of the characteristics of exponential growth and exponential decay functions?

- Can real-world situations be represented by a polynomial, quadratic or exponential function?

- How do you explain the benefits of multiple methods of representing exponential functions (tables, graphs, equations, and contextual situations)?

Prior Knowledge Key Vocabulary

Identify common preconceptions and prior student knowledge.

List all new key vocabulary for the lesson. Use the concept map you created for reference.

- Polynomials- Exponents

- Initial Amount- Final Amount- Rate of Growth - Time- Growth factor- Decay Factor

Learning ObjectivesInstructional learning objectives state the specific learning outcome in an observable

and measurable format.

Assessment(s)Include both formal and informal assessments used throughout the lesson.

SWBAT:

- Recognize the concept of exponential growth, exponential decay, and compound interest

- write equations for exponential growth or decay- use calculator to find an exponential equation for a given data set

Entrance Ticket: 1. During the exponential phase, E. coli bacteria in a culture

increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now? Round to the nearest hundredth place.

2. If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much money will be in the account after 5 years? Round to the nearest cent.

3. (a) Determine if the given graph is exponential growth or decay. (Refer to Entrance Ticket for graph)(b) What is the exponential function for the given graph? ____________________

4. The value of a car is $21,500. It loses 12% of its value every year.

(a) Write a function that represents the value y (in dollars) of the car after t years.

(b) Find the approximate monthly percent decrease in value.

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(c) Graph the function from part (a). Use the graph to estimate the value of the car after 6 years.

Exit Ticket: 1. In the exponential growth function y = a(1 + r)t, the quantity r is

called the ________.2. During normal breathing, about 12% of the air in the lungs is

replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?

3. A house was purchased for $90,000 in 1995. If the value of the home increases 5% per year, what is it worth in the year 2020?

4. How much money would you need to deposit today at 9% annual interest compounded monthly to have $12000 in the account after 6 years?

Advanced Preparations/SafetyAdvanced preparations include all tasks and activities that may be used to preparing the learning experience. Also include any safety concerns expected throughout the lesson.

Prior to the lesson, the teachers will need to create the necessary handouts. Additionally, the exit ticket for day one must be transferred to Plickers and a card must be assigned to each student.One student of the class has accommodations to have advanced completion time of problems, so proper preparations must be made.

5E Instructional Learning CycleLouisiana State University

GeauxTeach 5E Lesson Plan EDCI 3550 - Classroom Interactions

Teacher Candidate Team Members: Kiara Ferrygood Mentor Teacher: Richard Harsch Course: Algebra II

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and Mary Margaret Sanford

Date Lesson to be Taught: 3/26/2019 School: Baton Rouge High Classroom: 1124

Time Lesson to be Taught: 8:15-9:45 Grade Level: 10/11 Lesson Topic: Exponential Growth and Decay

ENGAGEMENT Approximate Time: 10 MinutesPique students’ interest and introduce them to the big ideas and essential questions. During the ENGAGEMENT students make connections between past and present learning

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experiences begin to ponder upcoming learning experiences. Students are recalling prior knowledge pertaining to key concepts and/or developing their own questions about a phenomenon. Overview In narrative format, provide an overview of the engagement phase of the lesson.

During the engagement, the students will receive an entrance ticket, which will assess students understanding of concepts. The entrance ticket will assess students’ understanding of concepts not introduced prior to the lesson. The concepts assessed on the assessment will be compound interest and exponential decay and growth. Furthermore, the graphing of exponential functions will also be tested on the assessment. A comparison between the entrance and exit ticket (Exit Ticket of 3/28/2019) will be made to analysis students’ progression. (Reference: “Entrance Ticket”)

What the Teacher Will Do Eliciting Questions/Student Responses What the Students Will Do

The teacher will inform students of the entrance ticket and pass out entrance tickets.

Q: During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the

current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the

population be 7.2 minutes from now? SR: 197.2 million

The students will complete entrance ticket.

The teacher will monitor student responses and offer assistance if needed.

Q: If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much

money will be in the account after 5 years? Round to the nearest cent.

SR: After 5 years there will be $5387.42 in the account.

Students will record responses using plickers question cards.

Q:SR:

Students will ask for assistance if needed.

TRANSITION (Engagement to Exploration)What question(s)/task are you asking of students that demonstrates proficiency? Successfully answering this question or completing this task shows that the teacher can move on to the next part of the lesson. If students do not demonstrate proficiency, how will you remediate? Provide both student outcomes. Evaluation/Decision Point Assessment Student Outcomes

- Teacher will examine students understanding or lack of understanding to will decipher how to proceed.

- If students are not successful, the teacher will clarify misconceptions throughout the duration of the lesson.

EXPLORATION Approximate Time: 15 MinutesInvolve students in EXPLORATION of the lesson topic and concepts. Activities using hands-on activities should be used to help students use prior knowledge, identify and advance their current understandings of the concepts, dispel misconceptions, generate new ideas, explore questions and possibilities, and design and conduct a preliminary investigation.

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Overview In narrative format, provide an overview of the exploration phase of the lesson. For the exploration phase of the lesson, students will work individual or in pairs to complete the assigned problems. The assigned problems will consist of table of x and y intercepts and will ask for the students to decipher if the points given reflect exponential growth or decay. (Reference: “Making Predictions”)


The teacher will give directions of the task and pass out the handouts.

Q: Do you notice a pattern in the x and y values?SR:Yes, the values are decreasing.

Students will work with a partner to solve the assigned problems.

The teacher will offer assistance when needed. Q: What are the characteristics of exponential decay?SR: As x increases, y decreases.

Students will ask for assistance if needed.

TRANSITION What question(s)/task are you asking of students that demonstrates proficiency? Successfully answering this question or completing this task shows that the teacher can move on to the next part of the lesson. If students do not demonstrate proficiency, how will you remediate? Provide both student outcomesEvaluation/Decision Point Assessment Student Outcomes

The teacher will evaluate students’ understanding of the given problems by assessing student responses and solutions. After evaluating student’s work, the teacher will decide whether or not to proceed to the explanation portion of the lesson.

If the students appear to understand the idea of decaying and growth, then the teacher will proceed to the explanation portion of the lesson. If the teacher notices possible misconceptions, the teacher will provide clarification using guided instruction and discussions.

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EXPLANATION Approximate Time: 20 MinutesStudents communicate with others to make rich connections and to provide an EXPLANATION for what they have experienced and learned during the Exploration phase of the lesson. As students’ communicate, they demonstrate their conceptual understanding, process skills or behaviors. Vocabulary is presented in correct context to redirect misconceptions.Overview In narrative format, provide an overview of the explanation phase of the lesson.

The teacher introduce the following concepts: Exponential Decay, Exponential Growth and Compound Interest. In order to promote student learning, the teacher will ask probing questions and inforce key vocabulary (Refer to Key Vocabulary). The students will take notes of the concepts on a given handout.


The teacher will pass out handouts and introduce students to the new concepts.

Q: What is the difference between exponential growth and exponential decay?

SR: The difference is exponential growth shows increase, while exponential decay shows decrease.

Students will answer the probing questions asked by the teacher.

The teacher will provide clarification of concepts if needed to clear up misconceptions.

Q: What is the decay factor in the exponential decay function?SR: (1-r)

Students will record note using the handout given.

The teacher will assess student understanding by asking probing questions.

Q: Can the exponential growth formula be obtained from the compound interest formula?

SR: Yes, if we plug in 1 for n, we get the exponential growth formula.

If needed, the students will ask questions for clarification.

TRANSITIONWhat question(s)/task are you asking of students that demonstrates proficiency? Successfully answering this question or completing this task shows that the teacher can move on to the next part of the lesson. If students do not demonstrate proficiency, how will you remediate? Provide both student outcomes.Evaluation/Decision Point Assessment Student Outcomes

The teachers will conduct an evaluation of the students during the explanation portion of the lesson by assessing student responses to eliciting questions.

If the students appear to understand the concepts, then the teacher will proceed to the elaboration portion of the lesson. If the teacher notices possible misconceptions, the teacher will provide clarification using guided instruction and discussions.

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ELABORATION Approximate Time: 35 MinutesStudents use new information to explore additional ideas and concepts; students revise explanations correctly apply vocabulary and develop connections between and across content. Teachers ask students to ELABORATE by using information in new ways. Overview In narrative format, provide an overview of the elaboration phase of the lesson.

The student will be separated into group of four to complete the following assignment: “Save the Town.”- Each group will be instructed to solve four problems using either exponential decay, exponential growth, or compounded interest formula. - One of the problems solved will be considered a crisis of the town. The students will have to find the solution and save the town. - The other three problems will be considered facts that the new governor needs to know.


The teacher will inform students of the instruction of the activity. Additionally, the teacher will give out the

necessary materials and handouts.

Q: How would you solve this problem?SR: Using decay formula, since the given rate says the

initial amount is decreasing.

Each student of the group will compute all of the problems.

The teacher will monitor the students and make sure they are completing the given assignment correctly. The

teachers will also assist the students if assistance is need.

Q: Since the solutions within your group solutions are different, where is the error?SR: The error is _______.

If a student answer is incorrect, then the group will assist their group member in finding the correct solution.

The teacher will provide little guidance to further students understanding.

Each group will present their solution for their town crisis to the class.


If students do not demonstrate proficiency, the teacher will provide clarification of concepts and provide assistance to ensure students are computing their solutions correctly.

If one-two groups are struggling with their problems, then the teachers will inform the students that they will have more time thursday to finish finding the town’s crisis.

If all of the groups understand have found their town’s crisis and solution, then the teacher will proceed.

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EVALUATION Approximate Time: 10 MinutesStudents answer questions that explain or show their thinking. They can describe the lessons big ideas, they successful create a product, and they successfully answer all essential questions. The teacher EVALUATES student understanding by providing insight into students’ progress throughout the lesson as well as at the end of a lesson. Overview In narrative format, provide an overview of the evaluation phase of the lesson.

A plickers-based assessment will be conducted to evaluate students’ understanding of Exponential Decay and Growth. (Reference: “Exit Ticket”)


The teacher will inform students of the exit ticket and pass out plicker response questions.

Q: In the exponential growth function y = a(1 + r)t, the quantity r is called the ________.SR:Rate of Growth (In decimal form)

The students will solve the problems using exponential decay, exponential growth, and compound interest

formulas.The teacher monitor student progression. Q:During normal breathing, about 12% of the air in

the lungs is replaced after one breath. Write an exponential decay model for the amount of the

original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the

original air is present after 240 breaths? SR:C=90,000 ¿

Students will record their answers using their plickers cards.

If time permits, the teacher will allow students with correct solutions to share their solutions.

Q:A house was purchased for $90,000 in 1995. If the value of the home increases 5% per year, what

is it worth in the year 2020? SR:P(t)=500¿mL

If time permits, students, with the correct solution, will explain their solution to a given problem to the class.

Closure Provide a overview of the lesson closure. As a closure of the lesson, the teacher will attempt to confirm the students’ understanding of the lesson by asking students to explain their understanding of exponential decay and growth.

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ResourcesInclude all professional and student resources and references needed for this teaching and learning cycle.

https://static.bigideasmath.com/protected/content/pe/hs/sections/alg2_pe_06_01.pdfhttps://www.jacksonsd.org/cms/lib/NJ01912744/Centricity/Domain/560/SE%206.4A.pdfhttp://www.softschools.com/math/algebra/topics/exponential_equations_exponential_growth_and_decay_application/

AssessmentsFormal and informal assessments throughout the learning cycle should be used to determine progress and to make adjustments in the learning cycle. Identify assessments used for prior knowledge and for individual and collective learning objectives. Attach all instruments and answer keys.

During the duration of the lesson, the following informal assessments will be used: bellringer, exit ticket, observations, plicker percentages, and the asking of essential questions. The lesson will not contain formal assessment.

AccommodationsIdentify any special accommodations or adjustments that may be needed for this lesson to meet the needs of individual students for this lesson. How can you ensure equitable lessons for all? Special accommodations may be needed for the lesson to meet the needs of one particular student. The student will need an increased time for completion. The accommodations for the student will be made by ensure the student has an adequate amount of time to complete the task.

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GeauxTeach Students: Kiara Ferrygood & Mary Margaret Stanford Date to be Taught: 3/26/2019

Time to be Taught:8:15-9:45

DATE Requested for Pick-up: 3/25/2019

Mentor Teacher: Mr. Harsh

Grade Level:11th

Lesson Topic: Exponential Decay and Growth

DATE to be returned: 3/28/2019

TIME Requested for Pick-up: 11:30 AM(pick up in 217B)

TIME to be returned: 11:30 AM(return to GeauxTeach Lair)

Material Request (only materials not available in the mentor’s classroom)

Items Requested # Requested # Returned

Colored Pencils 10 boxes

Giant Notepad (posters for presentations) 1

Entrance Ticket 35

Exit Ticket 35

Notes 35

Entrance Ticket (Answer Key) 2

Notes (for day 2) 35

Answer key for “Notes” day 2 2

Exit Ticket (for day 2) 25

Save the Town (groups 1-9) 4 per group

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Entrance Ticket (ANSWER KEY)

Name: __________________________________ Date: ____________________________

1. Approx. 197.2 million 2. After 5 years there will be $5387.42 in the account. 3. (a) exponential growth (b) f (x)=2x

3.

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Entrance Ticket

Name: __________________________________ Date: ____________________________

5. During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now? Round to the nearest hundredth place.

6. If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much money will be in the account after 5 years? Round to the nearest cent.

7. (a) Determine if the given graph is exponential growth or decay.

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(b) What is the exponential function for the given graph? ____________________





Exit Ticket

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Name: __________________________________ Date: ____________________________

5. In the exponential growth function y = a(1 + r)t, the quantity r is called the ________.

6. During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?

7. A house was purchased for $90,000 in 1995. If the value of the home increases 5% per year, what is it worth in the year 2020?

8. How much money would you need to deposit today at 9% annual interest compounded monthly to have $12000 in the account after 6 years?

Exit Ticket (Answer Key)Rate of Growth (In decimal form)

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P(t)=500 ¿mLC=90,000 ¿

You would need to deposit $7007.08 to have $12000 in 6 years.

Saving The Town

Group One

What is the name of the town?______________________________

Facts about the town:

Human Population:The population of the town, can be modeled byP=6191(1.04)t where t is the number of years since 1990.

A.) What was the population in 2019?

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B.) By what percent did the population increase by each year?

Animal Population: A population of 100 insects increases at an annual rate of 22%. How

many insects will there be in 5 years?

Number of Cell Phone Subscribers: In 2009, there were 285 cell phone subscribers in the town. The number of subscribers has increased by 75%

per year after 1985. How many subscribers were in the town in 2018?

Crisis: The town needs at least $20,000 in the account after 7 years to keep the library open, based on the situation below, is this possible? If not,

how many years until it is possible?

Funding for Stop Light: If governor deposits $6500 into an account for the town’s new stop light, paying 8% annual interest compounded monthly,

how much money will be in the account after 7 years?

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Saving The Town

Group Two



Human Population: A city has a population of 250,000. The population is expected to decrease by 1.5% annually for the next decade. Write a

function that represents this situation. Then predict the population in 10 years.

Funding for New Post Office: If the governor invest $3,000 in an investment account for a new post office, paying 3% interest compounded

quarterly, how much will be in the account in 10 years?

Value of a dollar: From 2011 to 2019, the value of the dollar has been shrinking. The value can be modeled by V=1.24(0.973)twhere t is the

number of years since 2014

a. Estimate the year in which the dollar was worth $1.07.

b. How much was a dollar worth in 2019?

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Crisis: A new virus is spreading around the town. In order to stop the virus, citizens are being given a drug, but must have at least 100 mg left in

their bloodstream after 4 hours to stop the virus. If a person takes A milligrams of a drug at time 0, then the equation y=A(0.8)tgives the

concentration left in the bloodstream after t hours. If the initial dose is 200 mg, what is the concentration of the drug in the bloodstream after 4 hours?

Can the doctors use this drug ?

Saving The Town

Group Three



Human Population: The population of the town is 160,525 in 2016 and was decreasing at a rate of about 1.5% per year. When will the city's

population be below 155,000? What is the exact year?

Funding for New Park: If the governor invest $6,000 in an investment account for park renovations, paying 16% interest compounded quarterly,

how much will be in the account in 10 years? Round to the nearest cent.

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Value of Sculpture: The value of a sculpture located in town has been growing at a rate of 5% per year for 4 years. If the sculpture is worth

$14,586.08 now, what was its value 4 years ago?

Zombie Attack: Strange behavior in the town last month has been linked to a new virus called Solanum. Government officials are advising citizens

to say at home to avoid getting infected since the virus is a zombie virus. There are currently 300 zombies in the town growing at a rate of 25%.

a. How many zombies will there be in 3 years?

a. Describe a possible way to stop the zombie apocalypse.

Saving The Town

Group Four


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Human Population: Suppose that the population of a town was 20,000 at the last census. If the population grows at an annual rate of 1.5%, by how

many people will the population increase in the next 6 years?

Salary of Mayor: The town’s mayor makes 90,000 a year and her salary goes up by 3% every year. How much does the mayor make after 3 years?

Insect Population: The town has a population of 8,000 insects. The town has been seeing a population decline by 10% every year. If this trend

continues, what will the population be in 7 years?

Crisis: Rats have recently become a nuisance in Sparrowtown. Efforts to control the rat problem have led to the rat population declining by 10%

every year. If the town currently has 16,000 rats, how many rats will there be in 4 years?

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Saving The Town

Group Five



Human Population: The population of your town in 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%. Estimate the

population in 2020 to the nearest hundred people.

Cell Phone Subscription: A town’s cell phone service has offered a deal that for every referral to their service, they will take an additional ten

percent off of their customers’ bills. If a customer refers 6 clients, and last month’s bill is $200, what will be the customer’s bill next month? (Round

to the nearest cent, if necessary)

Investments: The town invests their money in an interest earning account that promises to draw a 5% interest annually. If the town makes a deposit

of $30,000, how much will the town have after 10 years?

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Crisis: Due to pollution, the town’s health and environmental control agency has noted an 8% monthly decline in the fish population of a nearby

lake. If the current fish population is about 5,500 fish, how many fish will there be in 20 years? Can you think of a possible solution to reduce the

pollution in the town’s lake?

Saving The Town

Group Six



Restoration Fund: The town’s restoration fund has $50,000 and earns .75% per month. If the mayor makes a deposit into this account of $10,000

every year for ten years, how much money will be in the account?

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Donated Land: The town was donated land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year.

What is the approximate value of the land in the year 2011.

Town Computers: The town buys 50 computers for the public library. Each computer costs $2100 and the value of each computer decreases by 15%

annually. What will be the value of each computer after 10 years?

Crisis: The foundation of the town hall building has about 1,200 termites. The termites grow at a rate of 2.4% per day. How many termites will the

town have after a week? If the town house must be close if more than 1,300 termites are in the building, will it be shut down?

A. If the exterminator charges $50 per 100 termites, how much will it cost to resolve the crisis?

Saving The Town

Group Seven



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Human Population: The population of the town is 6,191 and has increased at a rate of 4% annually since 1990. What is the size of the population in

2015?

Beetle Population: Your town has a population of 800 beetles and grows at a rate of 5% each month. How many beetles will there be after a year?

Cell Phone Subscribers: In 1975 your town had 400 cell phone subscribers. The number of subscribers increased by 20% each year since then. Find

the number of cell phone subscribers in 2019.

Crisis: There is a type of weed (insert your own name here) which is destroying the other plants in the town. The pesticides decay the plant an acre at

a time, at a rate of 5% per year. If the plant covers 980 acres, how many acres will it cover after two years? How many after 5?

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Saving The Town

Group Eight



Tree Population: The population of the redwood trees in your town is 50,000. The population increases at a rate of 5% each year. What will the tree

population be in 20 years?

Fish Growth: The town’s fish pond has fish that grow about 15% each month. In January the town measures one of the fish in January and measure

it to be 20 centimeters long. What is the estimated length of that same fish in December?

New Books: The town deposited $1,000 into a savings account that earns 3% interest each month for the new books for the children's library. What

is the estimated balance after one year?

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Crisis: Your town has a problem with overpopulation. The population is 5,000 and the population grows at a rate of 5% each year, but there are only

9,899 houses (one house per citizen). When will they run out of houses for the population? If the population was 3,000 with the same growing rate,

how many years will it take before there was a shortage of houses?

Saving The Town

Group Nine



Squirrel Population: The town’s population of 20 squirrels increases by 9% each year. What is the estimated population after 20 years?

Human Population: Your town has a population of 20,000 and decreases by 2% every other year. What is the population after 20 years?

Charity Run: The first year of your town’s charity walk had an attendance of 500. If the attendance increased by 5% each year, what was the

attendance after 5 years?

Crisis: A flood has filled the streets of the town. The sewage drains the water at a rate of 5% every five minutes. If the water covers 10,000 feet of

street, how many feet of street will the water cover after an hour?

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Saving The Town (Answer Key)

Group One

Human Population:The population of the town, can be modeled by P=6191(1.04)t where t is the number of years since 1990. A.) What was the population in 2019? B.) By what percent did the population increase by each year? A. 19,307 B. 4%

Animal Population: A population of 100 frogs increases at an annual rate of 22%. How

many frogs will there be in 5 years? 270 frogsNumber of Cell Phone Subscribers: In 2009, there were 285 cell phone subscribers in the town. The number of subscribers has increased by 75%

per year after 1985. How many subscribers were in the town in 2018? 43872 subscribers

Crisis:The town needs at least 12,000 in the account after 7 years to keep the library open, based on the solution is this possible? If not, create about a possible solution.

Budget: If governor deposits $6500 into an account for the town’s new stop light, paying 8% annual interest compounded monthly, how much money will be in the account after 7 years?

After 7 years there will be $11,358.24 in the account. No, it won’t be possible.

Group Two

Human Population: A city has a population of 250,000. The population is expected to decrease by 1.5% annually for the next decade. Write a

function that represents this situation. Then predict the population in 10 years. 214932 people

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Funding for New Post Office: If the governor invest $3,000 in an investment account for a new post office, paying 3% interest compounded

quarterly, how much will be in the account in 10 years?

Value of a dollar: From 2011 to 2019, the value of the dollar has been shrinking. The value can be modeled by V=1.24(0.973)twhere t is the

number of years since 2014. a. Estimate the year in which the dollar was worth $1.07 → 2016 (5 years) b. How much was a dollar

worth in 2019. 1.14

Crisis: A new virus called ____is spreading around the town. In order to stop the virus citizens are being given a drug, but must have at least 100 mg

left in their bloodstream after 4 hours to stop the virus. If a person takes A milligrams of a drug at time 0 , then y=A(0.8)tgives the concentration left

in the bloodstream after t hours. If the initial dose is 200 mg, what is the concentration of the drug in the bloodstream after 4 hours? Can the doctors

use this drug ? 81.92→ 82 mg; No

Group Three

Human Population: The population of the town was 160,525 in 1990 and was decreasing at a rate of about 1.5% per year. When was the city's

population be below 155,000? 1993→ 153,409

Value of Sculpture: The value of a sculpture located in town has been growing at a rate of 5% per year for 4 years. If the sculpture is worth

$14,586.08 now, what was its value 4 years ago? A=1200

Funding for New Park: If the governor invest $6,000 in an investment account for park renovations, paying 16% interest compounded quarterly,

how much will be in the account in 10 years? Round to the nearest cent. 11237.89

Zombie Attack: Strange behavior in the town last month has been linked to a new virus, called Solanum. Government officials are advising citizens

to say at home to avoid getting infected since the virus is a zombie virus. There are currently 300 zombies in the town growing at a rate of 25%. A.

How many zombies will there be in 3 years? B. Describe a possible way to stop the zombie apocalypse. A. 585 zombies29

Group Four

Human Population: Suppose that the population of a town was 20,000 at the last census. If the population grows at an annual rate of 1.5%, by how

many people will the population increase in the next 6 years? A=21868 → 1868 increase

Salary of Mayor: The town’s mayor makes 90,000 a year and her salary goes up by 3% every year. How much does the mayor make after 3 years?

98,345.43

Crisis: Rats have recently become a nuisance in Sparrowtown. Efforts to control the rat problem have led to the rat population declining by 10% every year. If the town currently has 16,000 rats, how many rats will there be in 4 years? 10497.6 → 10498 Rats

Insect Population: The town has a population of 8,000 insects. The town has been seeing a population decline by 10% every year. If this trend

continues, what will the population be in 7 years. 3826 insects

Crisis: Rats have recently become a nuisance in Sparrowtown. Efforts to control the rat problem have led to the rat population declining by 10%

every year. If the town currently has 16,000 rats, how many rats will there be in 4 years? 10497 left

The governor predicts there will be less than 800 after 4 years, is he correct? No

Group Five

Human Population: The population of your town in 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%. Estimate the

population in 2020 to the nearest hundred people. 38,500

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Cell Phone Subscription: A town’s cell phone service has offered a deal that for every referral to their service, they will take an additional ten

percent off of their customers’ bills. If a customer refers 6 clients, and last month’s bill is $200, what will be the customer’s bill next month? (Round

to the nearest cent, if necessary) 3,200,000 people

Investments: The town invests their money in an interest earning account that promises to draw a 5% interest annually. If the town makes a deposit

of $30,000, how much will the town have after 10 years? $106.29

Crisis: Due to pollution, the town’s health and environmental control agency has noted an 8% monthly decline in the fish population of a nearby

lake. If the current fish population is about 5,500 fish, how many fish will there be in 20 years? Can you think of a possible solution to reduce the

pollution in the town’s lake? 1037 fish

Group Six

Restoration Fund: The town’s restoration fund has $50,000 and earns .75% per month. If the mayor makes a deposit into this account of $10,000

every year for ten years, how much money will be in the account? $53,879.13

Donated Land: The town was donated land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year.

What is the approximate value of the land in the year 2011. $361,223.09

Town Computers: The town buys 50 computers for the public library. Each computer costs $2100 and the value of each computer decreases by 15%

annually. What will be the value of each computer after 10 years? $413.44

Crisis: The foundation of the town hall building has about 1,200 termites. The termites grow at a rate of 2.4% per day. How many termites will the

town have after a week? If the town house must be close if more than 1,300 termites are in the building, will it be shut down? If the exterminator

charges $5 per 100 termites, how much will it cost to resolve the crisis?

1416; yes; $70,800

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Group Seven

Human Population: The population of the town is 6,191 and has increased at a rate of 4% annually since 1990. What is the size of the population in

2015? 16,504

Beetle Population: Your town has a population of 800 beetles and grows at a rate of 5% each month. How many beetles will there be after a year?

1,436

Cell Phone Subscribers: In 1975 your town had 400 cell phone subscribers. The number of subscribers increased by 20% each year since then. Find

the number of cell phone subscribers in 2019. 1,219,087

Crisis: There is a type of weed (insert your own name here) which is destroying the other plants in the town. The pesticides decay the plant an acre at

a time, at a rate of 5% per year. If the plant covers 980 acres, how many acres will it cover after two years? How many after 5? 884.45; 758.31

Group Eight

Tree Population: The population of the redwood trees in your town is 50,000. The population increases at a rate of 5% each year. What will the tree

population be in 20 years? 132,664

Fish Growth: The town’s fish pond has fish that grow about 15% each month. In January the town measures one of the fish in January and measure

it to be 20 centimeters long. What is the estimated length of that same fish in December? 107 cm

Bank Account: The town deposited $1,000 into a savings account that earns 3% interest each month. What is the estimated balance after one year?

$1425.76

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Crisis: Your town has a problem with overpopulation. The population is 5,000 and the population grows at a rate of 5% each year, but there are only

9,899 houses (one house per citizen). When will they run out of houses for the population? If the population was 3,000 with the same growing rate,

how many years will it take before there was a shortage of houses? 14 years (students can use trial and error to solve); 25 years

Group Nine

Squirrel Population: The town’s population of 20 squirrels increases by 9% each year. What is the estimated population after 20 years? 112

Human Population: Your town has a population of 20,000 and decreases by 2% every other year. What is the population after 20 years? 16,341

Charity Run: The first year of your town’s charity walk had an attendance of 500. If the attendance increased by 5% each year, what was the

attendance after 5 years? 638

Crisis: A flood has filled the streets of the town. The sewage drains the water at a rate of 5% every five minutes. If the water covers 10,000 feet of

street, how many feet of street will the water cover after an hour? 5,403 feet

Making Predictions

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Name: __________________________________ Date: ____________________________

Work with a partner. It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. By the 1960s, this number had dropped to about 500 nesting pairs. In 1967, the bald eagle was declared an endangered species in the United States. With protection, the nesting pair population began to increase. Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species.

Describe the pattern shown in the graph. Is it exponential growth? Assume the pattern continues. When will the population return to that of the late 1700s? Explain your reasoning.

Making PredictionsName: __________________________________ Date: ____________________________

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Work with a partner. A forensic pathologist was called to estimate the time of death of a person. At midnight, the body temperature was 80.5°F and the room temperature was a constant 60°F. One hour later, the body temperature was 78.5°F.

a. By what percent did the difference between the body temperature and the room temperature drop during the hour?

b. Assume that the original body temperature was 98.6°F. Use the percent decrease found in part (a) to make a table showing the decreases in body temperature. Use the table to estimate the time of death.

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Making Predictions (Answer Key)

NotesExponential Growth Functions

Occurs when a quantity __________________by the same factor over intervals of time.

A function of the form _________________________, where a>0 and

r>0, is an exponential growth function.

Exponential Decay Functions

Occurs when a quantity __________________by the same factor over intervals of time.

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A function of the form _________________________, where a>0 and 0<r<1, is an exponential decay function.

Compound InterestCompounded interest is the interest earned on the principal and on previously earned interest. The balance y of an account earning compound interest

is

P=r=t=n=

What happens if n=1?

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Notes (Answer Key)Exponential Growth Functions

Occurs when a quantity increases by the same factor over equal intervals of time.

Exponential Decay FunctionsOccurs when a quantity decreases by the same factor over equal intervals of time.

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Compound InterestCompounded interest is the interest earned on the principal and on previously earned interest. The balance y of an account earning compound interest

is

What happens if n=1?

For interest compounded yearly, you can substitute 1 for n in the formula to get y=P ¿.

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Day 2Exponential Growth and Decay (Continued)

Use an appropriate title to connect concept topics with real-world applications

Standards Louisiana State Standards for Science and Math;

Science must include appropriate PE, SEP, DCI, and CCC. Math must include appropriate Math Standards and Practices

Key Concepts Concepts include both tangible objects and abstract ideas. Identify the key concepts, knowledge, and skills that describe what the students will need to understand. Use the

concept map you created for reference. A2:F-LE.A.2: Given a graph, a description of a relationship, or two input-output pairs (including reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences, to solve multi-step problems. A2:F-LE.B.5: Interpret the parameters in a linear, quadratic, or exponential.

- Graphing Exponential Functions- Modeling Exponential Functions- Interpreting Exponential Graphs and Functions

Big IdeaBig ideas are important, enduring, and transferable beyond the scope of core concepts,

principles, theories and process.

Essential QuestionsEssential questions are thought provoking questions used to engage students’ interest

and to facilitate inquiry throughout the learning cycle of the instructional plan. Essential questions stimulate discussion and thinking over time.

How can we model an exponential function to determine its characteristics?How are exponential functions utilized in statistics?

Prior Knowledge Identify common preconceptions and prior student knowledge.

Key VocabularyList all new key vocabulary for the lesson. Use the concept map you created for

reference.- domain and range- exponential growth and decay- graphing functions

- asymptote - exponential function- exponential growth function- growth factor- exponential decay function- decay factor

Learning ObjectivesInstructional learning objectives state the specific learning outcome in an observable

and measurable format.

Assessment(s)Include both formal and informal assessments used throughout the lesson.

SWBAT: Write an exponential function from looking at a graph SWBAT: Create an exponential model from a given scenario

Informal Assessments- Providing answers to practice problems- Presentation- answering probing questions

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Formal Assessments- P.O.D.

Q: The population of Gilbert Corners at the beginning of 2001 was 12,546. If the population grew 15% each year, what was the population at the beginning of 2015?

SR: 88,772Q: The half-life of a radioactive kind of radon is 4 days. If you start with 96 grams of

it, how much will be left after 12 days?SR:12 grams

- Exit Ticket

Advanced Preparations/SafetyAdvanced preparations include all tasks and activities that may be used to preparing the learning experience. Also include any safety concerns expected throughout the lesson.

The teachers will need to print out the worksheets and make sure all of the materials are coherent before the lesson begins. The teachers will also need to make sure the students understand the previous lesson before beginning today’s lesson.

5E Instructional Learning CycleLouisiana State University

GeauxTeach 5E Lesson Plan EDCI 3550 - Classroom Interactions

Teacher Candidate Team Members: Kiara Ferrygood and Mary Margaret Sanford

Mentor Teacher: Richard Harsch Course: Algebra II

Date Lesson to be Taught: 3/28/2019 School: Baton Rouge High Classroom: 1124

Time Lesson to be Taught: 8:15-9:45 Grade Level: 10/11 Lesson Topic: Graphing Exponential Functions

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ENGAGEMENT Approximate Time: 15 MinutesPique students’ interest and introduce them to the big ideas and essential questions. During the ENGAGEMENT students make connections between past and present learning experiences begin to ponder upcoming learning experiences. Students are recalling prior knowledge pertaining to key concepts and/or developing their own questions about a phenomenon. Overview In narrative format, provide an overview of the engagement phase of the lesson.

The teachers will write a P.O.D. (Problem of the Day) in Mr. Harsch’s typical spot for the students to solve when they walk into the classroom. This P.O.D. consists of two word problems which are a review of the previous lesson the teachers taught.


The teacher will have the P.O.D. written on the board in the usual spot Mr. Harsch has for the students to solve

when they walk in.

Q: The population of Gilbert Corners at the beginning of 2001 was 12,546. If the population grew 15% each year,

what was the population at the beginning of 2015? SR: 88,772

Q: The half-life of a radioactive kind of radon is 4 days. If you start with 96 grams of it, how much will be left

after 12 days?SR:12 grams

The students will solve the P.O.D. and write the formulas for exponential growth and decay on the board

as an informal assessment of understanding.

The teacher will facilitate a discussion with the students on the solution to the P.O.D.

The teacher will be able to assess the students’ understanding of the lesson from the previous class

period.

Q: What is the formula for exponential growth?SR: a¿

Q: What is the formula for exponential decay?SR:a¿

The students will provide their solutions of the P.O.D.

TRANSITION (Engagement to Exploration)What question(s)/task are you asking of students that demonstrates proficiency? Successfully answering this question or completing this task shows that the teacher can move on to the next part of the lesson. If students do not demonstrate proficiency, how will you remediate? Provide both student outcomes. Evaluation/Decision Point Assessment Student Outcomes

If the students do not remember how to solve the exponential growth and decay problems, the teachers will provide a supplementary question

to walk the students through.

After this supplementary question is solved, the students should remember how to solve exponential growth and decay problems.

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EXPLORATION Approximate Time: 10 MinutesInvolve students in EXPLORATION of the lesson topic and concepts. Activities using hands-on activities should be used to help students use prior knowledge, identify and advance their current understandings of the concepts, dispel misconceptions, generate new ideas, explore questions and possibilities, and design and conduct a preliminary investigation.Overview In narrative format, provide an overview of the exploration phase of the lesson.

Students will work with a partner to identify graphs of exponential functions using the worksheet titled “Graph Identification.” The class will reconvene after 5 minutes for the students to provide their thoughts on the solutions. (Reference: “Graph Interpretation”)


The teacher will pass out the worksheets to the students and facilitate the lesson while the students attempt to

solve the problems

Q: For 1, what do the values you plugged in represent?SR: The “x” and “y” values of the graphQ: Which graph matches those values?

SR: Graph AQ: When you multiply an exponent to a fraction, what is

that exponent applied to?SR: The numerator and denominator

The students will work with a partner to match the graphs with their functions.

Teachers will walk around the classroom, assisting groups which need help.

Students will attempt to answer all questions on their own, but may ask for assistance if necessary.

The teachers will call on students to answer questions 1-6 and explain answers if needed

Q: What is the graph for question 1? SR: A

(Repeat for questions 2-6)*If students are confused about a certain answer*

Q: (Insert student name) can you explain your reasoning on how you got that graph?

SR: (answers may vary)

Students will answer the questions for the class to hear and explain their reasoning behind each answer

TRANSITION What question(s)/task are you asking of students that demonstrates proficiency? Successfully answering this question or completing this task shows that the teacher can move on to the next part of the lesson. If students do not demonstrate proficiency, how will you remediate? Provide both student outcomesEvaluation/Decision Point Assessment Student Outcomes

The teachers will call on students to present their answers to the class and explain their reasoning. The teachers will correct any mistakes if the students cannot critique their peers’ answers.

The students should understand how each solution was solved. If majority of the class does not understand how a problem is solved, the teachers will explain to the entire class.

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EXPLANATION Approximate Time: 20 MinutesStudents communicate with others to make rich connections and to provide an EXPLANATION for what they have experienced and learned during the Exploration phase of the lesson. As students’ communicate, they demonstrate their conceptual understanding, process skills or behaviors. Vocabulary is presented in correct context to redirect misconceptions.Overview In narrative format, provide an overview of the explanation phase of the lesson.

The students are provided with a partially filled in notes page to take notes in (Reference: “Notes”). The teachers will have the students fill in the notes based on the discovery and by asking probing questions. The teacher will then provide examples for the students to solve at the board as extra practice.


The teacher will guide the students at the board to fill in the blanks on the notes page

Refer to “Notes” handout for questions that will be asked The students will respond to the teacher with possible answers for the blanks

After the notes are finished being filled out, the teacher will draw a graph on the board an have the students

identify the key features of the graph

Q: Which type of function does this graph represent?SR: Exponential growth/decay

Q: What is the growth/decay factor?SR: student responses will vary

Q: what is the exponential function of this graph?SR: student responses will vary

the students will look at the graph(s) provided and identify the features of the graph based on the questions provided

by the teachers.

The teachers will provide examples for the students to solve at the board, as extra practice.

Q: Graph y=2x+4SR: *exponential growth graph with points (0,5), (1,6),

(2,8) and an asymptote at y=4*Q: Graph y=5−x

SR: *exponential decay graph with points (-2,25), (-1,5), (0,1) and an asymptote at y=0*

Q: Graph y=2(x+ 3)

SR: *exponential growth graph with points (-3,1), (-2,2), (-1,4), (0,8) and an asymptote at y=0*

The students will attempt to answer all three questions by themselves and then three students will come to the board

and put solutions on the board.


The teachers will ask probing questions for the students to answer. The teachers will assess the students’ initial understanding based off of responses.

The students should get some answers correct. If there are answers which confuse students, the teachers will provide clarification.

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ELABORATION Approximate Time: 35 MinutesStudents use new information to explore additional ideas and concepts; students revise explanations correctly apply vocabulary and develop connections between and across content. Teachers ask students to ELABORATE by using information in new ways. Overview In narrative format, provide an overview of the elaboration phase of the lesson.

The teachers will hand back the posters from the previous class period and have the students graph their problem. The groups will then present their posters and data to the class. The teachers will allow 10 minutes for groups to graph their functions and 25 minutes for presentations


The teacher will put the students back in their groups and allow them to reconvene for a few minutes on their data

from the previous class period. and then have the students graph their data from their problem.

After the students are finished graphing their posters, the teachers will have the groups present their findings

Q: How do you put your exponential growth problem into the form of an exponential function SR: The “1 + r” is the “b” part and t = x

Q: What is the next step?SR: plug in values to graph the function

The students will look at their work from the previous class period and make any quick adjustments if necessary. The

students will analyze their data and exponential function to graph their given problem and solution.

Each group will present their findings, explaining the facts about their town as well as the crisis presented to them.


Once the students are finished with their presentations, the teachers will ask if there are any questions from the presentations, and will explain further if necessary.

The students should have a broader understanding of how to solve and graph exponential equations.

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EVALUATION Approximate Time: 10 MinutesStudents answer questions that explain or show their thinking. They can describe the lessons big ideas, they successful create a product, and they successfully answer all essential questions. The teacher EVALUATES student understanding by providing insight into students’ progress throughout the lesson as well as at the end of a lesson. Overview In narrative format, provide an overview of the evaluation phase of the lesson.

Students will complete an Exit Ticket, which is identical to the Entrance Ticket given the previous class period. The students should be able to solve these problems a lot faster than the Entrance Ticket, as they have now been taught the lesson.


The teacher will pass out the Exit Ticket to the students Refer to worksheet titled “Exit Ticket” for eliciting questions and responses.

The students will solve the Exit Ticket

Closure Provide a overview of the lesson closure. At this point, the students should have an understanding of how to solve and graph exponential functions.

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ResourcesInclude all professional and student resources and references needed for this teaching and learning cycle.

https://static.bigideasmath.com/protected/content/pe/hs/sections/alg2_pe_06_01.pdf https://www.jacksonsd.org/cms/lib/NJ01912744/Centricity/Domain/560/SE%206.4A.pdf http://www.softschools.com/math/algebra/topics/exponential_equations_exponential_growth_and_decay_application/

AssessmentsFormal and informal assessments throughout the learning cycle should be used to determine progress and to make adjustments in the learning cycle. Identify assessments used for prior knowledge and for individual and collective learning objectives. Attach all instruments and answer keys. Informal Assessments

- Providing answers to practice problems- Presentation- Answering probing questions - Presentations

Formal Assessments- P.O.D.- Exit Ticket

AccommodationsIdentify any special accommodations or adjustments that may be needed for this lesson to meet the needs of individual students for this lesson. How can you ensure equitable lessons for all?

Eric Threadgill

- home/school communications

- use notebook for homework/assignments

- allows student to take pictures of posted assignments

- prior notice of tests

- increased time for completion

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http://www.softschools.com/math/algebra/topics/exponential_equations_exponential_growth_and_decay_application/

https://www.jacksonsd.org/cms/lib/NJ01912744/Centricity/Domain/560/SE%206.4A.pdf

https://static.bigideasmath.com/protected/content/pe/hs/sections/alg2_pe_06_01.pdf

GeauxTeach Students:

Date to be Taught:

Time to be Taught:

DATE Requested for Pick-up:

Mentor Teacher:

Grade Level:

Lesson Topic:

DATE to be returned:

TIME Requested for Pick-up: (pick up in 217B)

TIME to be returned: (return to GeauxTeach Lair)

Material Request (only materials not available in the mentor’s classroom)

Items Requested # Requested # Returned

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Graph Identification

Name: __________________________________ Date: ____________________________

Directions: Work with a partner to match each exponential function with its graph. You may use a table of values to sketch the graph of the function, if necessary.

1. f (x)=2x❑ Graph: _____________

2. f (x)=3x Graph: _____________

3. f (x)=4x Graph: _____________

4. f (x)=¿ Graph: _____________

5. f (x)=¿ Graph: _____________

6. f (x)=¿ Graph: _____________

Graph Identification (ANSWER KEY)

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Name: __________________________________ Date: ____________________________

Directions: Work with a partner to match each exponential function with its graph. You may use a table of values to sketch the graph of the function, if necessary.

1. f (x)=2x❑ Graph: A

2. f (x)=3x Graph: F

3. f (x)=4x Graph: C

4. f (x)=¿ Graph: D

5. f (x)=¿ Graph: B

6. f (x)=¿ Graph: E

Notes

An exponential function has the form _____________ where a ≠ 0and the base _______ is a positive real number other than 1

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If a>0and b>1,then y=a bxis an _____________________________ function and b is called the _________________________

Describe the graph’s movement in the space below:

The domain and range of the function is: ____________________________________

If a>0and 0<b<1 ,then y=abxis an ________________________________function and b is called the________________

Describe the graph’s movement below:

The domain and range of the function is: _______________________________

In both graphs, x-axis is an ______________________of the graph. This means the x-axis is: ____________________________________________

_______________________________________________________________________________________________________________________

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Notes (ANSWER KEY)

1An exponential function has the form y=a bx ,where a ≠ 0and the base b is a positive real number other than 1

1 Notice that (1+r) has been replaced by b and t has been replaced by x.53

If a>0and b>1,then y=a bxis an exponential growth function and b is called the growth factor.


Possible answers:

1. The graph rises from left to right 2. The graph passes through the points (0,1) and (1,b)

The domain and range of the function is: domain: all real numbers; range: y > 0

If a>0and 0<b<1 ,then y=abxis an exponential decay function and b is called the decay factor.


Possible answers:

1. The graph falls from left to right

2. The graph passes through the points (0,1) and (1,b)

The domain and range of the function is: domain: all real numbers; range: y > 0

In both graphs, x-axis is an asymptote of the graph. This means the x-axis is a line that a graph approaches more and more closely, but never touches.

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Exit Ticket

Name: __________________________________ Date: ____________________________

1. During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now? (Round your answers

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to the nearest hundredth.)

2. If you deposit $4000 into an account paying 6% annual interest compounded quarterly, how much money will be in the account after 5 years?

3. (a) Determine if the given graph is exponential growth or decay.

(b) What is the exponential function for the given graph? ____________________



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