SHALINI KAPOOR

Adjunct Certification Program

LS-Cy-fair

Table of Contents:

Snapshot

Student Preparation Strategy

Lesson Objectives

Participatory Learning

CAT

Rubric

Formal Assessment Questions

Technology

Exponential Power point

Jeopardy

Post Assessment

BOPPPS Lesson Plan

ACP Showcase Portfolio

Reflective Essay

Course Syllabus

Instructor contact information

Name : Shalini Kapoor

Email : [email protected]

Welcome:

Lone Star College wants every student to get their BEST START and continue on the path to success. In addition,

LSCS continues to garner worldwide accolades as high-performing and innovative college system. It will be a

privilege for me to work with you in a prestigious institute where you will have opportunity to see

firsthand what commitment, hard work, resources, and talent can accomplish.

I am your professor for this course and I’m excited about helping you to reach your goals. I have Bachelor of

Mathematical Science (Physics, Chemistry and Mathematics), Master of Science in Mathematics, and Bachelor of

Education. In addition to be a part of Lone Star, I’ve been in high school teaching for thirteen years.

About this class: Term and Year:

Class Days & Times:

Course Title: Class Room Location:

Course Subject: Office hours:

Course Number:

Credit Hours:

Course overview

Catalog Description:

In-depth study and Applications of Polynomial, rational, radical, absolute-value, piecewise defined, exponential

and logarithmic functions, equations, inequalities, graphing skills and systems of equations using matrices.

Additional topics such as sequences, series, probability, conics and Inverses may be included.

Student Learning Outcomes:

The Student will:

• Demonstrate And Apply Knowledge Of Properties Of Functions, Including Domain And Range, Operations,

Compositions, Inverses And Piecewise Defined Functions.

• Recognize, Graph And Apply Polynomial, Rational, Radical, Exponential, Logarithmic And Absolute Value

Functions And Solve Related Equations.

• Apply Graphing Techniques.

• Evaluate All Roots Of Higher Degree Polynomial And Rational Functions.

• Recognize, Solve And Apply Systems Of Linear Equations Using Matrices.

• Solve Absolute Value, Polynomial And Rational Inequalities.

In our efforts to prepare students for a changing world, students may be expected to utilize computer

technology while enrolled in classes, certificate, and/or degree programs within LSCS.

The specific requirements are listed below:

Completion of Math Lab homework Assignments

Online Quizzes

Use of calculators in problem solving

Use of google apps to show a deep understanding of the content.

Getting ready

Textbook Title: Lial, Hornsby, Schneider, Daniels; Essentials Of College Algebra, 11th Ed.; Pearson

Required MyMathLab Access: Students Must Buy An Access Code To MyMathLab, An Online Course Management

System Which Includes A Complete EBook; Students Will First Need A Course ID Provided By The Instructor In Order To

Register; Online Purchase Of MyMathLab Access At Www.Mymathlab.Com; Hard Copies Of Access Codes Available With

ISBN: 9780321199911

Hardbound Text (Optional), ISBN: 032191225X

Hardbound Text + Free MyMathLab Access, ISBN: 0321912152

Calculator: Graphing Calculator Required. TI 83, TI 84 Or TI 86 Series Calculators Recommended.

Calculators Capable Of Symbolic Manipulation Will Not Be Allowed On Tests. Examples Include, But Are Not Limited To, TI

89, TI 92, And Nspire CAS Models And HP 48 Models.

Neither Cell Phones Nor PDA’s Can Be Used As Calculators. Calculators May Be Cleared Before Tests.

Formulas: There is a collection of facts, formulas and identities from this course that students should be expected to

memorize because having them at ready recollection is essential for their success in future classes. Students must not be

allowed to bring these to the test on a formula sheet nor instructor will provide these formulas to them during the test.

Instructor guidelines and policies

Attendance: Be present and on time. I do not distinguish between excused and unexcused absences. If you are

not here, you are missing instruction. Attendance is mandatory and more than (2) misses or partial misses without

a valid explanation might result in drop. Partial misses include tardies and/or leaving early. If you miss a class it is

your responsibility to contact me or another student for assignment before the next class. Work assigned during

your absence that is due next class meeting is due for you as well.

Assignments: The daily grade will include quizzes and online assignments from “My Math Lab”. Some quizzes

may be based on class participation. Assignments submitted late may not be accepted or may be penalized.

Students unable to turn in an assignment on time should discuss the situation with the instructor. Homework

problems from the book will be assigned, but generally will not be turned in for a grade.

Make-up Exams: Make-ups are generally not allowed for quizzes or daily assignments turned in during class. It is

your responsibility to contact the instructor if an extension is needed. No student is guaranteed a make-up for a

missed exam. If you miss an exam due to an extreme emergency, and you wish to be considered for a make- up

exam, you must contact your instructor as soon as possible, definitely before next class meeting.

Classroom conduct and Electronic devices: Our classroom will have an environment conducive to learning.

Examples of disruptive behavior include, but are not limited to, talking while the instructor is teaching, discussing

non-mathematical issues during class, coming to class late, using profane language, sleeping, using food, and/or

tobacco products, etc. Please turn your cell phone to silent/ vibrate before class starts, however you can

use your cellphones during the break.

GRADE DETERMINATION:

There will be three chapter test, Quiz, and a cumulative final exam. Partial credit will be given. The more work you

show, the more credit possible. The final exam is comprehensive and mandatory. It will be held at the date and

time listed on the Lone Star College final exam schedule. Please note that there is no provision of any kind in

this course for "extra credit".

Exams and daily grades will be weighted as follows:

Your grade will be determined by the Percent of Final

following Rule Average

Three chapter test (15% each) 45%

Online assignments 20%

Class room Quiz 15%

Final Exam 20%

Total 100%

LETTER GRADE ASSIGNMENT: Final Average in Percent

90-100

Letter Grade 80-89

A Excellent Performance 70-79

B Good Performance 60-69

C Acceptable Performance 59 or lower

D Probably Will Not Transfer to Other Colleges

F Failing

I post material (power point/ work sheets, reviews etc.) on D2L under

content/ modules and sub modules. Students will watch attached power

point prior to the class and will note down new vocabulary and its meaning

in their in their own words. In addition, I will use “My Math Lab”, an online

program for home-work and pre-assessment assignments. Generally the

pre-assessments are due before students come for their next class. They

can either email me or bring a question to the class the one they had

problem in. In their warm up students will be asked to write the steps in

finding inverse of a function and they will complete three to four inverse

function questions in the beginning of the class for first 10-15 minutes.

Before we discuss the final answer, students will be encouraged to share

their answers with other students sitting in the same row of the class. I

usually ask for their collective answer per row so that we can share their

reasoning and logic behind their answers. Students will be asked to share

their questions from pre-assessment right before the actual lesson.

1. Post related material (power point, Worksheet, Vocabulary bank) on D2l.

2. Post Google form link

3. Add Videos, You tube links

4. My Math Lab Question

5. Bring your own question

Pre-Assessment Form

Lesson Objectives

By the end of this lesson, students will be able to analyze the behavior of inverse functions and will

Demonstrate what they learned by interchanging domain and range of exponential function in order to

graph logarithmic functions and will determine the domain and range of the Inverse (log function).

By the end of this lesson, students will be able to evaluate, graph exponential functions and will demonstrate

what they learned by applying them in real world (Compound interest, future value, population growth/decay.

The above objectives reflect the upper three levels of Bloom’s pyramid as students will analyze,

compare/contrast and will synthesize it into the given contexts. Of course some level of the

activities/lecture will be a level of knowledge and comprehension too.

Second P

Shalini Kapoor

COURSE: 1314

Lesson Title: Exponential functions

Course Student Learning Outcome: In depth study of exponential function including tables, equations, graphs and use of technology to analyze how this

remarkable function enable us to predict the future and rediscover the past.

Learning Objectives (these should be the ones you wrote in Module 1): By the end of this lesson, students will be able to evaluate, graph exponential

functions and will demonstrate what they learned by applying them in real world (Compound interest, future value, population growth/decay etc.)

Time Instructor Activities Learner Activities Lesson Materials

10 min Hand out card to each student to form the groups. Group work (3-4 students in group) Cubes, dice, colored cards to

Walk around and observe student work. Post answers Students will roll the dice to obtain three numbers and on form the groups.

10 min. at the end, the bases of those numbers they will attempt the question

15 min from the cube. Power point presentation

20 min Demonstration of how to solve exponential equations Students taking notes, asking Questions e-book (white-board view),

Guided practice, check for understanding, ask Work on problems, compare/share solutions with the Online calculator/Desmos

25 min questions. partners, ask Questions. Group Question, Markers,

5 min Group Activity - Use Algebraic/Graphing method in problem Graphing

5 min Monitor group work, facilitate, ask question, praise solving and use technology to check the validity of the Calculators/Desmos, Graph

creativity, motivate, point out any error. solution. At the end, post your summary /formula/ paper roll, Poster, PPT slides

graph/solution on poster board Poster board, Markers

Listen/record students response, ask questions Present their problem/ask-respond questions Questions prepared and

Closure- Use Socrative/Poll everywhere Respond to poll questions sent on socrative /poll

Document uploaded on

Share resources verbally/posted on D2L Check/note resources on D2L class D2L content

Attachments:

1. Cube activity Questions (Net for Cube)

2. Picture of Cubes (to have an idea of final product)

3. Cards (ways to group students)

4. Power point presentation

5. Real World problems/case study for groups

Resource:

1. My Math lab (e-book), Text Book-College Algebra-Lial)

2. Cube Activity (CAMT Math Conference)

3. DESMOS Google App.

4. http://www.moneychimp.com/features/rule72_why.htm

Reflection: The rationale behind the activities selected:

Cube activity basically contains warm up questions (something different I want to try). Instead of posting them on board, this activity will hook

students. Working in a group and attempting only three questions in place of six questions will leave no scope of sitting idle.

Teacher demonstration –guided practice –group work/presentation will lead to smooth transition of bloom’s levels.

Group activity is designed to motivate students by adding real word problems and to promote multiple ways to solve the problems (Algebraically,

Graphically). Technology is not an option in this activity.

Usage of Socrative/Poll everywhere—will help to have an informal assessment. (trying for the first time)

Posting extra resources on D2L will provide opportunities to explore/experiment on the topic covered during the class room time.

CATs in my lesson plan-

1-minute paper:

Kind of Evaluation: Course knowledge and skill

When to use: At the end of the class/Closure

How It's Done

1. Students answer the question “What was the most important

concept/step/objective you learned in this session?”

OR

Students create a quiz question on the basis of most important thing they learned

in the session.

2. Students write a question which they think remained unanswered.

The sequence of learning does not end with writing 1-minute paper. The students will be

encouraged to come up with the answers to the unanswered questions and the

discussion can be extended up to10-15 minutes.

Before winter holiday season, I would like to stretch 1 minute paper CAT to snow ball

fight where students crumple up their paper to a snow ball. The snow ball fight begins

and on music cue, students toss snowballs on each other. When the time is up, each

student is to pick up the nearest snow ball to answer the question from

quiz/unanswered question.

Brief Reflection:

I might insert a brief reflection if I anticipate/observe that students are struggling on a

particular section.

Kind of Evaluation: Course knowledge/prior skills for the next topic

When to use: Before transiting from one topic to another related topic or in the middle

of the lesson.

Graphing : Sinusoidal curve

Teacher Name: Ms. KAPOOR

Student Name: ________________________________________

CATEGORY/POINTS 4 32 1

Accuracy of Plot Correct shape. Incorrect

Includes complete Correct Correct shape. shape/Incomplete

Title cycle. Four cycle/ One or no

parameters- shape.Includes Includes complete parameter is graphed

Amplitude, Period, correctly

vertical and phase complete cycle. Three cycle.Two out of four

shift graphed

correctly. out of four parameters are

Title is creative and parameters are graphed correctly

clearly relates to the

given Graph graphed correctly

Title clearly relates to A title is present at A title is not present.

the problem being the top of the graph.

graphed

Labeling of X axis All four intervals are Three intervals are Two ends are labeled No interval is labeled

correcly

labeled correctly labeled correctly

Labeling of Y axis The Y axis has a clear, The Y axis has a clear, The Y axis has a clear, The Y axis is not

REMARK

neat label that neat label that neat label that labeled.

describes center, Max describes center, Max describes only center

and Min of the Graph or Min of the Graph

EXCELLENT GOOD SATISFACTORY NEEDS WORK

Q#1 (New BT: Analyzing)

Data from recent past years indicate the future amount of carbon oxide in the atmosphere may grow

according to the table, amounts are given in parts per millions.

a. Do the carbon di oxide levels appear to grow exponentially? Why or why not?

b. How can be the graphing calculator helpful to estimate when future level of carbon di oxide will double?

Q#2 (New BT: Applying)

What approach (Graphical/Algebraic) would you apply to prove that logarithmic and exponential functions

are inverse of each other? (If applicable, include examples with restrictions)

Q#3 (New BT: Evaluating/Analyzing)

What would happen if you accept the offer of an investment company to deposit $1 invested on 100%

interest rate continuously compounded for one year? Would you be able to pay off your mortgage or buy

your dream car in one year?

Q#4 (New BT: Creating/Evaluating)

Read the article below and summarize your thoughts (Written/equation/Graph) to discuss in next class in

order to justify/Defend author’s idea of being immortal and support your statement with your

own mathematical/ logical reasoning. Can you correlate the range approaching to infinity in

exponential graph with something author addressed in the article?

PS: In order to give students sufficient thought processing time, this question will be given as homework

assignment)

The year Humans Become Immortal

(Source: Blitzer College Algebra)

SLO: By the end of this lesson, students will be able to comprehend exponential functions and

they will demonstrate what they learned by applying exponential functions in real world problems.

Multiple Choice (BT: Comprehension)

1. Which is the best model for the data shown?

Multiple Choice (BT: APPLICATION)

2. Carmen invested $3000 in an account that pays 3.6% annual interest compounded monthly. To the

nearest dollar, what will be the balance in her account after 6 years?

Open ended Questions: Box your final answer. No credit will be given in the absence of clear,

correct work. Insufficient incorrect or unclear work will result in a deduction, even if the final

answer is correct.

BT: Synthesis/Evaluation

3. After graduating from college, you get a job of an archaeologist. Your first assignment is to

research on the living organism on the basis of carbon isotope C14 that existed in the living

organism decreases by 50% of its previous value every 5730 years.

Plan a solution and answer the following questions-

a. Write a function C(t) as dependent variable for the C14 ratio, where t represents the years

since organism died.

b. Sketch/label the graph on the grid provided below

c. Justify the domain and range in the context of the problem.

d. Is there any asymptote in the graph? What does it represent in the problem?

BT: Analysis

A calculator is not allowed for this question

4. Jonathan and Karina were given the following functions--

a.

XY

02

11

2 0.5

3 0.25

4 0.125

5 0.0625

6 0.03125

b. An exponential function with rate of decay of one-half and an initial amount of 2.

Karina thinks they are the same functions but Jonathan disagrees. Who is correct? Explain

your reasoning (Algebraically/Graphically)

Google- Form

https://docs.google.com/forms/d/18npAdUEBGi8Iy1BNT-jF-

omt1k6m15ma6kmaUb98Vhs/viewform?usp=send_form

FLUBAROO:

1. Click on Add on tab and choose Flubaroo

2. Flubaroo need to be enabled.

3. Click on Flubaroo to choose grade assignments

4. Select the form and establish the key

5. Go through the tabs and it will grade assignment.

Spreadsheet created by Flubaroo: First Tab Student submission

Spreadsheet: Second Tab Grades

http://www.superteachertools.us/jeopardyx/jeopardy-review-

game.php?gamefile=1560360

Objectives:

• Evaluate exponential functions.

• Graph exponential functions.

• Evaluate functions with base e.

• Use compound interest formulas.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

Definition of the Exponential Function

The exponential function f with base b is defined by

f (x) bx or y bx

where b is a positive constant other than 1 (b > 0 and

b 1) and x is any real number.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2

Example: Evaluating an Exponential Function

The exponential function f (x) 42.2(1.56)x models the

average amount spent, f(x), in dollars, at a shopping

mall after x hours. What is the average amount spent, to

the nearest dollar, after three hours at a shopping mall?

We substitute 3 for x and evaluate the function.

f (x) 42.2(1.56)x

f (3) 42.2(1.56)3 160.20876 160

After 3 hours at a shopping mall, the average amount

spent is $160.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 3

Example: Graphing an Exponential Function

Graph: f (x) 3x We set up a table of coordinates,

then plot these points, connecting

x f (x) 3x them with a smooth, continuous

–2 f (2) 32 1 curve.

9

–1 f (1) 31 1

3

0 f (0) 30 1

1 f (1) 31 3

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 4

Characteristics of Exponential Functions of the Form

f (x) bx

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 5

Formulas for Compound Interest

After t years, the balance, A, in an account with

principal P and annual interest rate r (in decimal form)

is given by the following formulas:

1. For n compounding periods per year:

A P 1 r nt

n

2. For continuous compounding:

A Pert

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 6

Example: Using Compound Interest Formulas

A sum of $10,000 is invested at an annual rate of 8%.

Find the balance in the account after 5 years subject to

quarterly compounding.

We will use the formula for n compounding periods per

year, with n = 4.

1 r nt 1 0.08 4 5

n 4

A P A 10, 000 14, 859.47

The balance of the account after 5 years subject to

quarterly compounding will be $14,859.47.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 7

The Natural Base e

The number e is defined as the value that 1 1 n

n

approaches as n gets larger and larger. As n

the approximate value of e to nine decimal places is

e 2.718281827

The irrational number, e, approximately 2.72, is called

the natural base. The function f (x) ex is called the

natural exponential function.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 8

Example: Evaluating Functions with Base e

The exponential function f (x) 1066e0.042x models the

gray wolf population of the Western Great Lakes, f(x), x

years after 1978. Project the gray wolf’s population in

the recovery area in 2012.

Because 2012 is 34 years after 1978, we substitute 34

for x in the given function.

f (x) 1066e0.042x f (34) 1066e0.042(34) 4446

This indicates that the gray wolf population in the

Western Great Lakes in the year 2012 is projected to

be approximately 4446.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 9

Example: Using Compound Interest Formulas

A sum of $10,000 is invested at an annual rate of 8%.

Find the balance in the account after 5 years subject to

continuous compounding.

We will use the formula for continuous compounding.

A Pert A 10,000e0.08(5) 14,918.25

The balance in the account after 5 years subject to

continuous compounding will be $14,918.25.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 10

Function Inverse Graphs Solving Real World

Functions 100 Equations Problems

(Set up only)

100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

Is the given set one-to one or many-to one

F {(2,2), (1,1), (0,0), (1,3), (2,5)}.

One to One function

What is

X

True/False

TRUE

What is Domain & Range of the

following Graph

a. Identify the function

b. Define the transformation in

f (x) 2x3

a. Exponential

b. Translating three points to

the left

What is interchanged in

Function and its Inverse

Domain & Range

Decide if functions are inverse

Yes/No

YES