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Math 1314: College

Algebra Math 1314-G002 Term and Year: Spring 2016
213 Class Days and Times: MW 5:30-6:50pm
Course Section:

Class Room:

Instructor contact information

Instructor: Jenny Ortiz Voicemail: N/A
Office Hours: Immediately after class
Office: 314A Class Website: www.mymathlab.com

Email Address: [email protected]

The full syllabus will be available online in My Lonestar.

Course overview

For details go to http://research.lonestar.edu/cat/catsrch.asp

Purpose:
College Algebra is designed to fulfill the minimum math requirements for graduation from a state
four-year college and to develop the algebraic skills and concepts needed for study in future math
courses.

Major Course Outcomes:
1. To solve quadratic and rational inequalities
2. To review the methods for solving quadratic equations, equations in quadratic form, and radical equations
3. To develop an understanding of the concept of a function including topics such as the domain and range
of a function, functional notation, piecewise-defined functions, function transformations, operations with
functions, and the inverse of a function
4. To study techniques of graphing functions; including polynomial, rational, exponential and logarithmic
functions.
5. To use distance and midpoint formulas to develop equations of circles. To convert the general form of a
circle’s equation to standard form.
6. Optional: To study the techniques for graphing quadratic equations in two variables; included are ellipses
and hyperbolas with centers at the origin.
7. To study the properties of logarithms and their applications in simplifying expressions and solving
exponential and logarithmic equations
8. To develop strategies for finding zeros of polynomial functions; included in this study are the Rational-
Roots Theorem and the Fundamental Theorem of Algebra
9. To study matrix solutions to linear systems by using reduced echelon form

Math 1314 Syllabus, Page 1 | 2
Revised 12/14

Materials Needed:

Textbook: College Algebra, Standard version for North Harris College, by Blitzer (6th Edition; Pearson/Prentice

Hall) including Student Access Kit for MyMathLab. The course id is ortiz32475.

Pencil and paper: It’s a fact of math: you will make mistakes. It is important to keep your work organized and
easy to read, so you should always use pencil so you can erase and correct small mistakes.
Calculator: TI 83 or TI 84

General Course Outline

Textbook sections 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4, 6.1, 6.2,
Note: Sections 7.1 & 7.2, are optional.

Other Resources:
Take a Teacher Home DVDs and Videotapes: This series was created in-house tailored to LSC-NH Math 1314
course that students may check out at the LSC-NH Library Circulation Desk to take home or view in the Learning
Center (LC) located in ACAD 200. Some of these videos are also available online. To access them, go to
http://apps.lonestar.edu/blogs/lsc-northharrismath/course-resources/math-1314/

The Khan Academy: Many ad-free videos and practice exercises can be found at www.khanacademy.org where
their mission is “Free education for anyone with internet access.”

Instructor guidelines and policies

Attendance: Attendance will be taken every day.You are responsible for material covered, any
announcement, and homework in your absence. Tardiness, non-participation, any form of disruptive
behavior and/or excessive absences (three absences) may result in an administrative withdrawal from
this class without notification. Only miss class when you cannot avoid it. Please contact me by email
anytime you will miss class.

Assignments:
• HOMEWORK: All homework will be completed online using MyMathLab.You will need the
following information to get started:
• Website: http://pearsonmylabandmastering.com
• Course ID: ortiz32475
• Course Name: College Algebra MW 5:30-6:50pm
Access Code: You must purchase an access code. It may be shrink-wrapped with your textbook
or you can buy it online on the website mentioned above. No homework grade will be dropped.

• QUIZZES: All quizzes will be MyMathLab. No quiz grade will be dropped.

• MAJOR EXAMS: There will be three to four exams scheduled on the course calendar. All
students are expected to complete their exams in class at the scheduled time. The ONE lowest
test grade will be dropped (not the Final Exam). If you are absent for a major test, there will
NOT be any MAKE-UP TESTS.

• FINAL EXAM: At the end of the semester, you will have a comprehensive and mandatory final
exam. You must earn at least a 60% to get an A, B, or C in this course. (Remember: No
calculator on a cell phone will be allowed.)

Math 1314 Syllabus, Page 2 | 2
Revised 12/14

Student Preparation Strategies

College Algebra –
I post my notes in “My Math Lab” under the course tools in the document sharing link. Students are to
look over the next section and work on the review sections of the notes. The review sections are
included in the notes because that prior concept will be used in the upcoming section. When the
students come to class, they will talk to one another regarding the review sections and ask questions to
me, if they have any. I will go over problems to make sure students are going in the correct direction.
Students will do assignments in “My Math Lab”, homework and quizzes. I encourage my students to
work with each other, use the online book, and problem guide link in “My Math Lab”.

BOPPPS Lesson

COURSE: MATH 1314 – College Algebra
Lesson Title: Circles
Course Student Learning Outcome:

To use distance and midpoint formulas to develop equations of circles. To convert the general form of a circle’s
equation to standard form.

Learning Objectives:

1. By the end of class, students will be able to identify the center and the radius from a standard form of an equation
of a circle.

2. By the end of class, students will be able to apply graphing techniques to sketch a circle using the center and the
radius.

Participatory Learning: Learner Activities Lesson Materials
Time Instructor Activities
5 Min. Review Assignment This assignment is done before class. 1. Print review assignment
Students will compare their answers with available online.
5 Min. Mini-Quiz each other at the beginning of class to
15 Min. Teacher-guided instruction make sure they understand how to find
the vertex of a quadratic equation.
10 Min. Student practice Answers will be shown and discussion
over any different answers between
students and myself.

Note Card Activity-Students are to define 1. Note card
center and radius of a circle in their own
words, share their note cards (pass
between two other students), and check if
definition is correct (thumbs up/down).

Introduction over the Standard form of an 1. Printed notes available
equation for a Circle – Writing an equation online
in standard form for a circle
Class Examples #1 – how to use the
standard form of an equation for a circle
Class Examples #2 – how to use the
equation to find the center and the radius.
Apply what they have from the equation
and graph the circle in the grid.

Student Examples - student will have time 1. Printed notes available
to practice their own problems online
We will go over the problem together to
make sure we are working out the
problem correctly.

15 Min. Student guided 1. Pair – work on specific problem 1. Assignment will be
2. Switch Partner – available in class
A. each student will share how to work out
their problem with new partner
B. New Pair will be assigned a new
problem to work out
3. Switch Partner (Different person) –
Share how to work out problem with
second new partner

5 Min. Poll Everywhere – Exit Ticket Check for understanding – 1. I will printed problems
Students will work 4 more problems. They and post it under
will go on their phone to answer the document camera for
question requested anonymously in Poll students to work.
Everywhere. We will discuss problem if
any answers are different.

Reminder:
1. Extra Practice with answer key, grids, and video is available at http://padlet.com/wall/tekwbq0h4kfq.
2. Look for link to next lesson.

See Attached Notes and Assignment

Quadratic Transformation Worksheet Name____________________________

1. Write the vertex form of a quadratic equation.

2. What does changing the "a" variable do to the graph of a quadratic?

3. Being specific, name 3 ways that a parabola changes with different types of "a"
values.

4. What does changing the "h" variable do to the graph of a quadratic?
5. If "h" is positive how does the parabola move? If negative?

6. What does changing the "k" variable do to the graph of a quadratic?
7. If "k" is positive how does the parabola move? If negative?
8. What conclusion can you make about the variables of h and k together?

Write the quadratic equation, in vertex form for each graph.
1. 2.

3. 4.

Graph the quadratic equation on the provided grid.

11. f (x) = (x − 0)2 + 3 12. f (x) = (x + 4)2 + 0

13. f (x) = −2(x − 0)2 + 0 14. f (x) = (x − 3)2 + 4

15. f (x) = 3(x − 4)2 − 6 16. f (x) = 1 (x + 2)2 + 3
2

Kuta Software - Infinite Geometry Name___________________________________
Date________________ Period____
Equations of Circles

Identify the center and radius of each. Then sketch the graph.

1) (x − 1)2 + (y + 3)2 = 4 2) (x − 2)2 + (y + 1)2 = 16

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

3) (x − 1)2 + (y + 4)2 = 9 4) 2 + (y − 3)2 = 14

y x
8
y
6 8

4 6

2 4

2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

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5) 2 + 4x − 20 − 2y = −x2 6) −9 = − 2 − 2

y y x

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

7) 9 = 2y − 2 − 6x − 2 8) 16 + 2 + 2 − 8x − 6y = 0

y x x y

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

Use the information provided to write the equation of each circle.

9) Center: (13, −13) 10) Center: (−13, −16)
Point on Circle: (−10, −16)
Radius: 4

11) Ends of a diameter: (18, −13) and (4, −3) 12) Center: (10, −14)

Tangent to x = 13

13) Center lies in the first quadrant 14) Center: (0, 13)
Tangent to x = 8, y = 3, and x = 14
Area: 25π

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Kuta Software - Infinite Algebra 2 Name___________________________________
Date________________ Period____
Graphing and Properties of Circles

Identify the center and radius of each.

1) 2 + 2 = 49 2) 2 + 2 = 324

x y x y

3) (x + 2)2 + (y − 3)2 = 183 4) (x + 7)2 + (y + 8)2 = 64

5) (x + 10)2 + (y + 9)2 = 36 6) (x + 5)2 + (y − 10)2 = 9

7) 2 + (y + 2)2 = 121 8) (x − 14)2 + (y − 2)2 = 4

x

9) 364 + 28y + 2 + 2 = −26x 10) 2 + 2 + 24x + 10 y + 160 = 0

y x x y

11) −6x = −x2 + 32 y − 264 − 2 12) −6x + 2 = 97 + 10 y − 2

y x y

Identify the center and radius of each. Then sketch the graph.

13) (x + 1)2 + (y − 2)2 = 9 14) (x + 2)2 + (y + 3)2 = 4

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

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15) (x + 1)2 + (y + 2)2 = 25 16) (x + 3)2 + (y − 3)2 = 8

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

17) (x + 3)2 + (y + 2)2 = 9 ( )18)x+ 5 2 14)2 = 9

y 2 + (y −
8
y
6 8

4 6

2 4

−8 −6 −4 −2 2 4 6 8x 2
−2
−4 −8 −6 −4 −2 2468
−6 −2 x
−8 −4
−6
−8

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Kuta Software - Infinite Algebra 2 Name___________________________________

Graphing and Properties of Circles Date________________ Period____

Identify the center and radius of each.

1) 2 + 2 = 49 2) 2 + 2 = 324

x y x y

Center: (0, 0) Center: (0, 0)

Radius: 7 Radius: 18

3) (x + 2)2 + (y − 3)2 = 183 4) (x + 7)2 + (y + 8)2 = 64
Center: (−2, 3)
Center: (−7, −8)
Radius: 183
Radius: 8

5) (x + 10)2 + (y + 9)2 = 36 6) (x + 5)2 + (y − 10)2 = 9

Center: (−10, −9) Center: (−5, 10)

Radius: 6 Radius: 3

7) 2 + (y + 2)2 = 121 8) (x − 14)2 + (y − 2)2 = 4

x Center: (14, 2)

Center: (0, −2) Radius: 2

Radius: 11

9) 364 + 28y + 2 + 2 = −26x 10) 2 + 2 + 24x + 10 y + 160 = 0

y x x y

Center: (−13, −14) Center: (−12, −5)

Radius: 1 Radius: 3

11) −6x = −x2 + 32 y − 264 − 2 12) −6x + 2 = 97 + 10 y − 2

y x y

Center: (3, 16) Center: (3, 5)

Radius: 1 Radius: 131

Identify the center and radius of each. Then sketch the graph.

13) (x + 1)2 + (y − 2)2 = 9 Center: (−1, 2) 14) (x + 2)2 + (y + 3)2 = 4 Center: (−2, −3)

y Radius: 3 y Radius: 2
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

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15) (x + 1)2 + (y + 2)2 = 25 Center: (−1, −2) 16) (x + 3)2 + (y − 3)2 = 8 Center: (−3, 3)

y Radius: 5 y Radius: 2 2
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

17) (x + 3)2 + (y + 2)2 = 9 ( )18)x+ 5 2 14)2 = 9

y 2 + (y −
8
Center: (−3, −2) ( )5
6
Radius: 3 Center: − , 14
4 2
y
2 8 Radius: 3

6

4

−8 −6 −4 −2 2 4 6 8x 2
−2
−4 −8 −6 −4 −2 2468
−6 −2 x
−8 −4
−6
−8

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

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Test Questions:

1. From the equation of a circle, what does the r represent? How do you define what r is?
(Knowledge)

_____________________________________________________________________________________

2. Explain how you find the center of the circle from the equation, ሺ‫ ݔ‬െ 2ሻଶ ൅ ሺ‫ ݕ‬൅ 5ሻଶ ൌ 16.
(Comprehension)

_____________________________________________________________________________________
_____________________________________________________________________________________

3. Make up your own equation for a circle.
(Synthesis)

Equation: __________________________________

4. a) From #3, explain where the center is located on the Cartesian plane and how you would graph the
circle from that point, knowing what the radius is.

(Evaluation)

____________________________________________________________________________________
____________________________________________________________________________________

b) Graph this graph on the Cartesian plane. (Apply)

Graphing Circle Rubric

Student’s Name: __________________________

Excellent Average Needs Improvement
3 pts 2 pts 1 pts

Find center and radius from Excellent Average Needs Improvement
an equation of a circle
The student missed more than one part
The student was able to identify the The student missed one part when when identifying the center or radius of a
correct center and radius from an identifying the center or radius of a circle. circle.
equation of a circle.

Describe how to graph the Excellent Average Needs Improvement
circle on the graph
From the student’s center and radius, the
From the student’s center and radius, the From the student’s center and radius, the student’s description has more than one
student described how they would find student’s description has one mistake on mistake on how they would find the center
the center and radius correctly on the how they would find the center and radius and radius on the graph.
graph. on the graph.

Graph circle on the graph Excellent Average Needs Improvement

From the student’s center and radius, the From the student’s center and radius, the From the student’s center and radius, the
student graphed the circle correctly on student graphed the circle with one mistake student graphed the circle with more than
the Cartesian plane. on the Cartesian plane. one mistake on the Cartesian plane.

ACP Showcase Portfolio

NAME: JENNY ORTIZ
DISCIPLINE: MATHEMATICS – COLLEGE ALGEBRA
DATE: 4/21/16

Table of Contents

X Student Preparation Strategy
X BOPPPS lesson-be sure to highlight the following:

X CAT
X Questions
X Technology

X Reflection

Describe student preparation strategy

X I post my notes in “My Math Lab” under the course tools in the document
sharing link. Students are to look over the next section and work on the
review sections of the notes. The review sections are included in the notes
because they are prior concepts that will be used in the upcoming
section. When the students come to class, they will talk to one another
regarding the review sections and ask questions to me, if they have any. I
will go over problems to make sure students are going in the correct
direction. Students will do assignments in “My Math Lab”, homework and
quizzes. I encourage my students to work with each other, use the online
book, and problem guide link in “My Math Lab”.

X Extra help: Go to http://padlet.com/wall/tekwbq0h4kfq for videos. Grid paper is
available to practice.

BOPPPS – BRIDGE

X I will bridge this lesson with Quadratic Transformation.

X Connection: The formulas are very similar. I want to remind the students how to perform the horizontal and
vertical shift to find the vertex on the graph. This information is will help the student find the center of the
circle.

X Quadratic Equation in Vertex form: ‫ ݕ‬ൌ ܽ ‫ ݔ‬െ ݄ ଶ ൅ ݇
X Circle Equation in Standard form: ‫ ݔ‬െ ݄ ଶ ൅ ‫ ݕ‬െ ݇ ଶ ൌ ‫ݎ‬ଶ

X Students will go to this link and work on the Review Quadratic Transformation assignment.

X http://padlet.com/wall/tekwbq0h4kfq
X After answering the questions, students will move around the classroom, pair up with another student, and

compare their answers with each other. They will analyze any differences in their answers. They will do this
twice. As a class, we will check the answers and discuss why some answers were different.

BOPPPS – OBJECTIVES

X 1. By the end of class, students will be able to identify the center and the
radius from a standard form of an equation of a circle. (Knowledge)

X 2. By the end of class, students will be able to apply graphing techniques
to sketch a circle using the center and the radius. (Application)

BOPPPS- PRE-ASSESSMENT

X A CAT can be used here. A “mini-quiz” using a note card. Students are to define
what a center of a circle is and what a radius is. Pass this anonymous card to
another student to check their definition. Thumbs up if correct and thumbs down is
not.

BOPPPS- PARTICIPATORY LESSON

X Teacher-guided instruction
X Student-led practices
X Classroom discussion

X Important questions:
1. Explain how you find the center and the radius of the circle from the equation,
‫ ݔ‬െ ʹ ଶ ൅ ‫ ݕ‬൅ ͷ ଶ ൌ ͳ͸Ǥ (Comprehension)

2. From # 1, explain where the center is located on the Cartesian plane and how you
would graph the circle from that point, knowing what the radius is. (Evaluation)

3. Demonstrate graphing techniques

BOPPPS- POST-ASSESSMENT

X How will you know if objectives have been met?

X After going over the notes, students will go to
http://padlet.com/wall/tekwbq0h4kfq. This site contains a Poll Everywhere
link and an exit assignment the student will work on. I will activate the poll,
so they can answer their free response from their phone to me
anonymously. After receiving all of the student’s response, I will show the
screen to the class and will discuss the answers we see as a class.

BOPPPS- SUMMARY

X Review over prior knowledge that will help in the new section.
X Know the outcome that the students will be able to perform.
X See what the students know about the new concept.
X Teacher-led notes with student-led practice over new concepts.
X Check to make sure students understand new concepts.
X Have students summarize what learned.

Personal Reflection on My ACP
Experience

X I have learned specific names for many things that we do for students
already. I enjoyed trying out different informal assessments. The
technology section was eye opening since we had the opportunity to test
out different educational links. I liked how this program brought all of us
together with different disciplines.

Reflective Essay
I had an interesting time trying to get into this program. I did not know what to expect
from this program, and Interim Dean Kelly Jacobs (department chair) helped me at the last
minute to get into this program. I got to relive my student life with all of these chapters to read,
assignments to turn in, and deadlines to meet. My favorite part of the program was listening to
other instructors reflect over their own classes in their respected fields. Everyone in this
program came from different subject areas. We all have a commonality – our students.
From this class, I was introduced to different ways to do informal assessments with my
students. I do not have to grade everything, if I just want to check the understanding of
different concepts. I am getting my students more involved with their own learning with
different peer groupings. I do not remember what it is called, but the students stand face-to-
face and answer my question to their classmates. The question could range from how to solve,
define a term, what do you know about, and many more things I can come up with. I really like
that my students are willing to talk to one another about problems. Even if the understanding is
not there, the students can listen to someone else explain something from their point of view.
Learning is happening. I want to introduce the Padlet technology into my classroom. Students
have asked me where they can go for more help online. From what I can see, I can link many
different videos, extra worksheets, and notes into one site to help my students. I do not have to
tell them to try to google search content. I will have it available, meaning that I need to watch
the videos I am recommending first. I know that technology is the way to the future with
classroom. I am very glad that I had the opportunity to test out different sites to see what is
available.

This program helped me become a more effective teacher by exposing me to different
teaching strategies. I have been teaching for over ten years, and sometime I feel like I am
trapped in my way of teaching. I know lecturing a class is out of style, and I need to find a
different approach to teach different types of students. I like trying different peer grouping
exercises. I did not do this for a very long time, but I know that the students need to be able to
talk to one another and explain in their own words. I learned to like technology and not be
afraid of it. Since the students are now exposed to everything, via phone, I need to figure out
how I can use their phone for my advantage to help them learn. I will continue to explore this.
The last thing that helped me become a more effective teacher is being with my own peers. I
got to listen to what they do in class, how they handled different situations, and how we all
worked as a team to help our students.

I have many things planned for my future in education. I made a big step when I
graduated with my Master’s degree last year and ventured into the world as a college educator.
I have been teaching as an adjunct professor at Lone Star College – Greenspoint and Victory
Center for two semesters. I had the opportunity to teach my students college algebra. I have
done extensive research on colleges, and I have found a doctoral program that focuses on
developmental math and reading. I am interested in this field since my ambition is to get a
faculty position to work with students in these types of developmental classes. I am always
seeking new strategies to help my students to discover ways to improve their problem solving
skills. I will attend more professional development classes to help me help my students. I just
want to see improvement in my students thinking skills and comfort in the classroom. The goal
is student success. Teacher facilitated while student led.