Survey of Algebra

COURSE GOALS:
Survey of Algebra is the second algebra course we offer (and would be better named
“Intermediate Algebra”). This course is also the prerequisite class for most of the college level
transfer classes we teach (MAT 120 “Math for Liberal Arts”, MAT 121 “College Algebra”, and
MAT 123 “Finite Math”, MAT 135 “Statistics”, and MAT 155/156 Integrated Math I/II “Math
for Elementary Teachers”). Note that MAT 106 is not a prerequisite for MAT 107 “Career
Math”. 22 of the 38 sections covered in MAT 106 are a review from MAT 090! This is
intentional.

Most students will take MAT 121 (College Algebra) after this course. In light of that, students
need to get a strong foundation in algebraic skills in this course, and end of the semester grades
should be with the notion that students need to be prepared for MAT 121.

Since there are so many options after 106, we want to give students (or at least discuss with
them) the Life After MAT 106 handout about other class choices. This discussion should take
place near the registration period. This allows students to register for the correct class initially
rather than arrive in 121, discover they could take another class, and have to rearrange their
schedule. Some 106 instructors have even made an assignment where students obtain (in writing
or off a web page), the math class they need for their FR degree or transfer institution.

GUIDING PRINCIPLES:
The following principles are intended to create the “framework for success” that our students
need in order to become confident and competent learners.

1. Memorizing is the lowest form of learning on Bloom’s Taxonomy. Memorizing basic
algebraic procedures is key to a strong foundation in College Algebra. For example,
students need to be able use the laws of exponents.

COURSE SUGGESTION: The use of note cards, class notes, or the textbook for an exam
is discouraged. The reason for this is to facilitate the memorization of basics of algebraic
procedures (i.e. factoring) and formulas and to motivate serious study. If note cards are
to be used, restrictions should be placed on what type of information can be placed on it.

2. At this level, it is important to keep students awake, alert, and engaged.

COURSE SUGGESTION: Make sure to give breaks. Have you heard this: “The brain
can only absorb as much as the tush can endure.” Most MAT 106 classes are twice a
week for 1 hour and 50 minutes. This time unit has a 10 minute break built into it. The
more the students sit and watch, the less their brain is engaged. It is better for students to
have this break half way through the class, versus being let out 10 minutes early. A break
allows the students to get up and get their blood pumping again. Breaks are even more
crucial to the Saturday morning classes.

COURSE SUGGESTION: Engaging students is critical. Students not only need to see
how problems are done, they need to try some of the problems during class. A format
that works well with this level of student is to teach for a few minutes, and then problems
for students to work on for a few minutes. If your lecture is over before class is over,
have students start trying to work homework problems, while you are still there to help.

3. In this foundational algebra course, it is important to emphasize good algebra habits.

COURSE SUGGESTION: It is important to emphasize proper vocabulary in the course.
For example, many students know to take the square root of both sides of x² = 49 yet say
“square both sides” when asked what step to do next.
.
COURSE SUGGESTION: The Dugopolski text has excellent Reading and Writing
exercises (usually the first few of each exercise set), called “Enriching your mathematical
word power”. It helps reinforce vocabulary and notation.

COURSE SUGGESTION: Besides the course content, it is important to emphasize the
difference between an expression and an equation, and what you can do with each.

COURSE SUGGESTION: Emphasize that and

4. Assessment of achievement should be taken seriously. We want grades to reflect student
achievement (see #5).

COURSE SUGGESTION: It is important to know who is taking the exams. Exclusive
use of take-home assessments is not allowed. Also, the in-class final exam needs to be
cumulative so that students have one last opportunity to “pull it all together”!

5. Grade on achievement. Grading on attitude, effort, behavior, or a student’s “need” for a
certain grade does a disservice to the student, to the student’s subsequent instructor, and
to Front Range Community College.

COURSE SUGGESTION: Remember, we are teaching more than math!!!! Sometimes
the lessons involve responsibility. Just because a student earns a low grade, does not
mean they did not learn anything.

GATEWAY TOPICS (if applicable): Currently not applicable for MAT 106.

CURRENT TEXTBOOK:
Intermediate Algebra, 5^th Edition, by Mark Dugopolski.

CONTENT:
22 of the 38 sections covered in MAT 106 are a review. The following sections are required.
See notes below about specific sections.
• All of chapter 2
• All of chapter 3
• 4.1 – 4.3 (only briefly on 4.3)
• All of chapter 5
• All of chapter 6
• All of chapter 7
• 8.1, 8.2, 8.4

Below is a possible schedule, broken down in 30 days of class. Adjust accordingly.
® means this is a review section, so in theory, you can cover it more quickly.

TECHNOLOGY:

MATHZONE  is a web-based supplement that is specific to our
textbook. It has unlimited number of exercises for practice; free access to live online tutoring via
NetTutor; e-Professor, animated step-by-step instruction for solving problems in the book; textspecific
lecture videos; and self-tests.

Calculators: The use of graphing calculators in 106 should be restricted so that students learn
graphing basics by hand. It is up to the instructor whether or not to require a calculator. Since
the graphing calculator rental program is reserved for college level courses (those above 106), if
any type of calculator is required in 106, one may want to consider using scientific calculators. I
personally don’t allow any calculators on my 106 exams.

Video Tapes & CD Lecture Series: Available at the Math Lab. The Media Center will also
have a copy of the video tapes which can be checked out and viewed on site. Some students find
it very helpful to see the lectures more than once. The video tapes are a great way to do that.
The videos are also available on MathZone.

NOTES ABOUT CURRENT TEXT: None

SUPPLEMENTS:
• “Life After 106” handout

Specific Things that Should be Emphasizes by Chapter:
Thoughts from Monica and Ryan
A Work in Progress. Looking for input from 106 and 121 instructors.

CHAPTER ANALYSIS:
Chapter 2: Linear Equations and Inequalities in One Variable
• Calculator Comments
o Only allow scientific calculators
• Section 2.4
o Interval Notation
• Section 2.6
o Point out that the absolute value definition is piecewise.

Chapter 3: Linear Equations and Inequalities in Two Variables
• Calculator Comments
o Only allow scientific calculators
• Sections 3.1-3.5
o Being able to graph functions using a T table (plotting points)
o Function notation f(x) does not mean “f times x”
o Students need to have strong foundation in functions (linear). They need to have
strong graphing skills, as well as graph reading skills.
o Graph Reading
a. Evaluate the function at an x-value, i.e. f(3)=
b. Determine x when f(x) is given, i.e. When f(x) = 3, x =
c. Write the domain using interval notation
d. Write the range using interval notation
e. Write the x-intercepts using ordered pairs
f. Write the y-intercept using ordered pairs
g. Determine the slope of a line
h. Determine points of discontinuity, i.e. x = 3

Chapter 4: Systems of Linear Equations
• Calculator Comments
o Only allow scientific calculators
o Solve these systems by hand ! ☺
• Sections 4.1-4.3
o Word problems: especially setting up and defining the variables.

Chapter 5: Exponents and Polynomails
• Calculator Comments
o NO calculator at all – in order to help reinforce operations of signed numbers
• Sections 5.1 – 5.2
o Rules of exponents should be memorized.

Chapter 6: Rational Expressions and Functions
• Calculator Comments
o NO calculator at all – in order to help reinforce operations of signed numbers

Chapter 7: Radicals and Rational Expressions
• Calculator Comments
o NO calculator at all – in order to help reinforce operations of signed numbers

Chapter 8: Quadratic Equations, Functions, and Inequalities
• Calculator Comments
o NO calculator. Students need to be able simplify the quadratic formula. For
example, they need to be able to simplify without a calculator. They
need to know . This is a super
important skill – and should be done without a calculator. In fact, you may want
to emphasize this example in the quadratic formula section.

• Sections 8.1-8.2
o Completing the Square
o Quadratic Formula
Quadratic Formula should be memorized. College Algebra teachers will
be expecting students to have it memorized!!! In fact, this is majorly
important…College Algebra students should ALREADY know
this!!!!!!!!!☺