Concepts and Principles of Mathematics

Course Description

This course provides a review of the fundamentals of mathematical operations and theorems. Topics include:
decimal numbers , fractions, percents, ratio, rates, proportions, and basic concepts of geometry. An introduction to
integers and the number line are also included. The goal of this course is to provide students with the skills
necessary to begin the study of algebra . This course does not count towards credit requirements for associate
degree programs.

Note: A grade of ‘C’ or better must be obtained to successfully complete this course and go on to Math 099.
Calculators may not be used in this course.


Students will learn to add, subtract, multiply, and divide fractions and decimals . Students will be able to compute
percentage problems, convert fractions and decimals to percents and decimal and percents to fractions. Students
will learn the fundamentals of proportionality. In preparation for Math 099, students will be introduced to integers
and the number line. Students will also develop basic skills to add and subtract signed numbers using the number
line. Students will learn to apply their basic math skills found in the workplace and in everyday experiences.

Instructional Text

Howett, Jerry. Contemporary’s Number Power 2: A Real World Approach to Math. McGraw-Hill, Chicago.

Teaching Strategies
Lecture and Demonstration
Student Practice and Activities
Assigned Homework
Quizzes and tests
Computer Lab

Learning Outcomes
At the successful conclusion of this course, students will be able to:
Operations on Whole and Mixed Decimal Numbers
• Order of Operations and Exponential Notation
• Identify place value of mixed decimal numbers
• Round whole and decimal numbers to a given place value
Estimate sums , differences, products, and quotients
• Apply rules and properties of addition, subtraction, multiplication, and division to strategically solve word
• Identify and use the commutative property
• Identify and use the associative property
• Identify and use the distributive property
• Use a test of reasonableness or estimation to check answers
• Use geometric formulas to calculate perimeter, area, and volume of a rectangle and the circumference and
area of a circle .
• Find the prime factorization of a composite number
• Determine if a number is divisible by 2, 3, 4, 5, 6, or 9
• Find the greatest common factor of a group of numbers
Operations on Fractions
• Identify forms of fractions and convert fractional forms
• Use factors to simplify fractions
• Add, subtract, multiply and divide fractions with like and unlike denominators
• Find the least common multiple of a group of numbers
• Determine whether two fractions are proportional
• Convert fractions to decimals or percents
• Convert decimals to fractions or percents
• Convert percents to decimals or fractions
Rate, Ration, Proportion
• Write a ration and reduce to its simplest form
• Write a rate and reduce to its simplest form.
• Write a proportion
• Find the rate, base, and amount in percent problems
Glimpse of Pre-Algebra
• Identify the set of real numbers
• Represent an integer on a number line
• Use inequality signs to order integers
• Identify opposites on the number line
• Identify and simplify absolute value expressions
• Add two numbers with the same sign
• Add two numbers with opposite signs

Methods of Evaluation

Attendance and Participation   10%
Homework and In-Class   10%
Quizzes   20%
Tests   40%
Final Exam   20%

Attendance and Class Policies
Students are expected to attend every class. Similarly, all students are expected to arrive on time and be
prepared for class. Arriving late or leaving early will have an impact on 10% of a student’s grade. Participation in
classroom projects is vital to the learning process and attendance is a key ingredient to success at Goodwin

If a student finds it necessary to miss a class or part of one, it is his/her responsibility to contact a classmate or the
instructor to identify and complete any missed in-class assignments, homework, tests or other material by the
next class. Work submitted after this date will have points deducted for each day that it is late, unless other
arrangements are made with the instructor in advance. Any quiz/test missed will be made up as soon as the
student returns to class. All assignments and the final exam must be completed.

Instructors expect the integrity from students to do their own assignments, quizzes, and tests. Any student that
acquires answers from another source or does not submit his/her own work will automatically receive a “0” for that
grade. No use of any type of calculator is permitted.

Cell phones need to be turned off before class starts. If an important call is expected, set your phone to “vibrate”.
Leave the room if you plan to make or receive a phone call.


Students must have a passing grade in order to receive an incomplete. All coursework must be completed within
two weeks after the end of the course. Failure to complete work within the two-week period will result in a failing
grade. All incompletes must be arranged with the instructor. Students can not progress to the next course for
that particular subject until the incomplete status is changed.


Any student wishing to withdraw officially from this course must see an academic advisor immediately.


Students with physical, psychiatric/emotional, medical, or learning disabilities that may affect their ability to carry
out the assigned course work are urged to contact the Assistant Dean of Academic Support Services. The
Assistant Dean of Academic Support Services will review your concerns and determine, with each individual, what
accommodations are necessary and appropriate. All information and documentation of disability are confidential.

MATH 089 - Course Outline (A )

Week 1 Course syllabus, policies/procedures, textbook layout

Brief Review- Operations of Addition, Subtraction, Multiplication
and Division on Whole Numbers.
Order of Operations and Exponential Notation
Decimal and mixed decimal place values
Reading and Writing decimals
Unnecessary zeros
Comparing and Rounding decimals
Chapters are not

Lecture and teacher

Pages 60-66
Teacher handouts

Pages 70-71

Week 2 Decimals
Estimating decimals
Adding and Subtracting with decimals
Multiplying with decimals
Dividing with decimals
Applying Skills
Pages 73-93
Teacher handouts
Week 3 Fractions – Multiplication and Division
Understanding and Writing fractions
Equivalent fractions
Simplifying fractions and Raising fractions
Identifying and Converting forms of fractions
Multiplying with Fractions
Rounding and Estimating
Dividing with Fractions
Applying Skills
Converting between fractions and decimals
Pages 8-21

Teacher handouts

Pages 39-56


Pages 67-69

Week 4 Adding and Subtracting Fractions
Adding and subtracting fractions with like denominators
Adding and subtracting fractions with unlike denominators
Finding a common denominator
Adding and subtracting with mixed numbers
Borrowing and Carrying with fractions
Applying Skills and Review
Pages 22-38

Teacher handouts

Page 58

Week 5 Solving Geometric Applications –lightly cover—to learn
substitution and fundamentals of formulas
Perimeter, Area, and Volume of a rectangle,
Circumference and Area of a circle
Writing percents as fractions and decimals
Writing decimals and fractions as percents
Identifying the parts of a percent problem and solving it
Applying Skills
Pages 136-144


Page 96-120
Teacher handouts

Week 6 Ratios, Rates and Proportions
Rates and unit pricing
Solving proportions
Teacher handouts
Week 7 The Real Number System
Real numbers and order (as time permits)
Adding real numbers—Integers – not fractions
Subtracting real numbers – Integers not fractions
Teacher handoutsWeek 71/2
Week 71/2 FINAL EXAM  
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