Union, New Jersey
INTEGRATED ARITHMETIC AND ALGEBRA
Course Number: Math 0900
Semester Hours: Non-credit (three institutional credits)
Prerequisites: Placement by the Placement Test
Type of Course: General Education Academic Foundations Support
Limitations on Enrollment: 22
Topics include the following: the real number system , operations with real numbers, absolute values, fractions, complex fractions, factoring, roots, radicals, algebraic expressions, and rational expressions. Other topics included are operations with algebraic expressions, exponents,, and rational expressions as well as solving absolute value equations, linear equations and inequalities. An introduction to the "notion of a function" will be supported using graphing calculator technology to visualize linear and other types of functions.
I. COURSE OBJECTIVES
A. Cognitive Skills
Upon successful completion of this course, students will be able to:
1. Develop analytic thinking skills by:
a) Drawing reasonable inferences from observations and logical premises
b) Discerning independently internal structure, pattern, and organization using models from various approaches in solving problems.
c) Recognizing and analyzing problems in a variety of situations, both independently and cooperatively with others.
d) Explaining the stages of the problem-solving process in both objective and subjective contexts.
e) Identifying, analyzing, and critiquing the different approaches to solving problems.
f) Presenting arithmetic and algebra in an integrated approach so there is a natural transition from the arithmetic to the analogous concept in algebra and to present both using the same approach. (For example: distributive property - adding like terms )
2. Strengthen evaluative thinking by:
a) Identifying assumptions and limitations in problem solving and evaluating the adequacy of one's own and others approaches to problems.
b) Applying prior knowledge and previously learned concepts to analyze
and solve new problems.
c) Allowing students to see the relationship between arithmetic and
algebra and to realize that much of the algebra is arithmetic from a
general point of view made possible by the use of variables.
3. Articulate an understanding of mathematical reasoning
a) Listing, defining, and explaining the uses of the algebraic concepts in
b) Mastering all the arithmetic skills necessary for the average citizen to
function in our society and all the algebra needed as a prerequisite for
Algebra for College Students.
c) Demonstrating an understanding of the development of mathematical
definitions, theories, and their applications through modeling and
d) Demonstrating an understanding of mathematical modeling that
represents and solves problems for practical applications.
e) Demonstrating an understanding of mathematical logic, symbolic
representation, and information processes.
4. Apply technology to integrate cognitive skills by:
a) Using a web-based tutorial program to strengthen cognitive skills.
b) Using graphing calculator technology as a tool to explore various types of
functions and problem settings.
c) Using the Internet to research sources.
d) Using Internet-based communication tools, such as e-mail and Web
Board, to post and discuss projects.
Through completing the activities in this course, students
will be able to:
1. Interact cooperatively and constructively in pairs, small groups and classroom situations.
2. Articulate diverse perspectives that contribute to problem solving and to the interpretation of results through examination of variables such as rules, definitions, and theories.
3. Demonstrate intellectual flexibility and the capacity to adapt to change in various problem settings, contexts, and situations.
Through the activities in this course, students will:
1. Identify their own preferred learning styles and their own strengths and weaknesses as learners.
2. Demonstrate independence of thought in problem solving and implement these skills in an effective way
3. Understand how different ways of learning may support productive collaboration in the classroom and workplace.
II. COURSE CONTENT
A. Basic Ideas
1. A Brief Introduction to Fractions
2. Addition, Subtraction, Multiplication, and Division of Decimal Numbers
B. Addition and Subtraction of Integers and Polynomials
1. Exponents and Variables
2. Order of Operations
3. Introduction to Integers
4. Addition of Integers and Properties of Addition
5. Subtraction of Integers
6. Algebraic Terms and Polynomials
7. Combining Like Terms and Simplifying Polynomials
C. Multiplication and Division of Integers and
1. Multiplication of Integers2. Laws of Integers Exponents - Product Rule
3. Products of Polynomials
4. Special Products
5. Division of Integers
6. Order of Operations on Integers
7. Laws of Integers Exponents -- Quotient Rule
8. Power Rule for Integers Exponents and Applying Combined Laws of Exponents
9. Division of Polynomials With a Monomial Divisor
10. An Application of Exponents: Scientific Notation
D,. Linear Equations and Inequalities
1. Addition Property of Equality
2. Multiplication Property of Equality
3. Combining Properties in Solving Linear Equations
4. Solving Linear Inequalities
E. Graphing Linear Equations and Inequalities
1. Ordered Pairs and Solutions of Linear Equations in Two Variables
2. Graphing Linear Equations in Two Variables
3. Writing Linear Equations in Slope- Intercept Form
4. Introduction to Functions
F. Factors, Divisors, and Factoring
1. Prime Factorization
2. Greatest Common Factor of Natural Numbers and Exponents
3. Factoring Polynomials with Common Factors and by Grouping
4. Factoring Trinomials with Leading Coefficients of One
5. Factoring Trinomials with Leading Coefficients Other Than One
6. Factoring Binomials
7. Factoring Perfect Square Trinomials
8. Mixed Factoring
9. Solving Quadratic Equations by Factoring
G. Operations on Rational Numbers and Expressions
1. Introduction to Fractions (Rational Numbers), and Rational Expressions
2. Rewriting Rational Numbers as Division and Graphing Rational Numbers
3. Reducing Rational Numbers and Rational Expressions
4. Further Reduction of Rational Expressions
5. Multiplication of Rational Numbers and Expressions
6. Further Multiplication of Rational Expressions
7. Division of Rational Numbers and Expressions
8. Addition and Subtraction of Rational Numbers and Expressions with Common Denominators
9. Addition and Subtraction of Rational Numbers and Expressions with Different Denominators