# INTEGRATED_ARITHMETIC_AND_ALGEBRA

# KEAN UNIVERSITY

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

**Catalog Description:**

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
by:

a) Listing, defining, and explaining the uses of the algebraic concepts in

various problems.

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

simulation.

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.

**B. Diversity**

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.

**C. Values **

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
Polynomials**

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

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