Math 093: Beginning Algebra – Course Syllabus and Study Guide

Math 093: Beginning Algebra – Course Syllabus and Study Guide

Course Overview

This course introduces students to foundational algebraic concepts, focusing on arithmetic computations, algebraic expressions, and problem-solving strategies. It is designed to prepare students for further study in mathematics and related fields.

• Credit Hours: 3

• Class Location: Zoom

• Class Time: Thursday 5-8 PM

• Instructor: Dana Haug

• Prerequisite: Arithmetic score of 241 or higher on Accuplacer

Vision and Mission Statements

• Vision Statement: To provide outstanding instruction, service, resources, and support to qualifying students in developmental math, reading, and writing within a context of best-practice and research-based methodology.

• Mission Statement: To equip students with the skills, strength, and support to begin their college career, succeed in higher education, and lead a fulfilling, productive life after college.

Course Description

By the end of this course, students will be able to:

• Perform arithmetic computations involving real numbers, algebraic expressions, and equations with accuracy and fluency.

• Simplify mathematical expressions using grouping symbols, properties of arithmetic, and the correct order of operations.

• Analyze and solve real-world problems using arithmetic strategies and mathematical reasoning.

• Apply mathematical reasoning to everyday situations and communicate their problem-solving processes and results.

• Recognize and appreciate the role of mathematics within their own culture and other disciplines.

Course Goals

• Understand and apply arithmetic computations involving real numbers, algebraic expressions, and equations.

• Simplify expressions using grouping symbols, properties of arithmetic, and the order of operations.

Course Rationale

This course is designed to teach basic algebra skills using grouping symbols and properties of arithmetic: addition, subtraction, multiplication, and division. Equation-solving skills are developed and strengthened.

Student Learning Outcomes

Outcome	Description
1	Understand and utilize arithmetic computations involving whole numbers, fractions, decimals, percentages, rounding, and estimating.
2	Add, subtract, multiply, and divide real numbers with like and unlike signs; use the order of operations to simplify a numerical expression.
3	Use the distributive property to simplify algebraic expressions and identify and combine like terms.
4	Evaluate an algebraic expression for a specified value and evaluate a formula by substituting values.
5	Simplify algebraic expressions by removing grouping symbols.
6	Use addition, multiplication, and division principles to solve equations of the forms: $x + b = c$ $(1/a)x = b$ $ax = b$ $ax + b = c$ Equations with the variable on both sides Equations with parentheses
7	Solve a formula for a specified value.
8	Translate English phrases into algebraic expressions, use equations to solve word problems involving money, percent, and geometric formulas.

Key Algebraic Concepts

Real Numbers and Arithmetic Operations

Real numbers include all rational and irrational numbers. Arithmetic operations are the basic calculations: addition, subtraction, multiplication, and division.

• Whole numbers: $0, 1, 2, 3, \ldots$

• Integers: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$

• Rational numbers: Numbers that can be written as $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.

• Irrational numbers: Numbers that cannot be written as a simple fraction (e.g., $\sqrt{2}$, $\pi$).

Order of Operations: The sequence in which operations should be performed:

• Parentheses

• Exponents

• Multiplication and Division (from left to right)

• Addition and Subtraction (from left to right)

Example: Simplify $3 + 6 \times (5 + 4) \div 3^2$

Solution:

• First, calculate inside the parentheses: $5 + 4 = 9$

• Then exponents: $3^2 = 9$

• Multiplication: $6 \times 9 = 54$

• Division: $54 \div 9 = 6$

• Addition: $3 + 6 = 9$

Algebraic Expressions and Simplification

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols.

• Like terms: Terms that have the same variable raised to the same power.

• Combining like terms: Add or subtract coefficients of like terms.

• Distributive property: $a(b + c) = ab + ac$

Example: Simplify $2x + 3x - 4$

Solution: $2x + 3x = 5x$, so the expression simplifies to $5x - 4$.

Solving Linear Equations

Linear equations are equations of the first degree (the variable has an exponent of 1). The goal is to find the value of the variable that makes the equation true.

• One-step equations: $x + b = c$

• Two-step equations: $ax + b = c$

• Equations with variables on both sides: $ax + b = cx + d$

• Equations with parentheses: Use the distributive property first.

Example: Solve $2x + 3 = 11$

Solution:

• Subtract 3 from both sides: $2x = 8$

• Divide both sides by 2: $x = 4$

Translating and Solving Word Problems

Word problems require translating English phrases into algebraic expressions or equations, then solving for the unknown.

• Identify key information and assign variables.

• Write an equation based on the problem statement.

• Solve the equation using algebraic methods.

Example: If a number increased by 7 is 15, what is the number?

Let $x$ be the number. $x + 7 = 15$

Subtract 7: $x = 8$

Evaluation and Grading

• Assignments are completed online using MyMathLab.

• Students are expected to spend at least one hour on homework for each hour of class.

• Letter grades are assigned as follows:

Percentage	Grade
90% - 100%	A
80% - 89%	B
70% - 79%	C
60% - 69%	D
0% - 59%	F

Course Policies and Expectations

• Attend class faithfully and arrive prepared.

• Complete and turn in assignments on time.

• Participate in class discussions and activities.

• Refrain from using cell phones and other distractions during class.

Additional Information

• Disability accommodations are available through the Office of Student Affairs.

• Academic honesty is required; violations may result in disciplinary action.

• Attendance and participation are essential for success in this course.