Pre-Algebra Course Syllabus and Foundations for Intermediate Algebra

Course Overview

This Pre-Algebra course serves as a foundational bridge between elementary mathematics and Algebra. It introduces students to key algebraic concepts and prepares them for Intermediate Algebra. The curriculum emphasizes problem-solving, reasoning, estimation, and real-world applications, using technology and cooperative learning.

Course Structure and Evaluation

• Textbook: Martín-Gay, E. Pre-Algebra. 9th Edition. 2025. Pearson Education

• Grading: Based on tests, quizzes, homework, projects, and classwork. Grades are calculated by points and converted to percentages and letter grades.

• Exams: Weekly quizzes, chapter tests, mid-term, and final exams.

• Homework: Frequent assignments, with penalties for late submissions.

Course Schedule and Main Topics

The course is organized into weekly chapters, each focusing on fundamental mathematical concepts. Many of these topics are directly relevant to Intermediate Algebra, especially those covering algebraic expressions, linear equations, polynomials, factoring, exponents, graphing, and statistics.

Chapter 1: Whole Numbers

• Place Value and Names for Numbers: Understanding the value of digits in numbers and reading tables.

• Operations: Addition, subtraction, multiplication, and division of whole numbers.

• Exponents and Order of Operations: Introduction to powers and the correct sequence for evaluating expressions.

• Variables and Algebraic Expressions: Basic introduction to using symbols to represent numbers.

Chapter 2: Integers and Introduction to Solving Equations

• Integers: Definition and operations (addition, subtraction, multiplication, division).

• Order of Operations: Reinforcement of PEMDAS/BODMAS rules.

• Solving Equations: Using addition and multiplication properties to solve simple equations.

Chapter 3: Solving Equations and Problem Solving

• Simplifying Algebraic Expressions: Combining like terms and using distributive property.

• Solving Linear Equations in One Variable: Step-by-step methods for isolating the variable.

• Word Problems: Applying equations to real-life scenarios.

Chapter 4: Fractions and Mixed Numbers

• Operations with Fractions: Addition, subtraction, multiplication, division, and simplification.

• Least Common Denominator: Finding common denominators for addition/subtraction.

• Solving Equations with Fractions: Techniques for handling fractional equations.

Chapter 5: Decimals

• Operations with Decimals: Addition, subtraction, multiplication, division.

• Order of Operations: Applying rules to decimal expressions.

• Applications: Mean, median, mode, and solving equations with decimals.

Chapter 6: Ratio, Proportion, and Triangle Applications

• Ratios and Rates: Comparing quantities and understanding rates.

• Proportions: Solving equations involving equivalent ratios.

• Square Roots and Pythagorean Theorem: Introduction to roots and geometric applications.

• Congruent and Similar Triangles: Basic geometric properties.

Chapter 7: Percent

• Percents, Decimals, and Fractions: Converting between forms.

• Solving Percent Problems: Using equations and proportions.

• Applications: Sales tax, commission, discount, and interest calculations.

Chapter 8: Graphing and Introduction to Statistics and Probability

• Types of Graphs: Pictographs, bar graphs, histograms, line graphs, circle graphs.

• Rectangular Coordinate System: Introduction to plotting points and paired data.

• Graphing Linear Equations: Basics of plotting lines in two variables.

• Probability: Counting and introductory probability concepts.

Chapter 9: Geometry and Measurements

• Lines and Angles: Definitions and properties.

• Perimeter, Area, Volume, Surface Area: Calculating measurements for various shapes.

• Linear Measurements, Weight, Mass, Capacity, Temperature: Understanding and converting units, including between U.S. and metric systems.

Chapter 10: Exponents and Polynomials

• Adding and Subtracting Polynomials: Combining like terms.

• Multiplication Properties of Exponents: Applying exponent rules.

• Multiplying Polynomials: Using distributive property and FOIL method.

• Introduction to Factoring Polynomials: Basic techniques for factoring.

Key Definitions and Examples

• Variable: A symbol (usually a letter) used to represent a number.

• Algebraic Expression: A combination of numbers, variables, and operations (e.g., $2x + 3$).

• Linear Equation: An equation of the form $ax + b = c$.

• Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication (e.g., $x^2 + 2x + 1$).

• Exponent Rules: $a^m \times a^n = a^{m+n}$, $\frac{a^m}{a^n} = a^{m-n}$, $(a^m)^n = a^{mn}$

• Factoring: Writing a polynomial as a product of its factors (e.g., $x^2 + 2x + 1 = (x + 1)^2$).

• Order of Operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

• Proportion: An equation stating that two ratios are equal, $\frac{a}{b} = \frac{c}{d}$.

• Pythagorean Theorem: $a^2 + b^2 = c^2$ for right triangles.

Sample Table: Grading Scale

Letter Grade	Percentage Range
A	100 – 90%
B	89 – 80%
C	79 – 70%
D	69 – 60%
F	Below 60%

Relevance to Intermediate Algebra

Many chapters in this Pre-Algebra syllabus directly align with the foundational topics of Intermediate Algebra, including real numbers, linear equations, exponents, polynomials, factoring, rational expressions, graphing, and statistics. Mastery of these concepts is essential for success in Intermediate Algebra and further mathematical studies.