Greetings, this is Mrs. C, The Innovative Tutor. If you seek a clear, straightforward approach to mastering math concepts, this is the class for you. While I employ a variety of teaching methods, my primary objective is to ensure that students thoroughly understand and master the material. My goal is to foster learning and knowledge acquisition.

The term “teacher” signifies someone who is adept at teaching. A good teacher is one who can explain and demonstrate concepts in multiple ways to accommodate different learners and learning styles. Moreover, a good teacher is also a good learner, adapting their teaching methods based on how their students learn. This is the standard I strive to achieve in my classes.

This course introduces the fundamental concepts of algebra, catering to students with diverse backgrounds and learning styles. Each topic builds upon previously covered material, highlighting the cohesiveness and structure of mathematics. Students enrolled in Basic Mathematics and Pre-algebra classes often face unique challenges. Many have struggled in previous math courses, believing they understand some math while their foundational knowledge remains incomplete. Additionally, these students need to develop essential skills beyond the course content, such as study techniques, time management, and coping with math anxiety.

Coverage and Scope
Pre-algebra employs a nontraditional approach in its content presentation. The initial stages are designed as a series of small, manageable steps to help students build confidence in their ability to succeed. The sequence of topics has been meticulously planned to highlight the logical progression of the course, ensuring a comprehensive understanding of each concept.

Chapter 1: Whole Numbers
Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is thoroughly modeled and explained. As each operation is introduced, we also cover algebraic notation, operation signs, translating algebraic expressions into word phrases, and practical applications.
Lesson 1  
 Part 1.1 Place Value, Rounding, & Arithmetic
 Part 1.2 Number Classification - Real and Absolute Value

Lesson 2
 Part 1.3 Factors - Prime Factorization
 Part 1.4 Exponents
 Part 1.5 Greatest Common Factor & Least Common Multiple

Lesson 3
Part 1.6 Fractions

Lesson 4
Part 1.7 Ratios and Proportions

Lesson 5
Part 1.8 Fractions 
Part 1.9 Decimal Equivalents

Lesson 6
Part 1.10 Percent - Basics

Lesson 7 
Part 1.11 Percents, & Bases & Applications



Chapter 2: The Language of Algebra
Mathematical vocabulary as it applies to the whole numbers is presented. The use of variables, which
distinguishes algebra from arithmetic, is introduced early in the chapter, and the development of and practice with arithmetic concepts use variables as well as numeric expressions. In addition, the difference between expressions and equations is discussed, word problems are introduced, and the process for   solving one-step equations is modeled.
Lesson 2  
Part 2.1 Use the Language of Algebra                  
Part 2.2 Evaluate, Simplify, and Translate Expressions
Part 2.3 Solving Equations Using the Subtraction and Addition 

Properties of Equality
Lesson 3 
 Part 2.4 Find Multiples and Factors
Part 2.5 Prime Factorization and the Least Common Multiple

Chapter 3: Integers
While introducing the basic operations with negative numbers, students continue to practice simplifying,
evaluating, and translating algebraic expressions. The Division Property of Equality is introduced and used to solve one-step equations.
Lesson 4 Friday, December 8, 2023 Part 3.1 Introduction to Integers
 Part 3.2 Add Integers
 Part 3.3 Subtract Integers

Lesson 5  
Part 3.4 Multiply and Divide Integers
Part 3.5 Solve Equations Using Integers; Division Property of 
Equality

Chapter 4: Fractions
Fraction circles and bars are used to help make fractions real and to develop operations on them. Students
continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication
Property of Equality to solve equations involving fractions.
Lesson 6 
Part 4.1 Visualize Fractions
Part 4.2 Multiply and Divide Fractions

Lesson 7  
Part 4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Lesson 8  
Part 4.4 Add and Subtract Fractions with Common Denominators
Part 4.5 Add and Subtract Fractions with Different Denominators
Part 4.6 Add and Subtract Mixed Numbers

Lesson 9  
Part 4.7 Solve Equations with Fractions

Chapter 5: Decimals
Basic operations with decimals are presented, as well as methods for converting fractions to decimals and vice versa. Averages and probability, unit rates and unit prices, and square roots are included to provide opportunities to use and round decimals.
Lesson 10 
Part 5.1 Decimals
Part 5.2 Decimal Operations
Part 5.3 Decimals and Fractions

Lesson 11  
Part 5.4 Solve Equations with Decimals

Lesson 12  
Part 5.5 Averages and Probability
Part 5.6 Ratios and Rate

Lesson 13  
Part 5.7 Simplify and Use Square Roots

Chapter 6: Percents
Conversions among percents, fractions, and decimals are explored. Applications of percent include calculating sales tax, commission, and simple interest. Proportions and solving percent equations as proportions are addressed as well
Lesson 14  
6.1 Understand Percent
Solve General Applications of Percent
Solve Sales Tax, Commission, and Discount Applications

Lesson 15  
6.4 Solve Simple Interest Applications

Lesson 16  
6.5 Solve Proportions and their Applications

Chapter 7: The Properties of Real Numbers
The properties of real numbers are introduced and applied as a culmination of the work done thus far, and to prepare students for the upcoming chapters on equations, polynomials, and graphing.
Lesson 17  
7.1 Rational and Irrational Numbers

Lesson 18  
7.2 Commutative and Associative Properties
7.3 Distributive Property
7.4 Properties of Identity, Inverses, and Zero

Lesson 19  
7.5 Systems of Measurement

Chapter 8: Solving Linear Equations
A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with
constants on both sides, variables on both sides, variables and constants on both sides, and fraction and decimal coefficients.
Lesson 20  
Part 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
Part 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
Part 8.3 Solve Equations with Variable and Constants on Both Sides

Lesson 21  
Part 8.4 Solve Equations with Fraction or Decimal Coefficients

Chapter 9: Math Models and Geometry
The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean
Theorem, and volume and surface areas of solids. Distance-rate-time problems and formulas are included as well.
Lesson 22  
Part 9.1 Use a Problem-Solving Strategy
Part 9.2 Solve Money Applications

Lesson 23  
Part 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
Part 9.4 Use Properties of Rectangles, Triangles, and Trapezoids

Lesson 24  
Part 9.5 Solve Geometry Applications: Circles and Irregular Figures
Part 9.6 Solve Geometry Applications: Volume and Surface Area

Lesson 25  
Part 9.7 Solve a Formula for a Specific Variable

Chapter 10: Polynomials
Adding and subtracting polynomials is presented as an extension of prior work on combining like terms. Integer exponents are defined and then applied to scientific notation. The chapter concludes with a brief introduction to factoring polynomials.
Lesson 26  
Part 10.1 Add and Subtract Polynomials

Lesson 27  
Part 10.2 Use Multiplication Properties of Exponents

Lesson 28  
Part 10.3 Multiply Polynomials
Part 10.4 Divide Monomials

Lesson 29  
Part 10.5 Integer Exponents and Scientific Notation

Lesson 30  
Part 10.6 Introduction to Factoring Polynomials

Chapter 11: Graphs
This chapter is placed last so that all of the algebra with one variable is completed before working with linear equations in two variables. Examples progress from plotting points to graphing lines by making a table of solutions to an equation. Properties of vertical and horizontal lines and intercepts are included. Graphing linear equations at the end of the course gives students a good opportunity to review evaluating expressions and solving equations
Lesson 31   
Part 11.1 Use the Rectangular Coordinate System

Lesson 32  
Part 11.2 Graphing Linear Equations

Lesson 33  
Part 11.3 Graphing with Intercepts

Lesson 34  
                       Part 11.4 Understand Slope of a Line