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Pre-Algebra Course Curriculum |
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Chapter 1: Introduction to Algebra Terms and
Concepts
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This chapter introduces students to basic terms and concepts used in algebra. Time
is taken to ensure the student understands basic number operations, variables and
their applications. Additionaly, the student gains a fundamental sense of equations, inequalities and their
solutions.
Sections:
• Number Operations
• Variables
• Order of Operations
• Translating Verbal and Algebraic Phrases
• Equations/Inequalities/Solutions
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Chapter 2: Real Numbers and Simplifying Variable Expressions |
This chapter focuses on getting the student to master working with the Real Numbers.
Students learn the rules of integers and practice through many examples. Also, students
will learn to apply the Distributive property and simplify variable expressions
by combining like terms.
Sections:
• Real Numbers/Simplifying Variable Expressions
• Real Number System
• Adding Real Numbers
• Subtracting Real Numbers
• Multiplying and Dividing Real Numbers
• Distributive Property
• Simplifying by Combining Like Terms
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Chapter 3: Fractions and Decimals
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This chapter reviews how to work with fractions. Although it is assumed students
posses these skills, time is taken to ensure the student has mastered the procedures
to perform operations involving fractions.
Sections:
• Introduction to Fractions and Decimals
• Least Common Multiple/Denominator
• Multiplying and Dividing Fractions
• Adding and Subtracting Fractions
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Chapter 4: Solving Equations
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The chapter breaks down the steps to solve multi-step linear equations. Students
will build up their skills as they progress from one and two-step equations to more
advance equations. Core concepts involved will be reviewed to include the distributive
property and combining like terms.
Sections:
• One Step Equations
• Solving Two Step Equations
• Solving Multi-Step Equations
• Formulas and Literal Equations
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Chapter 5: Inequalities
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In this chapter students will apply their equation solving skills to solve linear
inequalities. Basic concepts and terms are introduced first, along with how to graph
inequalities. Also, a section is dedicated to explain and teach how to solve absolute
value equations.
Sections:
• Linear Inequalities
• Compound Inequalities
• Graphing Linear Inequalities in Two Variables
• Absolute Value Inequalities
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Chapter 6: Graphing Linear Equations
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This very important chapter walks the student
step-by-step to master how to graph linear equations. Concepts involving the coordinate plane, slope and methods to graph
lines are thoroughly reviewed and introduced.
Upon completion of the chapter students will gain the necessary knowledge and skills
needed to learn more advance topics
involving linear equations.
Sections:
• Graphing Lines with One Variable
• Graphing Lines with Two Variables
• The Slope of a Line
• Slope Intercept Method
• XY Intercept Method
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Chapter 7: Writing the Equations
of Lines
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The chapter builds on the student’s prior knowledge and skill of linear
equations. Various methods to find and write the equation of a line are introduced
and practiced. The chapter focuses on the proper way to set-up and use formulas
to write linear equations. Additional related topics are explored to include linear
models, linear
regression and word problems.
Sections:
• Using Slope-Intercept Form
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Using Point-Slope intercept
• Given the Slope and a Point
• Given Two Points
• Standard
Form of Linear Equations
• Best Fitting Line
• Linear Models/Word Problems
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Chapter
8: Introduction to Systems
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Understanding systems and the methods to solve them are
vital in algebra. This chapter introduces the student to systems and what their
solutions represent. Techniques
to solve systems
will build from the student’s prior
knowledge of solving linear equations. Upon completion of the chapter a student
will have a solid skill set in systems that prepares them for Algebra 1 and 2.
Sections:
• Solving Systems by Graphing
• Solving Systems Substitution Method
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Solving Systems by Elimination/Linear Combination
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Chapter 9: Absolute Value |
Absolute
value problems can be challenging for some students to grasp. Time is taken to teach
students core concepts and build understanding. Students will learn how
to graph
absolute value functions and apply the steps to solve absolute value equations/inequalities.
Sections:
• Introduction to Absolute Value
• Graphing Absolute Value Equations
• Solving Absolute Value Equations
• Absolute Value Inequalities
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Chapter 10: Powers
and Exponents
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This chapter covers the rules of
powers and exponents a student needs to learn in
algebra. Also, important applications of these rules are
covered to include scientific notation, compound interest and exponential growth
and decay.
Sections:
• Product and Power Rules of Exponents
• Negative and Zero
Exponents Rules
• Division Rules of Exponents
• Scientific Notation
• Compound Interest
• Exponential Growth and Decay
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Chapter 11: Polynomials
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Polynomials are the key building
blocks of algebra. The chapter starts by covering the parts of a polynomial and
related terminology. Students then learn how to perform
various polynomial operations, and a special focus is placed on avoiding common mistakes. Lastly, there is a section
dedicated to introduce quadratic equations which are extremely important in more
advance topics in algebra.
Sections:
• Introduction to Polynomials
• Adding and Subtracting Polynomials
• Multiplying Polynomials
• Introduction to Quadratic Equations
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Chapter 12: Rational Expressions |
This chapter takes the student through fundamental
rational expressions to include ratios, proportions, percent and variation. Students
will learn different methods to solve rational expression problems. The section
on simplifying rational algebraic expressions starts by reviewing basic examples
using numbers before introducing variable examples.
Sections:
• Ratios and Proportions
• Percent
• Direct and Inverse Variation
• Simplifying Rational Expressions
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Chapter
13: Introduction to Functions and Relations
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Functions and relations transcend all
through mathematics. This chapter explains core concepts at the Pre-Algebra level
and prepares the student for more advance study of the topic. Time is taken to
explain the difference between a function and relation; and introduce the student
to the language of functions to include the domain,
range and linear/nonlinear
functions.
Sections:
• Introduction to Functions and Relations
• Graphing Functions
• Linear and Nonlinear Functions
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Chapter 14: Area and Volume
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This chapter explores
the link between algebra and geometry. Basic formulas for area and volume are covered. Also, a section is dedicated to explain concepts related to circles to include area,
volume, diameter, radius, and pi.
Sections:
• Area of Basic Figures
• Circles: Area
and Circumference
• Surface Area of Basic Figures
• Volume of Basic Figures
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Chapter
15: Right Triangle Theorems and Formulas
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Properties of right triangles form the
basis of many more advance topics in algebra, geometry and trigonometry. Sections
in the chapter introduce fundamental theorems and formulas to include the distance
and mid-point formula and the Pythagorean Theorem.
Sections:
• The Distance and
Mid-Point Formula
• The Pythagorean Theorem
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