Algebra
912
Course Overview
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Students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts central to the abstraction and generalization that algebra makes possible. Students learn to use number properties to simplify expressions or justify statements; describe sets with set notation and find the union and intersection of sets; simplify and evaluate expressions involving variables, fractions, exponents, and radicals; work with integers, rational numbers, and irrational numbers; and graph and solve equations, inequalities, and systems of equations. They learn to determine whether a relation is a function and how to describe its domain and range; use factoring, formulas, and other techniques to solve quadratic and other polynomial equations; formulate and evaluate valid mathematical arguments using various types of reasoning; and translate word problems into mathematical equations and then use the equations to solve the original problems. Students who take Algebra are expected to have mastered the skills and concepts presented in the K12 PreAlgebra course (or equivalent).
Course Outline
SEMESTER ONE
Unit 1: Algebra Basics
The English word algebra and the Spanish word algebrista both come from the Arabic word aljabr, which means "restoration". A barber in medieval times often called himself an algebrista. The algebrista also was a bonesetter who restored or fixed bones. Mathematicians today use algebra to solve problems. Algebra can find solutions and "fix" certain problems that you encounter.

Semester Introduction

Expressions

Variables

Translating Words into Variable Expressions

Equations

Translating Words into Equations

Replacement Sets

Problem Solving
Unit 2: Properties of Real Numbers
There are many kinds of numbers. Negative numbers, positive numbers, integers, fractions, and decimals are just a few of the many groups of numbers. What do these varieties of numbers have in common? They all obey the rules of arithmetic. They can be added, subtracted, multiplied, and divided.

Number Lines

Sets

Comparing Expressions

Number Properties

Measurement, Precision, and Estimation

Distributive Property

Algebraic Proof

Opposites and Absolute Value
Unit 3: Operations with Real Numbers
There are many kinds of numbers. Negative numbers, positive numbers, integers, fractions, and decimals are just a few of the many groups of numbers. What do these varieties of numbers have in common? They all obey the rules of arithmetic. They can be added, subtracted, multiplied, and divided.

Addition

Subtraction

Multiplication

Reciprocals and Division

Applications: Number Problems
Unit 4: Solving Equations
The Greek mathematician Diophantus is often called "the father of algebra." His book Arithmetica described the solutions to 130 problems. He did not discover all of these solutions himself, but he did collect many solutions that had been found by Greeks, Egyptians, and Babylonians before him. Some people of long ago obviously enjoyed doing algebra. It also helped them—and can help you—solve many realworld problems.

Addition and Subtraction Equations

Multiplication and Division Equations

Patterns

Multiple Transformations

Variables on Both Sides of an Equation

Transforming Formulas

Estimating Solutions

Cost Problems
Unit 5: Solving Inequalities
Every mathematician knows that 5 is less than 7, but when is y < x? An inequality symbol can be used to describe how one number compares to another. It can also indicate a relationship between values.

Inequalities

Solving Inequalities

Combined Inequalities

Absolute Value Equations and Inequalities

Applications: Inequalities
Unit 6: Applying Fractions
What do a scale drawing, a bicycle's gears, and a sale at the local store all have in common? They all present problems that can be solved using equations with fractions.

Ratios

Proportions

Unit Conversions

Percents

Applications: Percents

Applications: Mixture Problems
Unit 7: Linear Equations and Inequalities
You have probably heard the phrase, "That's where I draw the line!" In algebra, you can take this expression literally. Linear functions and their graphs play an important role in the neverending quest to model the real world.

Equations in Two Variables

Graphs

Lines and Intercepts

Slope

Using Slope as a Rate

SlopeIntercept Form

PointSlope Form

Parallel and Perpendicular Lines

Equations from Graphs

Applications: Linear Models

Graphing Linear Inequalities

Inequalities from Graphs
Unit 8: Systems of Equations
When two people meet, they often shake hands or say "hello" to each other. Once they start talking to each other, they can find out what they have in common. What happens when two lines meet? Do they say anything? Probably not, but whenever two lines meet, you know they have at least one point in common. Finding the point at which they meet can help you solve problems in the real world.

Systems of Equations

Substitution Method

Linear Combination

Linear Combination with Multiplication

Applications: Systems of Linear Equations

Systems of Linear Inequalities
Unit 9: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
Unit 1: Relations and Functions
A solar cell is a little machine that takes in solar energy and puts out electricity. A mathematical function is a machine that takes in a number as an input and produces another number as an output. There are many kinds of functions. Some have graphs that look like lines, while others have graphs that curve like a parabola. Functions can take other forms as well. Not every function has a graph that looks like a line or a parabola. Not every function has an equation. The important thing to remember is that if you put any valid input into a function, you will get a single result out of it.

Semester Introduction

Relations

Functions

Function Equations

Order of Operations

Absolute Value Functions

Direct Linear Variation

Quadratic Variation

Inverse Variation

Translating Functions
Unit 2: Rationals, Irrationals, and Radicals
Are rational numbers very levelheaded? Are irrational numbers hard to reason with? Not really, but rational and irrational numbers have things in common and things that make them different.

Rational Numbers

Terminating and Repeating Numbers

Square Roots

Dimensional Analysis

Irrational Numbers

Evaluating and Estimating Square Roots

Radicals with Variables

Using Square Roots to Solve Equations

The Pythagorean Theorem

Higher Roots
Unit 3: Working with Polynomials
Just as a train is built from linking railcars together, a polynomial is built by bringing terms together and linking them with plus or minus signs. You can perform basic operations on polynomials in the same way that you add, subtract, multiply, and divide numbers.

Overview of Polynomials

Adding and Subtracting Polynomials

Multiplying Monomials

Multiplying Polynomials by Monomials

Multiplying Polynomials

FOIL
Unit 4: Factoring Polynomials
A polynomial is an expression that has variables that represent numbers. A number can be factored, so you should be able to factor a polynomial, right? Sometimes you can and sometimes you cannot. Finding ways to write a polynomial as a product of factors can be quite useful.

Factoring Integers

Dividing Monomials

Common Factors of Polynomials

Dividing Polynomials by Monomials

Factoring Perfect Squares

Factoring Differences of Squares

Factoring Quadratic Trinomials

Factoring Completely

Finding Roots of a Polynomial
Unit 5: Quadratic Equations
Solving equations can help you find answers to many kinds of problems in your daily life. Linear equations usually have one solution, but what about quadratic equations? How can you solve them and what do the solutions look like?

Solving Perfect Square Equations

Completing the Square

Scientific Notation

The Quadratic Formula

Solving Quadratic Equations

Equations and Graphs: Roots and Intercepts

Applications: Area Problems

Applications: Projectile Motion
Unit 6: Rational Expressions
A fraction always has a number in the numerator and in the denominator. However, those numbers can actually be expressions that represent numbers, which means you can do all sorts of interesting things with fractions. Fractions with variable expressions in the numerator and denominator can help you solve many kinds of problems.

Simplifying Rational Expressions

Multiplying Rational Expressions

Dividing Rational Expressions

Like Denominators

Adding and Subtracting Rational Expressions
Unit 7: Logic and Reasoning
Professionals use logical reasoning in a variety of ways. Just as lawyers use logical reasoning to formulate convincing arguments, mathematicians use logical reasoning to formulate and prove theorems. Once you have mastered the uses of inductive and deductive reasoning, you will be able to make and understand arguments in many areas.

Reasoning and Arguments

Hypothesis and Conclusion

Forms of Conditional Statements

Using Data to Make Arguments

Inductive and Deductive Reasoning

Algebraic Proof

Counter Example
Unit 8: Semester Review and Test

Semester Review

Semester Test
SUPPLEMENTAL UNITS
Two supplemental units provide additional coursework. Measurement and Geometry provides some of the essentials for beginning geometry students and Counting, Probability, and Statistics provides a solid foundation for further studies in statistics and probability.
A–1: Measurement and Geometry
A tessellation is a way of repeating a shape over and over again to cover a plane surface. The artist Maurits Cornelis (M.C.) Escher was fascinated with tessellations. He used tessellations and geometric ideas such as points, segments, angles, and congruence to make lots of beautiful, interesting art.

Points, Lines, and Angles

Pairs of Angles

Triangles

Polygons

Congruence and Similarity

Area

Volume

Scale
A–2: Counting, Probability, and Statistics
How much corn can a farmer get from an acre of land? Which countries export the most corn? How has the price of corn changed over time and how will it change moving forward? Data are all around us. With a good understanding of probability and statistics, people can make better decisions.

Counting

Permutations and Combinations

Probability

Combined Probability

Graphs

Summary Statistics

Frequency Distributions

Samples and Prediction
f Independent and Dependent Event