PreAlgebra
912
Course Overview
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Students take a broader look at computational and problemsolving skills while learning the language of algebra. Students translate word phrases and sentences into mathematical expressions; analyze geometric figures; solve problems involving percentages, ratios, and proportions; graph different kinds of equations and inequalities; calculate statistical measures and probabilities; apply the Pythagorean theorem; and explain strategies for solving realworld problems. Online lessons provide demonstrations of key concepts, as well as interactive problems with contextual feedback. A textbook supplements the online material. Students who take PreAlgebra are expected to have mastered the skills and concepts presented in the Fundamentals of Geometry and Algebra course (or equivalent).
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Course Outline
SEMESTER ONE
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Unit 1: The Basics
Let us start at the very beginning; it is an incredibly good place to start. Just as you need to know basic grammar and vocabulary as you begin to learn any language, you need to know some basic building blocks as you begin to learn algebra.
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Order of Operations

Variable Expressions

Writing Expressions for Word Phrases

Comparing Expressions

Replacement Sets

Related Equations

Solving Problems
Unit 2: Addition and Subtraction
If you have two oranges and a friend gives you three oranges, how many do you have? If you then give four oranges to your friend, how many are you left with? This sort of addition and subtraction problem with passing fruit back and forth is the type of simple math you have done since you were young. When you expand your addition and subtraction skills to negative numbers and decimals, you can solve many more complicated problems.
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Integers on a Number Line

Adding Integers

Subtracting Integers

Decimals on a Number Line

Adding Decimals

Subtracting Decimals

Addition and Subtraction Properties

Equations Involving Addition and Subtraction

Addition and Subtraction Applications
Unit 3: Multiplication and Division
Isaac Newton's third law of motion is often paraphrased as “for every action, there is an equal and opposite reaction.” Just as forces come in pairs, so can mathematical operations. Multiplication and division are inverse operations. They undo each other and can both be used to solve many types of problems.
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Multiplying Integers and Decimals

Dividing Integers and Decimals

Multiplication and Division Properties

Rounding and Estimation

Equations Involving Multiplication and Division

Multiplication and Division Applications
Unit 4: Fractions
Every fraction can be written as a decimal and every decimal can be written as a fraction. As a result, you could do just about all math with only fractions or only decimals, but decimals are used for certain applications just as fractions are used for others. For example, carpenters use fractions and mixed numbers quite a bit; anybody building a house or a deck deals with lots of fractions.
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Equivalent Fractions

Multiplying Fractions

Dividing Fractions

Common Denominators

Adding and Subtracting Fractions

Working with Improper Fractions and Mixed Numbers

Multiplying and Dividing Mixed Numbers

Equations with Fractions and Mixed Numbers
Unit 5: Combined Operations
Many yachts can be powered by the wind, by a gas engine, or both. A hybrid automobile can run on gasoline or electric power. These combinations are powerful. Combining addition or subtraction with multiplication or division is powerful as well. You can use equations and expressions with mixed operations to solve many complex problems.
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The Distributive Property

Like Terms

Expressions with Mixed Operations

Equations with Mixed Operations

Error Analysis

Inequalities
Unit 6: Number Properties
Astronomers study things that are extremely far away. For example, the Horsehead Nebula is about 14,000 trillion kilometers away. On the other extreme, molecular geneticists study things that are ridiculously small. A double helix of DNA has a diameter of about one nanometer (a billionth of a meter.) With exponents, you can describe very great or exceedingly small distances.
Positive Exponents
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Factors and Primes

GCF and Relative Primes

Negative Exponents

Powers of Ten

Scientific Notation
Unit 7: Geometry Basics
Shapes such as polygons and circles provide us with shelter, art, and transportation. Some artists use geometric shapes in their art, but most painters and photographers use rectangular frames to surround their art. Look at any art museum, and you will see triangles, rectangles, and other polygons in the structure of the building and in the artwork inside.
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Points, Lines and Planes

Rays and Angles

Parallel Lines and Transversals

Triangles

Polygons

Circles

Transformations

Congruence
Unit 8: Semester Review and Test

Semester Review

Semester Test
SEMESTER TWO
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Unit 1: Ratio, Proportion and Percent
Model builders use ratios and percents to describe how their models compare to real objects. They can use proportions to figure out the length of every item in the model.
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Ratio

Proportion

Percents, Fractions and Decimals

Similarity and Scale

Working with Percent

Percent of Increase or Decrease

Simple Interest
Unit 2: Analytic Geometry
A pilot uses numbers to locate the airport she is flying to. An air traffic controller uses numbers on a radar screen to locate each airplane approaching the airport. Without a system of locating points, airplanes would have a hard time getting anywhere safely.
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Points on the Plane

TwoVariable Equations

Linear Equations and Intercepts

Slope

Problem Solving

Relations and Functions

Systems of Linear Equations
Unit 3: Perimeter and Area
You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass for a piece of stainedglass art, stainedglass artists need to understand perimeter and area to solve many practical problems.
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Types of Polygons

Perimeter

Areas of Rectangles and Triangles

Special Quadrilaterals

Areas of Special Quadrilaterals

Circumference

Areas of Circles
Unit 4: Square Roots and Right Triangles
Since ancient times, people have used right triangles to survey land and build structures. Even before Pythagoras was born, the relationship between the side lengths of a right triangle has been essential to anyone building just about any structure, including pyramids, houses, skyscrapers, and bridges.
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Rational Square Roots

Irrational Square Roots

The Pythagorean Theorem

The Distance Formula

Special Types of Triangles

Trigonometric Ratios
Unit 5: Solid Figures
Gaspowered engines are driven by little explosions that move pistons up and down in cylinders. When you add up the volume of all the cylinders, you get the displacement of the engine. For instance, each cylinder in a fourcylinder, 1000 cc engine has a volume of 250 cubic centimeters. Engineers and mechanics must accurately compute volume when they build or maintain engines.
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Volume and Capacity

Volumes of Prisms and Cylinders

Volumes of Pyramids and Cones

Surface Area

Surface Areas of Prisms and Cylinders
Unit 6: Counting and Probability
How many apples have mass between 100 and 200 grams? How many are bruised? How many are not yet ripe? Checking every single apple would probably be impractical, but if you understand probability and sampling, you could make a good estimate.
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Counting Principles

Permutations

Combinations

Probability

Mutually Exclusive Events

Samples and Prediction
Unit 7: Statistics
Data are everywhere. When you look at a group of people, you could use many numbers to describe them. How tall are they? How long is their hair? How old are they? What is their gender? What color are their eyes? Statistics helps you make sense of data.
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Graphs

Measures of Center

StemandLeaf Plots

BoxandWhisker Plots

Frequency Tables and Histograms
Unit 8: Semester Review and Test

Semester Review

Semester Test