# MTH107: Developmental Algebra

This list is representative of the materials provided or used in this course. Keep in mind that the actual materials used may vary, depending on the school in which you are enrolled, and whether you are taking the course as Independent Study.

**For a complete list of the materials to be used in this course by your enrolled student, please visit MyInfo**. All lists are subject to change at any time.

Scope & Sequence : Scope & Sequence documents describe *what* is covered in a course (the scope) and also the *order* in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K12 Scope & Sequence documents for each course include:

## Course Overview

This is the first course in a two-year algebra sequence that concludes with Continuing Algebra. In this course, students begin to explore the tools and principles of algebra. Students learn to identify the structure and properties of the real number system; complete operations with integers and other rational numbers; work with square roots and irrational numbers; graph linear equations; solve linear equations and inequalities in one variable; and solve systems of linear equations. Sophisticated virtual manipulatives and online graphing tools help students visualize algebraic relationships.

Developmental Algebra covers fewer topics than a one-year algebra course, providing students with more time to learn and practice key concepts and skills. After completing Developmental Algebra, students will be prepared to take Continuing Algebra.

back to top## Course Outline

### SEMESTER 1

#### Developmental Algebra, Unit 1: Algebra Basics, Part 1

The English word algebra and the Spanish word algebrista both come from the Arabic word al-jabr, 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.

- Semester Introduction
- Foundations
- Foundations Wrap-Up
- Expressions
- Expressions Wrap-Up
- Variables
- Variables Wrap-Up
- Translating Words into Variable Expressions
- Translating Words into Variable Expressions Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 2: Algebra Basics, Part 2

Math can help solve many problems. For example, if Cindy wants to purchase items at the grocery store, she can use math to figure out how much her groceries will cost before she has to pay at the check-out line. Cindy could use Equations to solve this and many more challenging problems.

- Foundations
- Foundations Wrap-Up
- Equations
- Equations Wrap-Up
- Translating Words into Equations
- Translating Words into Equations Wrap-Up
- Replacement Sets
- Replacement Sets Wrap-Up
- Problem Solving
- Problem Solving Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 3: Properties of Real Numbers, Part 1

Every rainbow contains the colors red, orange, yellow, green, blue, indigo, and violet. These seven colors form a set with properties that scientists, engineers, and artists use every day. Numbers can also be grouped into sets, and these number sets have properties that can help solve problems.

- Foundations
- Foundations Wrap-Up
- Number Lines
- Number Lines Wrap-Up
- Sets
- Sets Wrap-Up
- Comparing Expressions
- Comparing Expressions Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 4: Properties of Real Numbers, Part 2

It has been said that there is a reason for everything. Though this statement may not always be true, it is just about always true when it comes to mathematics. For every math problem, there is a reason for every step used to solve it.

- Foundations
- Foundations Wrap-Up
- Number Properties
- Number Properties Wrap-Up
- Distributive Property
- Distributive Property Wrap-Up
- Algebraic Proof
- Algebraic Proof Wrap-Up
- Opposites and Absolute Value
- Opposites and Absolute Value Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 5: Operations with Real Numbers

There are many different 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.

- Foundations
- Foundations Wrap-Up
- Addition 1
- Addition 2
- Addition Wrap-Up
- Subtraction
- Subtraction Wrap-Up
- Multiplication
- Multiplication Wrap-Up
- Reciprocals and Division
- Reciprocals and Division Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 6: 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 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 solve many real-world problems.

- Foundations
- Foundations Wrap-Up
- Addition and Subtraction Equations
- Addition and Subtraction Equations Wrap-Up
- Multiplication and Division Equations 1
- Multiplication and Division Equations 2
- Multiplication and Division Equations Wrap-Up
- Multiple Transformations
- Multiple Transformations Wrap-Up
- Variables on Both Sides of an Equation
- Variables on Both Sides of an Equation Wrap-Up
- Transforming Formulas
- Transforming Formulas Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 7: Semester Review and Test

- Semester Review
- Semester Test

### SEMESTER 2

#### Developmental Algebra, Unit 1: 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.

- Foundations
- Foundations Wrap-Up
- Inequalities
- Inequalities Wrap-Up
- Solving Inequalities
- Solving Inequalities Wrap-Up
- Combined Inequalities
- Combined Inequalities Wrap-Up
- Absolute Value Equations and Inequalities
- Absolute Value Equations and Inequalities Wrap-Up
- Applications: Inequalities
- Applications: Inequalities Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 2: 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.

- Foundations
- Foundations Wrap-Up
- Ratios 1
- Ratios 2
- Ratios Wrap-Up
- Proportions
- Proportions Wrap-Up
- Percents 1
- Percents 2
- Percents Wrap-Up
- Applications: Percents
- Applications: Percents Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 3: Linear Equations and Inequalities, Part 1

You’ve probably heard the phrase, “That’s where I draw the line!” In algebra, this expression can be taken literally. Linear functions and their graphs play an important role in the never-ending quest to model the real world.

- Foundations
- Foundations Wrap-Up
- Graphs
- Graphs Wrap-Up
- Equations in Two Variables
- Equations in Two Variables Wrap-Up
- Lines and Intercepts
- Lines and Intercepts Wrap-Up
- Slope
- Slope Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 4: Linear Equations and Inequalities, Part 2

Equations of lines provide useful information about many real-world situations. But how do you write the equation of a line? The answer depends on what information you have about the line to begin with.

- Foundations
- Foundations Wrap-Up
- Slope-Intercept Form
- Slope-Intercept Form Wrap-Up
- Point-Slope Form
- Point-Slope Form Wrap-Up
- Parallel and Perpendicular Lines
- Parallel and Perpendicular Lines Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 5: Linear Equations and Inequalities, Part 3

The formula F = 1.8C + 32 is a linear equation. It can be used to change a temperature from degrees Celsius to Fahrenheit. Linear equations like these are sometimes called models that can help us solve real world problems.

- Foundations
- Foundations Wrap-Up
- Equations from Graphs
- Equations from Graphs Wrap-Up
- Applications: Linear Models
- Applications: Linear Models Wrap-Up
- Graphing Linear Equations
- Graphing Linear Equations Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 6: 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, they have at least one point in common. Finding the point at which they meet can help solve problems in the real world.

- Foundations
- Foundations Wrap-Up
- Systems of Equations
- Systems of Equations Wrap-Up
- Substitution Method
- Substitution Method Wrap-Up
- Linear Combination
- Linear Combination Wrap-Up
- Applications: Systems of Linear Equations
- Applications: Systems of Linear Equations Wrap-Up
- Systems of Linear Inequalities
- Systems of Linear Equations Wrap-Up
- Unit Review
- Unit Test

#### Developmental Algebra, Unit 7: Semester Review and Test

- Semester Review
- Semester Test

### K12 Scope & Sequence documents for each course include:

- Course Overview (as seen above)
- Course Outline
- Lesson Time and Scheduling