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Pre-Algebra, Semester 1 (MTH113A)

Pre-Algebra, Semester 1 (MTH113A)

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Quick Overview

In this course, students take a broader look at computational and problem-solving 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 real-world problems. Lessons provide demonstrations of key concepts as well as interactive problems with contextual feedback. A textbook supplements the online material. This is the first semester of a two semester course.
Teacher-Led Course (one-time payment)   $450.00

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Unit 1: The Basics

Let's start at the very beginning; it's a very 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.

  • Semester Introduction
  • 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 very young. When you expand your addition and subtraction skills to negative numbers and decimals, you can solve many more complicated problems.

  • Integers on a Number Line
  • Adding Integers
  • Subtracting Integers
  • Discuss: 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.

  • 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.

  • Equivalent Fractions
  • Multiplying Fractions
  • Dividing Fractions
  • Discuss: Fractions
  • Common Denominators
  • Adding and Subtracting Fractions
  • Working with Mixed Numbers
  • Multiplying and Dividing Mixed Numbers
  • Equations with Fractions

 Unit 5: Combined Operations

Many yachts can be powered by the wind, by a gas engine, or by both. A hybrid automobile can run on gasoline or electric power. These combinations are very 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.

  • 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 very, very far away. For example, the Horsehead Nebula is about 14,000 trillion kilometers away. At the other extreme, molecular geneticists study things that are very, very 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 very small distances.

  • Positive Exponents
  • 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.

  • Points, Lines, and Planes
  • Rays and Angles
  • Parallel Lines and Transversals
  • Discuss: Shapes
  • Triangles
  • Polygons
  • Circles
  • Transformations
  • Congruence

 Unit 8: Semester Review and Test


Additional Information

Course Length 4 Months
Prerequisites N/A
Course Materials

Many K12 courses utilize physical materials in addition to the online content.  These materials may include the following.

Standard Kits

STANDARD kits contain K12 course materials that are required for completion of the course.  These kits include K12 authored materials and/or difficult to procure materials that a student needs to complete a course. Printed reference guides are not included in Standard kits.


CONSUMABLE kits contain only those materials from the standard kit that are intended for one time use. Families who purchase a Standard kit for Child A could later purchase a Consumable kit for Child B to complete the same course.


Offered for added convenience, ADDITIONAL kits contain easily obtained materials needed for the course which a family may already have in their home. 

Coach and/or Student Reference Guides are available for purchase with some courses.  Electronic versions of these reference guides are also available within digital courses.

Course Start Date

Courses Taught by a K12 Teacher

Courses with a teacher have designated start dates throughout Fall, Spring, and Summer. Full-year courses last 10 months and semester courses last 4 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.

Teacher Assisted Yes, this course is taught by a K12 International Academy teacher. If you are looking for a teacher-supported option with additional flexibility and year-round start dates, click here to learn about the Keystone School, another K12 online private schooling option.
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To use this course, you'll need a computer with an Internet connection.  Some courses require additional free software programs, which you can download from the Internet.

Hardware and Browsers (Minimum Recommendations)

Windows OS

  • CPU: 1.8 GHz or faster processor (or equivalent)

  • RAM: 1GB of RAM

  • Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher

  • At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)


Mac OS

  • CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

  • RAM: 1GB of RAM

  • Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)

Internet Connections

It is highly recommended that a broadband connection be used instead of dial up.


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