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Honors Pre-algebra

Prerequisites: Qualifying math score and completion of grade 5 math or equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Course Code: HPA

Course Description


This is a full-length online Honors Pre-Algebra course for accelerated students. This course is aligned to both Grades 7 and 8 Common Core Mathematics Standards.  In this course, students will be introduced to algebraic concepts through both theory and applications. Modeling and real-world problems are introduced throughout the course. This course focuses on the study of algebraic manipulation and graphical interpretations, and covers topics normally taught in middle school for preparation of Honors Algebra I.

Online course materials, such as videos, notes, interactive webpages, and practice problems with solutions, are provided for the student. Students progress through the course at their own pace and are expected to watch videos and review notes regularly. Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructors via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include homework, chapter exams, and a cumulative midterm and final.

Instructors use virtual classroom software allowing video, voice, text, screen sharing, and whiteboard interaction. Students are strongly encouraged to work on the course at least 1 hour a day, 5 days a week (for a 6-month enrollment), and email their instructors at least once per week.

Topics include:

  • Variables, Expressions, and Arithmetic Review
  • Solving Equations
  • Problem Solving with Equations and Inequalities
  • Exponents
  • Rational Numbers and Applications
  • Geometry
  • Data Analysis and Statistics
  • Probability
  • Square Roots and the Pythagorean Theorem
  • Relations and Functions

Please see the "List of Topics" tab for the full scope and sequence.

Materials Needed

A graphing calculator is required. 

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Variables, Expressions, and Arithmetic Review

  • Variables and Expressions
  • Translating Between Words and Math
  • Introduction to Integers
  • Arithmetic Operations of Integers
  • Absolute Value of Integers
  • Introduction to Exponents
  • Using the Order of Operations
  • Factors, Multiples, and Equivalent Fractions
  • Multiplying and Dividing Fractions and Mixed Numbers
  • Adding and Subtracting Fractions and Mixed Numbers
  • Adding and Subtracting Decimals
  • Multiplying and Dividing Decimals

Solving Equations

  • Properties
  • Simplifying Algebraic Expressions
  • Translating Between Tables and Expressions
  • Equations and Their Solutions
  • Solving Addition and Subtraction Equations
  • Solving Multiplication and Division Equations
  • Solving Equations Containing Integers
  • Solving Equations Containing Fractions and Decimals

Problem Solving with Equations and Inequalities

  • Writing and Solving Two-Step Equations
  • Writing and Solving Multi-Step Equations
  • Solving Equations with Variables on Both Sides
  • Solving Inequalities by Adding or Subtracting
  • Solving Inequalities by Multiplying or Dividing
  • Solving Two-Step Inequalities


  • Product and Power Properties of Exponents
  • Integer Exponents
  • Quotient Properties of Exponents
  • An Application of Exponents: Scientific Notation
  • Introduction to Polynomials
  • Simplifying Polynomials
  • Adding and Subtracting Polynomials
  • Multiplying and Dividing Monomials
  • Multiplying Monomials by Polynomials

Rational Numbers and Applications

  • Rational and Irrational Numbers
  • Working with Rational Numbers
  • Percents
  • Percent Word Problems
  • Ratios and Unit Rates
  • Proportional Relationships
  • Proportions in Equations
  • Simple and Compound Interest
  • Estimating with Percents
  • Percent Increase and Decrease


  • Triangles, Quadrilaterals, Polygons
  • Angles Formed by Transversals
  • Similar Figures
  • Congruent Figures
  • Perimeter
  • Area
  • Circumference and Area of a Circle
  • Introduction to 3D Shapes
  • Volume
  • Surface Area
  • Volume and Surface Area of Spheres
  • Reflections
  • Translations
  • Rotations
  • Dilations


  • Collecting Data
  • Interpreting Data
  • Organizing Data
  • Line Graphs
  • Bar Graphs and Histograms
  • Circle Graphs
  • Box-and-Whisker Plots
  • Scatter Plots and Two Way Tables


  • Introduction to Probability
  • Probability and Odds
  • Experimental Probability
  • Permutations and Combinations
  • Probability of Compound Events
  • Independent and Dependent Events

Square Roots and the Pythagorean Theorem

  • Square and Cube Roots
  • Simplifying Roots and Operations with Roots
  • Pythagorean Theorem; Proof and Converse
  • Structure of Numbers; Real Numbers; Applications
  • Special Right Triangles
  • The Distance and Midpoint Formulas
  • The Tangent Ratio
  • The Sine and Cosine Ratios

Relations and Functions

  • An Introduction to Functions
  • Linear Equations in Two Variables
  • Working with Functions
  • The Slope of a Line
  • Intercepts
  • Writing Linear Equations
  • Direct Variation
  • Applications of Linear Concepts
  • Function Notation and Values
  • Linear Systems in Two Variables
  • Linear Inequalities in Two Variables

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Problem Solving Help Room

Help Room

Each week, all students are invited to a Problem Solving Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week. 

The Problem Solving Help Room meets each Tuesday from 7 – 8 p.m. ET. 


Sample Video 

Sample Video

Pre-algebra demo


Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.