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Problem Solving in Pre-algebra

Prerequisites: Qualifying math score and successful completion of Pre-algebra or equivalent

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: PS2

Course Description


CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on software provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging homework, quizzes, and chapter tests. A cumulative midterm and final exam help reinforce concepts and gain mastery. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of math concepts at each level.

Problem Solving in Pre-algebra prepares students for a more formal study of mathematics in middle school. It is appropriate for students who have a good understanding of concepts in pre-algebra, but who wish to enrich their skills through interesting word problems and applications. Students continue the study of numbers and their operations. Upon successful completion of this course, students will understand topics in:

  • algebraic concepts
  • geometry
  • radicals and exponents
  • ratios
  • proportions
  • statistics
  • probability

Students apply what they have learned to solve sets of questions at varying levels of difficulty. 

This course provides an excellent foundation for students who will be advancing into Honors Algebra I.


Materials Needed

There are no required materials for this course.

List of Topics

Chapter 1: Essentials of Algebra

Evaluating an Algebraic Expression

  • Variables and Expressions

Simplifying Algebraic Expressions

  • Equations and Their Solutions
  • Simplifying Algebraic Expressions

Solving Simple Equations

  • Solving Addition Equations
  • Solving Subtraction Equations
  • Solving Multiplications Equations
  • Solving Division Equations

Solving with Variables on Both Sides of the Equation

Solving Literal Equations

  • Translating Between Words and Math

Chapter 2: Fundamentals of Geometry

Geometry Fundamentals

  • Angles and Their Relationships


Volume and Surface Area

  • Introduction to Three-Dimensional Figures
  • Volume of Prisms and Cylinders
  • Surface Area of Prisms and Cylinders 

Chapter 3: Radicals and Exponents

Introduction to Radicals and Pythagorean Theorem

  • Square Roots and the Pythagorean Theorem 

Introduction to Scientific Notation

  • An Application of Exponents: Scientific Notation

Chapter 4: Ratio and Proportion


  • Ratios and Rates
  • Applying Rates and Ratios


  • Proportions

Direct and Inverse Variation

  • Direct Variation
  • Inverse Variation

Similar Polygons

  • Similar Figures

Chapter 5: Statistics

Interpreting and Constructing Graphs

  • Line Graphs
  • Bar Graphs and Histograms
  • Reading and Interpreting Circle Graphs

The Mean, Median, and Mode

  • Mean, Median, Mode, and Range 

Frequency Distribution and Histograms

  • Frequency Tables
  • Bar Graphs and Histograms
  • Histograms

Chapter 6: Probability

Simple Probability

  • Introduction to Probability 

Probability of Combined Events

  • Probability of Independent and Dependent Events
  • Counting Methods and Sample Spaces


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 Lecture

Sample Video



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.