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Problem Solving in Pre-algebra

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Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: 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.

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

Topics in:

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

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

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.


Materials Needed

There are no required materials for this course.

List of Topics

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

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 

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

Ratio and Proportion


  • Ratios and Rates
  • Applying Rates and Ratios


  • Proportions

Direct and Inverse Variation

  • Direct Variation
  • Inverse Variation

Similar Polygons

  • Similar Figures


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


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.

Zoom online virtual classroom
This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.