Pre-Algebra: Semester I



This course is NOT a lecture: participation and questions are expected. I will focus on developing fluency with rational numbers and proportional relationships. I’ll encourage students to extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal Algebra and Geometry, and then to Pre-Calculus and Calculus.


Meets for one hour twice per week for 20 weeks.

This course has a prerequisite, which you can find here. Students to not have to have taken my course to qualify, but they must have a solid understanding of numbers to proceed, so please review the skills in the previously linked course to ensure your child is ready. If in doubt, please contact me for a placement test. This course is the equivalent of quarters 1 and 2 in a typical Pre-algebra classroom (taken between grades 7 and 9 in public schools, but there is no grade/age requirement for this class. If students are ready for the material, they’re welcome in my class.) I will provide all printable material necessary, and each week will include videos, virtual flashcard decks, and more as needed.

We will cover the following topics in this course:

  • Review of natural number arithmetic
  • New types of numbers such as integers, fractions, decimals and negative numbers
  • Factorization of natural numbers
  • Properties of operations such as associativity and distributivity
  • Simple (integer) roots and powers
  • Rules of evaluation of expressions, such as operator precedence and use of parentheses
  • Basics of equations, including rules for invariant manipulation of equations
  • Understanding of variable manipulation
  • Manipulation and arithmetic with the standard 4-quadrant Cartesian coordinate plane

Students will learn to think flexibly about relationships among fractions, decimals, and percents. They will also learn to recognize and generate equivalent expressions and solve single-variable equations and inequalities. We will investigate and explore mathematical ideas and develop multiple strategies for analyzing complex situations. As a group, we will analyze situations verbally, numerically, graphically, and symbolically. I’ll also expect my students to apply mathematical skills and make meaningful connections to their life experiences, and will provide opportunities and projects to facilitate this requirement.

Anticipated Course Outline

Class 1: Words, Variables, and Expressions
Class 2: Properties
Class 3: Coordinate Plane
Class 4: Words, Equations, Tables, and Graphs
Class 5: Scatter Plots
Class 6: Integers and Absolute Value
Class 7: Adding and Subtracting Integers
Class 8: Multiplying and Dividing Integers
Class 9: Graphing in Four Quadrants
Class 10: Translations and Reflections on the Coordinate Plane
Class 11: Fractions and Decimals
Class 12: Rational Numbers
Class 13: Multiplying and Dividing Rational Numbers
Class 14: Adding and Subtracting Like Fractions
Class 15: Adding and Subtracting Unlike Fractions
Class 16: The Distributive Property
Class 17: Simplifying Algebraic Expressions
Class 18: Solving Equations by Adding or Subtracting
Class 19: Solving Equations by Multiplying or Dividing
Class 20: Midterm and Review
Class 21: Solving Two-Step Equations
Class 22: Writing Equations
Class 23: Perimeter and Area
Class 24: Solving Equations with Variables on Each Side
Class 25: Inequalities and Solving Inequalities
Class 26: Solving Multi-Step Equations and Inequalities
Class 27: Ratios
Class 28: Unit Rates
Class 29: Converting Rates and Measurements
Class 30: Proportional and Nonproportional Relationships
Class 31: Solving Proportions
Class 32: Fractions and Percents
Class 33: Fractions, Decimals, and Percents
Class 34: Using the Percent Proportion
Class 35: Using Percent Equations
Class 36: Percent of Change
Class 37: Simple/Compound Interest
Class 38: Circle Graphs
Class 39: Review
Class 40: Final Exam

Parent Information

  • Students are required to have this calculator. A more expensive one is not necessary; at the time of this course creation, this calculator was $10 on Amazon. TI-30X IIS calculator is required for this class.
  • Students are required to keep a math notebook/binder. I recommend one dedicated to this course.
  • Please ensure your children complete the homework assigned. I do not assign busy work, so anything I’ve asked them to complete is absolutely imperative for learning.
  • No textbooks or workbooks are required for this course. I will provide printables, handouts, and more as needed.