Foundations of Algebra

Below are lesson resources related to a Foundations of Algebra unit.

Introduction to Variables 1 (What are variables?)

This video develops a robust definition of “variables” that does not place students in a narrow box of thinking about them only as letters or unknowns. It also includes suggestions about how to enrich students’ early experiences with variables.

Introduction to Variables 2 (Student Stumbles)

Coming soon!


This video addresses the common misunderstandings that students have about variables and how you can delve into those misunderstandings and turn them into learning opportunities.

Introduction to Expressions

This activity (15-30 mins) from Desmos involves sorting cards with written expressions, symbolic expressions, tile diagrams, and tables and then having a discussion about algebraic equivalence.

Introduction to Equations and Equality

This lesson (40 mins) from Illustrative Mathematics helps students recall the meaning of equations and how to solve them conceptually. It uses tape diagrams (aka, bar diagrams) to draw attention to the structure of the relationships embedded in the equations.

From Patterns to Algebra




Using patterns to make predictions and generalizations, Creating a linear function that matches a situation. HSF.LE.A.2

This lesson, from the CUNY High School Equivalency Curriculum Framework, involves students working with a visual pattern and progressing from concrete to abstract (symbolic) ways of representing structure.

Algebraic Order of Operations

The video (8 mins) is an explanation that PEMDAS is misleading and expires once students move to higher-level math. The lesson (30-45 minutes) from Desmos involve students coming up with the operations that will yield matching results, and they have opportunities to discuss the order of operations and make their own expressions with various operations.

Introduction to Graphing



Graph points on the coordinate plane to solve real-world and mathematical problems. Be able to give the ratio of rise over run for slope. 6.NS.C.8, 7.RP.A.2.A, 8.EE.B.5

This lesson reviews the coordinate plane, provides applets for students to practice plotting points, and also looks at the graphs of linear functions.

Proportional and Multiplicative Reasoning

This text (19 pages) provides research-based explanations of proportional reasoning and multiplicative reasoning (contrasted with additive reasoning), and it contains 20 problems that could be drawn from to incorporate into a lesson plan.

Next unit coming soon!

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