Math Unit – Expressions is a homeschool math curriculum for ages 11–13 that develops algebraic reasoning through expressions, equations, proportional graphs, slope, and linear relationships. Students begin by using the Commutative, Associative, and Distributive Properties to rearrange, regroup, expand, and simplify expressions, then apply algebra to sales tax, discounts, markup, perimeter, area, and fixed and variable costs. Activities such as Properties Quest, “Graphing Proportional Relationships – Data Tables,” and “Drawing Triangles to Find Slope” give students repeated practice moving between symbolic, numerical, and graphical representations.

At a Glance

Age Range: Ages 11–13 (usually 7th grade)
Estimated Time Commitment: 18 lessons, approximately 45 minutes each
Prerequisites: Ability to work with ratios, rational numbers, equations, like terms, and order of operations
Student Independence: Designed for students to work independently, with parent support as needed
Includes: Student-directed lessons, Parent Plan sections, Student Activity Pages, answer keys, unit assessment materials, and final-project instructions
Required items: Math Materials Kit sold separately

This unit is part of the age 11-13 full year math program, which covers approximately half of the seventh-grade math standards and all of the eight-grade standards.

Key Features

• Algebraic Manipulation: Students use the Commutative, Associative, and Distributive Properties to reorganize and simplify algebraic expressions. In Properties Quest, they simplify expressions and use the answers to uncover letters that spell “Algebra.”
• Real-World Algebra: Students rewrite expressions for sales tax, discounts, markup, profit margin, and fixed and variable costs, then apply equations to perimeter and area problems. The optional Coffee Shop Game extends these ideas through decisions about pricing, inventory, costs, markup, and profitability.
• Graphing Proportional Relationships: Students connect proportional relationships across tables, equations, graphs, and word problems. In “Graphing Proportional Relationships – Data Tables” and “Graphing Proportional Relationships - Equations,” they calculate unit rates, graph data, and compare rates using contexts such as running pace, subscription costs, faucet flow, bicycle speed, and wages.
• Slope and Linear Models: Students draw right triangles on graphs to calculate slope using rise over run, then compare similar triangles to see why slope remains constant along a straight line. In the (y=mx+b) lessons, they investigate how changing (m) affects steepness and how changing (b) moves a line vertically.

Learning Outcomes

By the end of this unit, students will be able to:

• Simplify algebraic expressions using the Commutative, Associative, and Distributive Properties.
• Combine like terms and expand expressions using distribution.
• Rewrite algebraic expressions for financial and geometric situations.
• Solve equations involving perimeter, area, and forms such as (ax+b=c) and (a(x+b)=c).
• Identify and graph proportional relationships from tables, equations, and contextual descriptions.
• Calculate and interpret slope using rise over run.
• Explain why slope remains constant along a straight line using similar triangles.
• Write, rearrange, and graph linear equations in slope-intercept form (y=mx+b).

Math Unit – Expressions moves students from simplifying expressions to interpreting and constructing linear relationships. Through algebraic properties, real-world applications, proportional graphing, and slope-intercept work, students connect symbolic procedures with tables, graphs, geometry, and practical situations.

This item includes free online access to Beyond the Page Online for 18 months. This includes Learning Gates, Portfolio and any curriculum or student activity pages that you have purchased.