Math Unit – Functions is a homeschool math curriculum for ages 11–13 that develops understanding of functions through input-output relationships, multiple representations, linear and nonlinear behavior, graph interpretation, slope, intercepts, and equations of lines. Students begin by identifying functions in ordered pairs, tables, graphs, and mapping diagrams, then translate function rules into tables, coordinate points, and graphs. Activities include creating a function machine, “Linear or Nonlinear Data,” “Mixed Review Intercepts,” and the optional “Graph that Song!” extension.

At a Glance

Age Range: Ages 11–13 (usually 7th grade)
Estimated Time Commitment: 14 supported instructional lessons, approximately 45 minutes each
Prerequisites: Ability to graph coordinates, solve equations, and work with slope, intercepts, and linear equations
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, and graphing activities
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

• Multiple Function Representations: Students identify functions using ordered pairs, tables, mapping diagrams, equations, and graphs. In “Graphing Data,” they start with a function rule, calculate outputs, create ordered pairs, and plot the points, connecting several representations of the same relationship.
• Linear and Nonlinear Analysis: Students use rate of change and graph shape to distinguish linear from nonlinear functions. In “Linear or Nonlinear Equations,” they substitute x-values, calculate y-values, complete tables, graph the results, and classify relationships as linear or nonlinear.
• Graph Interpretation: Students interpret increasing, decreasing, and constant portions of graphs and connect graph shapes with situations involving motion, plant growth, earnings, and filling or draining. The optional “Graph that Song!” activity asks students to represent changes in a song’s energy or emotion over time with a graph.
• Linear Function Structure: Students identify x- and y-intercepts from graphs, tables, and equations, then combine these skills with slope. Later work has students calculate slope from two table points, solve for the y-intercept, write the equation of the line, and verify it using another point.
• Review and Skill Retention: Learning Gates provide lesson-level checks on concepts such as function identification and linear versus nonlinear relationships. A Cumulative Unit Quiz reviews function identification, graphing, slope, intercepts, and equation writing from the completed lessons.

Learning Outcomes

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

• Determine whether a relationship is a function using ordered pairs, tables, graphs, and mapping diagrams.
• Apply the Vertical Line Test to identify functions from graphs.
• Translate function rules into tables, ordered pairs, and graphs.
• Distinguish linear and nonlinear relationships using rate of change and graph shape.
• Interpret graphs as increasing, decreasing, or constant and connect their behavior to real-world situations.
• Identify x- and y-intercepts from graphs, tables, and equations.
• Calculate slope and determine a y-intercept from tabular data.
• Write and verify equations of linear functions using slope and intercept information.

Math Unit – Functions moves students from identifying basic input-output relationships to analyzing how functions behave and how linear relationships can be described algebraically. Through tables, mapping diagrams, graphs, real-world graph stories, slope, and intercepts, students examine functions from several connected perspectives.

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.