Introduction to Linear Relationships (IM Grade 8, Unit 3, Lesson 5)
Task
Lesson Purpose In this lesson, students examine linear relationships with positive rates of change. They consider a situation where the height of a stack of styrofoam cups is not proportional to the number of cups in the stack. Using graphs, tables, and equations, they observe that each cup increases the height of the stack by the same amount. Since one quantity has a constant rate of change with respect to the other, this is an example of a linear relationship. How Tuva Enhances the lesson Using Tuva to graph and analyze the cup stack data allows students to visualize the constant rate of change that defines a linear relationship. As students plot the number of cups versus height, they can dynamically explore how the points form a straight line and discuss why the relationship is linear but not proportional. The interactive tools in Tuva help students calculate and interpret slope directly from the graph, connect the rate of change to the steepness of the line, and observe how the line’s vertical intercept represents the initial height of one cup. Tuva’s visual and interactive environment supports deeper reasoning and helps students articulate how slope and intercept appear in both the context and the graph.
Activity 1; “Stacks of Cups” Let’s explore some relationships between 2 variables. Think to yourself: How tall is one of the stacks? How many cups do you think it takes to reach a certain height?
Topics and standards: Grade 8, Illustrative Math & Tuva