Two Related Quantities, Part 1 (IM Grade 6, Unit 6, Lesson 16)
Task
Lesson Purpose In this activity, students analyze the relationship between two quantities that form a ratio, and think about how tables, graphs, and equations represent the relationship. Students begin by completing a table of equivalent ratios and plotting the values. Then students describe the relationship between the two quantities. Thinking about how one quantity relates to the other in turns allows students to interpret and write equations with variables. Along the way, students reason quantitatively and abstractly (MP2). How Tuva Enhances the lesson This lesson focuses on understanding how two quantities are related and how that relationship can be represented in multiple ways. Tuva allows students to explore the same ratio relationship dynamically, rather than creating multiple static graphs. By switching axes, zooming in on key values, and clicking individual data points, students can see that the relationship between red and yellow paint does not change — only the way it is viewed. This reduces cognitive load, supports conceptual understanding of unit rates and equations, and makes the ideas of dependent and independent variables more accessible. Unlike static graphs, Tuva enables students to instantly compare representations and focus on meaning rather than graph construction.
Two Related Quantities Let’s use tables, equations, and graphs to describe relationships. Have you ever tried to mix colors—like paint, slime, or food coloring—to get just the right shade? Lin needs to mix a specific shade of orange paint. To make it, she mixes red paint and yellow paint. She discovers that the color only looks right when the amounts of red and yellow follow a consistent pattern.
Topics and standards: 6-EE-C-9, 6-RP-A-3-A, HSS-ID-B-6-A, Grade 6, Illustrative Math & Tuva