Comparing Situations by Examining Ratios (IM Grade 6, Unit 2, Lesson 10)
Task
Lesson Purpose In this activity, students work with pairs of ratios involving distance run and elapsed time to determine which of two runners ran faster. In making comparisons, students interpret objects with equivalent distance-time ratios as having the same speed or moving “at the same rate.” How Tuva Enhances the lesson Using Tuva enhances this lesson by giving students another powerful visual representation to make sense of rates. As students compare distance and time for different runners, the coordinate graphs in Tuva help them see what it means to move “at the same rate.” Even though students have not yet learned about slope, this activity provides an early visual connection to that concept. Tuva also allows all four runners to be displayed on the same graph—making it easy to compare their data, even when distances are measured in different units. Students actively interact with the data and tools, deepening their understanding of equivalent ratios and constant rates through exploration.
Before we jump into math, let’s build some background knowledge to help us make sense of today’s problem. What do you know about treadmills? A treadmill is a machine used for walking or running indoors. Even though you stay in the same place, the treadmill’s computer keeps track of the distance traveled as if you were running outside. Think about the image: What do you notice? What do you wonder? (Hint: Click on the image to make it larger.)
Topics and standards: Grade 6, Illustrative Math & Tuva