### Lesson Summary

### Overview

In this *Cyberchase* activity, students solve simple speed and distance problems as a means to develop a generalization of the distance equation d = rt. They apply this equation to decide which route Bianca should take to reach the movie premiere as quickly as possible. The assessments examine whether students can solve equivalent forms of the equation for different variables.

### Why is this an important concept?

Students write mathematical expressions and equations that involve distance, rate, and time. They learn to solve the rate-time-distance equation, d = rt, for any of the three variables, and understand that expressions in different forms can be equivalent. They solve simple one step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation.

### Grade Level:

4-8

### Suggested Time

1 hour

### Media Resources

Bianca Goes to the Movie QuickTime Video

### Materials

Handout: An Equation Relating Time, Rate, and Distance

Assessment: Level A

Assessment: Level B

Answer Key

### The Lesson

### Part I: Learning Activity

1. Have the students work in pairs for this activity.

2. Read the following to your students: "Bianca is rushing to get to a movie opening. She has two routes she could take to get there. On one route, she can travel 25 miles per hour on average (due to stop signs, city limits, and traffic). By this first route the distance to the theater is 30 miles. This route is more direct than the second one. The second route is a freeway where she can travel 60 miles per hour on average. But the freeway takes a more roundabout way to the theater, so that the distance is longer, 40 miles. Which way do you think will get her to the theater more quickly, and why?"

3. Ask student pairs to work through the problem in order to devise a method and reach a conclusion.

4. Play the Bianca Goes to the Movie QuickTime Video. Ask the students to record Bianca's answer and to be prepared to discuss how she figured out which route was a better way to get her to the movie premiere on time.

5. Discuss the students' responses and compare them to Bianca's method.

6. Discuss the relationship between distance, rate, and time in the video.

7. Distribute Handout: An Equation Relating Time, Rate, and Distance and have the students complete it in pairs.

8. Discuss the Handout. Students should eventually understand that distance, rate (speed) and time are interrelated. They should understand that if they know the value of two of these, they can find the third.

### Part II: Assessment

Assessment: Level A (proficiency): Students apply their knowledge of the rate-time-distance equation, d = rt, to determine how far a lion and an antelope can run in various amounts of time.

Assessment: Level B (above proficiency): Students use their knowledge of d = rt to determine the position of a zebra and a lion at various times.