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Episode 2 Supports
Episode Description
Exploring: Christopher and Kate explore how to make the red car go the same speed as the blue car when the blue car travels 10 miles in 4 minutes. They create a table to record and test their conjectures.
Focus Questions
For use in the classroom, pause the video and ask these questions:
- [Pause video at 2:03] Kate and Christopher are going to use a table to keep track of their guesses. What information does their table record? Make you own table to track your own guesses and race results.
- [Pause video at 4:45] What does it mean for an equal sign to be in the a.f. and a.l. columns. What is equal? How do you know?
- [Pause video at 2:03] Kate and Christopher are going to use a table to keep track of their guesses. What information does their table record? Make you own table to track your own guesses and race results.
Supporting Dialogue
When engaging in the tasks in class, invite your students to consider the varied student work in the room on by considering the student tables created in Focus Question #1.
- As students build their own tables, find two different ways that the students are expressing their ideas and ask the students if they would be willing to share their work with the class.
- As students share their work, ask another student in the classroom to compare what they heard. For example: “Can someone say how William’s and Jacob’s tables are different? How are they similar?”
- As students build their own tables, find two different ways that the students are expressing their ideas and ask the students if they would be willing to share their work with the class.
Mathematics in this Lesson
Lesson Description
Math Content
Math Practices
Lesson Description
Kate and Christopher use the Races applet to figure out how to make two cars go the same speed when the cars travel different amounts of distance and time.
Math Content
CCSS.M.6.RP.A.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
In this lesson, students create a family of distance and time values that all represent the same speed. They begin using language such as “10 miles for 4 minutes” and “every 5 miles, it is 2 minutes” to represent speed as a relationship between two quantities. They make and test conjectures about patterns that will result in two cars going the same speed (such as doubling, halving, and multiplying the time and distance values for one car by a constant).
Math Practices
CCSS.MATH.PRACTICE.MP8: Look for and express regularity in repeated reasoning.
In this lesson, Kate and Christopher make a table of time and distance values that result in the red car going the same speed as the blue car, which travels 10 miles in 4 seconds. As stated in the Common Core’s description of Math Practice 8, they “continually evaluate the reasonableness of their intermediate results.” First they use the Races applet to check their guesses. Then they notice and test a pattern of doubling both distance and time values [1:00 in Episode 3]. Kate and Christopher use and adapt this pattern as they look “for general methods and for shortcuts” to make the red car go the same speed as the blue car. For example, at 1:19 in Episode 4, Kate and Christopher create a shortcut of dividing both the number of miles and the number of minutes by the same number. In later lessons, Kate and Christopher determine why this general method works.
