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Episode 3 Supports

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    Episode Description

    Repeating Your Reasoning: The students continue their work from Episode 2 by looking for more distance and time values that will make the red car go the same speed as the blue car.

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    Focus Questions

    For use in a classroom, pause the video and ask these questions:

     

    1. [Pause video at 0:39] What are you going to do? How will you know that the combinations of distance and time amounts that you chose work or do not work?
    2. [Pause video at 2:29] Compare your table entries with Kate and Christopher's. What is similar? What is different?

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    Supporting Dialogue

    Support students' ability to attend to the mathematical claims of others by asking them to:

     

    • Share their responses to Focus Question #2 by contributing both combinations of values for distance and time that worked and those that did not work, so the class can begin to construct a shared table.
    • Contribute one claim at a time to the class table. Then ask the class who else had the same claim. Then ask the students to share another new claim with the class.

     



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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.