Home

Episode 4 Supports

  •  

    Episode Description

    Repeating Your Reasoning: Kate and Christopher find how long the red car should take to travel 2.5 miles so that it goes at the same speed as the blue car, which travels 10 miles in 4 minutes.

  •  

    Focus Questions

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

     

    1. [Pause video at 1:34] Can someone revoice Christopher's reasoning?
    2.  [Pause video at 4:55] Can someone revoice Kate's idea?

  •  

    Supporting Dialogue

    Support students' ability to build on the mathematical claims of others by asking the students to:

     

    • Notice Christopher's suggestion to find the number of minutes the red car needs to travel so that is travels 100 miles at the same speed as the blue car, which travels in 10 miles in 4 minutes. Can someone share their thinking about how to answer that question?

    • Notice that Christopher also suggested solving the same speed task for the case when the red car travels 80 miles. Talk with your neighbor about whether you think his suggestions of tasks where the red car goes 100 miles or 80 miles have something in common, or are they just random numbers of miles he is mentioning. Prepare to share your thoughts with the class.



1

2

3

4

 

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.