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Episode 6 Supports

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    Episode Description

    Reflecting: By acting out races with their hands, Christopher and Kate explain why a car that goes a greater distance than another car in the same amount of time will be faster than that car.

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    Focus Questions

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

     

    1. [Pause video at 0:40] What did Kate and Christopher just do? Try it for yourself. What do you notice?

    2. [Pause video at 1:45] Describe the two lines in Christopher’s diagram. What do they represent? Make and label your own diagram that shows why the red car is going slower than blue car when they are both traveling for the same amount of time.

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    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 diagrams from Focus Question #2:

     

    • As students build their own diagrams, 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 Selena’s and Alma’s diagrams are different? How are they similar?”



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Mathematics in this Lesson

Lesson Description

Math Content

Math Practices

Lesson Description

 

Kate and Christopher begin to make sense of proportional reasoning in a speed context.  They use an applet called Races to explore how to make one car go slower or faster than another car.

Math Content

 

CCSS.M.6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems.

 

In this lesson, students explore how the quantities of time and distance relate to a car’s speed—a quantity that will be measured by forming a ratio in later lessons. They investigate the following relationships in a racing context:

 

  • When two cars travel the same distance:
    • the car that travels for less time is the faster car
    • the car that travels for more time is the slower car
  • When two cars travel for the same amount of time:
    • the car that covers more distance is the faster car
    • the car that covers less distance is the slower car

 

Math Practices

 

CCSS.MATH.PRACTICE.MP2: Reason abstractly and quantitatively.

 

According to the Common Core’s description of Math Practice 2, mathematically proficient students are able to reason quantitatively as they “make sense of quantities and their relationships in problem situations” while “flexibly using different properties of operations and objects.” Kate and Christopher use a simulation of a two-car race and reason quantitatively in three different ways about the quantities of time, distance, and speed. First, they see relative speed in the arrows that mark the position of each car in the race, where faster speed is captured by an arrow pulling ahead [2:18 in Episode 1]. Second, they enter the same amount of distance for two cars into speed simulation software and reason that giving one car more time than the other car will make it slower [1:56 in Episode 2]. This is a quantitative relationship that Christopher later expresses in a general written statement at 2:15 in Episode 3. Finally, they use hand races to quantify an embodied sense of motion as faster or slower speed. When their hands travel different quantities of distance in the same amount of time, they feel that the hand traveling a greater amount of distance needs to move faster than the other hand [0:23 in Episode 6].