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Episode 1 Supports

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    Episode Description

    Making Sense: Kate and Christopher compare two different ways of reasoning – multiplicative reasoning and additive reasoning.

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    Focus Questions

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

     

    1. [Pause video at 1:56] Christopher says, "It is just adding 6." 6 what? What is the 6 being added to?

    2. [Pause video at 2:45] Kate said "hoping." Christopher says he heard 4 miles for every 3 minutes. How would you revoice Kate's observation?

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    Supporting Dialogue

    When engaging in the tasks in class, invite your students to attend to and critique the strategies of others:

     

    • Pause the video at 3:19. Kate and Christopher just said that both solutions might work. Talk with your neighbor about that. Can both solutions work?

    • Resume watching the video through 4:03. Work with a neighbor to create an argument to explain why one way worked and one way did not work. Prepare to share your thinking with the class.



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Mathematics in this Lesson

Lesson Description

Math Content

Math Practices

Lesson Description

 

Kate and Christopher extend their use of diagrams to form a unit ratio in a speed context.

Math Content

 

CCSS.M.7.RP.A.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

 

In this lesson, the students use two strategies to identify a unit rate for a car that is traveling 10 miles in 4 minutes.  First, they find the unit rate by a numerical operation. They divide both the number of miles and minutes by 4. They state that this car is going at a speed of 2.5 miles in 1 minute. Secondly, the students also create a diagram to determine the unit rate of this car. They partition the diagram representing a car going 10 miles in 4 minutes into four identical little trips of 2.5 miles in 1 minutes.

 

Math Practices

 

CCSS.MATH.PRACTICE.MP4: Model with mathematics.

 

According to the Common Core’s description of Math Practice 4, mathematically proficient students “identify important quantities in a practical situation and map their relationships using such tools as diagrams.” In this lesson, Kate and Christopher, use diagrams in two productive ways. First, they use a diagram to show why traveling 2.5 miles in 1 minute is the same speed as traveling 10 miles in 4 minutes by iterating identical small journeys of 2.5 miles in 1 minute to make up the larger journey of 10 miles in 4 minutes [2:39 in Episode 2]. Later, they identify that a journey of 10 miles in 4 minutes can be partitioned into four identical trips of 2.5 miles in 1 minute [6:02 in Episode 3].