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Episode 2 Supports

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    Episode Description

    Exploring: Christopher and Kate figure out how many miles a car should travel in one minute so it goes the same speed as a car traveling 10 miles in 4 minutes. This results in a unit ratio.

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    Focus Questions

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

     

    1. [Pause video at 1:23] Can someone revoice Christopher's idea?

    2. [Pause video at 2:30] Make your own diagram that shows why a car traveling 2.5 miles in 1 minute travels at the same speed as a car traveling 10 miles in 4 minutes.

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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 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 Diana’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 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].