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Episode 1 Supports

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    Episode Description

    Making Sense: Kate and Christopher use the Races applet to find the number of miles and minutes the red car should travel to go at the same speed as the blue car, which travels 12 miles in 9 minutes. They note some patterns that work and others that don’t work.

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    Focus Questions

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

     

    1. [Pause video at 1:53] Can someone revoice Kate and Christopher's conjecture? Who thinks it will work? Who thinks it will not work?

    2. [Pause video at 3:28] Can someone revoice Christopher's conjecture? Who thinks that the two cars have amounts of time and distance that will make the cars travel at the same speed? Who thinks that the two cars will travel at different speeds?

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    Supporting Dialogue

    When engaging in the tasks in class, invite your students to notice the many different quantities that are represented in the applet and student work:

     

    • Stop at the video at 3:42. Note that Kate just mentioned that she needs to compare the speeds of each car, not the times traveled of each car. These are examples of two different quantities in the problem. Work with your neighbor to name all the different quantities that are represented in the problem.

    • Ask students to share the quantities from their lists. Ask students to show where they see the quantity represented. Ask other students if they see it the same way or differently. Continue to ask students to share and explain where and how they see different quantities.

     



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Mathematics in this Lesson

Lesson Description

Math Content

Math Practices

Lesson Description

 

Kate and Christopher discover a way to solve proportional reasoning problems in a speed context, by drawing diagrams and repeating (iterating) a ratio of distance and time.

Math Content

 

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

 

In this lesson, students create a diagram to solve a real-world problem. They find the time it should take a car to travel a certain distance, so that it is goes the same speed as a car traveling 12 miles in 9 minutes. The students iterate a trip of 12 miles in 9 minutes until the diagram shows a journey of 48 miles. The students can then see that a car traveling at the same speed as a car traveling 12 miles in 9 minutes must travel 36 minutes to go 48 miles. The students notice that there are four copies of smaller identical trips that make up a journey of 48 miles in 36 minutes. Each little trip is represented in the diagram by both the miles traveled and the time it took to travel those miles. The diagram reinforces the idea that quantities of time and distance are joined together to form a ratio that represents the speed of the car.

 

Math Practices

 

CCSS.MATH.PRACTICE.MP6: Attend to precision.

 

According to the Common Core's description of Math Practice 6, mathematically proficient students “try to communicate precisely with others” while they “examine claims and make explicit use of definitions.” In this lesson, as Kate and Christopher begin to create diagrams to solve more challenging same speed problems, they attend to precision in two ways. First, they attend to the precise meaning of a car going at the same speed as another car [3:06 in Episode 1]. Christopher’s language becomes more precise when he says, “They (the two cars) are going at the same speed, but they will arrive at different times.” Second, they attend to the key details in their diagram with precision. When Kate and Christopher redraw their diagram to find the time it should take a car to travel 60 miles so that it goes the same speed as a car traveling 12 miles in 9 minutes, they no longer include images of people or houses. They also alter their diagram so that the size of each representation of a little trip of 12 miles in 9 minutes is about the same size [3:15 in Episode 2].