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Episode 2 Supports

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    Episode Description

    Making Sense: The students continue to suggest and test patterns. They are surprised that some patterns do not work.

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    Focus Questions

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

     

    1. [Pause video at 1:57] What was Christopher's idea? Why did it not work?

    2. [Pause video at 4:05] Does the pattern of adding two to the number of miles and two to the number of minutes of a same speed journey produce another journey at the same speed? Why or why not?

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    Supporting Dialogue

    When engaging in the tasks in class, invite your students to build on the arguments of others by:

     

    • Stop the video at 1:17. Ask students: Write down Christopher’s idea for a pattern in your own words.  Share your statement of Christopher's idea with your neighbor.

    • Continue the video to 1:57. Ask students: Work with a neighbor to restate in your own words Christopher's argument of why the pattern does not work. Prepare to share your argument with the class.



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Mathematics in this Lesson

Lesson Description

Math Content

Math Practices

Lesson Description

 

Kate and Christopher create a diagram to explain why the distance and times values for two cars make them go the same speed. In the process, they form a ratio by joining the distance and time values for one car into a unit or “little trip,” which can be repeated (iterated) or split apart (partitioned) to solve proportional reasoning problems.

Math Content

 

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

 

In this lesson, students create a diagram to explain why two cars, one traveling 20 miles in 8 minutes and the other traveling 10 miles in 4 minutes, are going at the same speed. The diagram shows how the two quantities of distance and time are joined together to form a ratio that represents speed. The students iterate the 10 miles in 4 minutes trip to show how a journey of 20 miles in 8 minutes is made up of two identical trips of 10 miles in 4 minutes. They also create a new diagram by partitioning a journey of 10 miles in 4 minutes into two identical trips of 5 miles in 2 minutes. Their final diagram shows that a journey of 15 miles in 6 minutes is made up of 3 identical trips of 5 miles in 2 minutes.

Math Practices

 

CCSS.MATH.PRACTICE.MP3: Construct viable arguments and critique the reasoning of others.

 

According to the Common Core’s description of Math Practice 3, mathematically proficient students are able to “make conjectures and build a logical progression of statements to explore the truth of their conjecture.” In this lesson, Kate and Christopher look for patterns in their list of amounts of distance and time that make the red car go at the same speed as the blue car, which travels 10 miles in 4 minutes. After naming some patterns that work, Christopher suggests a pattern that does not work and explains the reasoning behind his new conjecture [0:32 in Episode 2]. When Kate expresses doubt and suggests some evidence that contradicts Christopher’s conjecture, Christopher responds by admitting that he is now unsure about his idea. They then test the conjecture to find that it does not work. Christopher then begins to notice a flaw in his argument [1:06 in Episode 2] and later explains what it is [1:48 in Episode 2]. In Episode 3, Kate and Christopher continue this progression of suggesting, checking, consulting, adjusting, and then defending their approach to building a diagram that explains why the pattern of doubling works.