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Episode 3 Supports

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    Episode Description

    Exploring: Christopher and Kate draw a diagram to find the amount of white paint to mix with a given amount of red paint to match a certain shade of pink. They develop a new way to think about the problem by forming a multiplicative comparison between the amount of white and red paint in a batch of paint.

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    Focus Questions

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

     

    1. [Pause video at 1:20] Can someone revoice Kate's strategy? Who think it will work? Who thinks it will not work?

    2. [Pause video at 2:52] Can someone revoice Kate's idea about 3 fitting into there? 3 what into what? Can you come up to the video display to show what you mean?

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    Supporting Dialogue

    Allow students the opportunity to revoice others’ ideas by asking students to:

     

    • Stop the video at 4:20. Ask students to talk to a neighbor about Kate and Christopher's idea, striving for precise language. Invite the students to prepare their observations to share with the class.

    • When students share, ask another student to revoice what they heard by asking: Who can revoice what Natalie just shared?



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Mathematics in this Lesson

Lesson Description

Math Content

Math Practices

Lesson Description

 

Kate and Christopher use an applet called Making Pink Paint to solve proportional reasoning problems. They choose amounts of red and white paint to make two batches of paint that are the same shade of pink. In the process, they form ratios by comparing amounts of white paint to red paint multiplicatively.

Math Content

 

CCSS.M.6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

 

As this lesson progresses, the students form ratios by multiplicatively comparing amounts of two different quantities: the amount of red paint to the amount of white paint in one batch of pink paint. The ratio represents “pinkness.” The students use a ratio representing “pinkness” of a first batch of paint to find the amount of white paint they must to add to a certain amount of red paint to make a second batch of paint that is the same shade of pink as a first batch of paint.

Math Practices

 

CCSS.MATH.PRACTICE.MP1: Make sense of problems and persevere in solving them.

 

Common Core Practice 1 states that proficient students will “analyze givens, constraints, relationships, and goals,” “make conjectures…and plan a solution pathway” In this lesson, Kate and Christopher consider a different kind of proportional reasoning problem: mixing amounts of red and white paint to make two batches of paint that are the same shade of pink. As they attempt to make two batches of paint with the same “pinkness,” they first use a solution path from previous lessons.  They double, quadruple, and halve both the amount of red paint and white paint of a given batch of pink paint to create a second batch that is the same shade of pink. When the students are asked how much white paint to add to 2 ounces of red paint to make a batch with the “pinkness” of a batch with 1.5 ounces of red paint and 4.5 ounces of white paint, they struggle. The students persist by creating a diagram that, in the end, multiplicatively compares the amount of red paint to the amount of white paint in the given batch [2:14 in Episode 3]. Once they have persevered to form this new solution path, the students solve a series of similar pink paint problems using the strategy of creating equal ratios of amounts of red and white paint for both batches of paint.