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Episode 4 Supports

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    Episode Description

    Repeating Your Reasoning: Kate and Christopher use multiplicative comparisons to make two batches of paint that are the same shade of pink.

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    Focus Questions

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

     

    1. [Pause video at 0:29] What is Kate and Christopher's reasoning from Episode 3? As you work, draw a diagram to show why your two batches of paint are the same shade of pink.

    2. [Pause video at 1:07] Can someone revoice Kate's reasoning about what makes her first batch of paint easy to work with in order to create another batch of paint that is the same shade of pink?

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    Supporting Dialogue

    Invite your students to consider the varied student work in the room on the diagrams from Focus Question 1:

     

    • As students work, find two different ways that the students are expressing their diagrams 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 Selena’s and Jacob’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 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.