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Episode 3 Supports
Episode Description
Reflecting: Kate and Christopher use diagrams to demonstrate why additive reasoning does not work to find a unit ratio.
Focus Questions
For use in a classroom, pause the video and ask these questions:
- [Pause video at 1:50] Can someone revoice Christopher's idea? What do you think about that method to determine the amount of time and distance for a car to travel at the same speed?
- [Pause video at 3:03] What do you think about the possibility of two different amounts of miles that would make a car travel for 1 minute at the same speed as a car traveling 10 miles in 4 minutes?
- [Pause video at 1:50] Can someone revoice Christopher's idea? What do you think about that method to determine the amount of time and distance for a car to travel at the same speed?
Supporting Dialogue
When engaging in the tasks in class, invite your students to consider features of mathematical diagrams by asking students to:
- Compare diagrams at 4:46 and at 6:02. Ask a student “Can someone say how these two diagrams are different? How are they similar?
- Share differing models. For example, ask "Does anyone else have a model that is different from these that they would like to share?" Follow up by asking "Can someone say how this diagram is different? How is it similar?"
- Compare diagrams at 4:46 and at 6:02. Ask a student “Can someone say how these two diagrams are different? How are they similar?
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].
