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Episode 1 Supports
Episode Description
Making Sense: Kate and Christopher use number sentences to determine the number of minutes it should take the red car to travel 200 miles so that it goes at the same speed as a car traveling 10 miles in 4 minutes.
Focus Questions
For use in a classroom, pause the video and ask these questions:
- [Pause video at 1:56] Christopher says, "it is just adding 6." Six what? What is the 6 being added to?
- [Pause video at 2:45] Kate said "hoping." Christopher says he heard 4 miles for every 3 minutes. How would you revoice Kate's observation?
- [Pause video at 1:56] Christopher says, "it is just adding 6." Six what? What is the 6 being added to?
Supporting Dialogue
When engaging in the tasks in class, invite your students to attend to and critique the strategies of others:
- Pause the video at 3:19. Kate and Christopher just said that both solutions might work. Talk with your neighbor about that. Can both solutions work?
- Resume watching the video through 4:03. Work with a neighbor to create an argument to explain why one way worked and one way did not work. Prepare to share your thinking with the class.
- Pause the video at 3:19. Kate and Christopher just said that both solutions might work. Talk with your neighbor about that. Can both solutions work?
Mathematics in this Lesson
Lesson Description
Math Content
Math Practices
Lesson Description
Kate and Christopher make connections between their speed diagrams and the operations of multiplication and division. This helps give meaning to number sentences used to solve proportion problems.
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 create diagrams and number sentences to show why the multiplicative comparison method works to calculate equivalent ratios that represent a constant speed. For example, the students create a diagram to show that a journey of a car that travels 200 miles at the same speed as a car traveling 10 miles in 4 minutes, is made of 20 groups of the 10 minutes in 4 minutes trip. The students connect the number of groups of the smaller trip to the numerical operation of multiplying both 10 miles and 4 minutes by 20, to determine that a car must complete a 200-mile journey in 80 minutes to go at the same speed as a car traveling 10 miles in 4 minutes.
Math Practices
CCSS.MATH.PRACTICE.MP7: Look for and make use of structure.
The Common Core Practice 4 states that mathematically proficient students “step back for an overview and shift perspective… and see complicated things…as single objects or as being composed of several objects.” In this lesson, Kate and Christopher continue to solve same speed tasks by iterating and partitioning a diagram showing the joined distance and time that represents the speed of a car traveling 10 miles in 4 minutes. As they solve a more challenging problem, they anticipate the number of little 10 miles in 4 minutes trips that go into a car’s longer journey of 65 miles that will make the two cars go at the same speed [0:38 in Episode 4]. They create a diagram of groups of 10 miles in 4 minutes trips to show that their guess works. They then connect the mathematically important features of their diagram to the features of their number sentence in several ways. They relate each number and symbol in their number sentences to the structure of their diagrams. They also draw “half” of a 10-miles-in-4-minutes trip to relate the diagram to the number of .5 in their number sentence [5:37 in Episode 4].
