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Episode 3 Supports
Episode Description
Reflecting: Kate and Christopher see four little trips of 12 miles in 9 minutes in a diagram that shows a journey of 48 miles in 36 minutes.
Focus Questions
For use in a classroom, pause the video and ask this question:
- [Pause video at 0:49] Where is the times 4 represented in the diagram?
- [Pause video at 0:49] Where is the times 4 represented in the diagram?
Supporting Dialogue
When engaging in the tasks in class, invite your students to build on the work of others by asking students to:
- Work with a neighbor to identify features of Kate and Christopher's diagram that you think work well. Then identify features that you would change.
- Contribute ideas to create a class diagram to show why a car traveling 48 miles in 36 minutes travels at the same speed as a car traveling 12 miles in 9 minutes.
- Work with a neighbor to identify features of Kate and Christopher's diagram that you think work well. Then identify features that you would change.
Mathematics in this Lesson
Lesson Description
Math Content
Math Practices
Lesson Description
Kate and Christopher discover a way to solve proportional reasoning problems in a speed context, by drawing diagrams and repeating (iterating) a ratio of distance and time.
Math Content
CCSS.Math.Content.6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems.
In this lesson, students create a diagram to solve a real-world problem. They find the time it should take a car to travel a certain distance, so that it is goes the same speed as a car traveling 12 miles in 9 minutes. The students iterate a trip of 12 miles in 9 minutes until the diagram shows a journey of 48 miles. The students can then see that a car traveling at the same speed as a car traveling 12 miles in 9 minutes must travel 36 minutes to go 48 miles. The students notice that there are four copies of smaller identical trips that make up a journey of 48 miles in 36 minutes. Each little trip is represented in the diagram by both the miles traveled and the time it took to travel those miles. The diagram reinforces the idea that quantities of time and distance are joined together to form a ratio that represents the speed of the car.
Math Practices
CCSS.MATH.PRACTICE.MP6: Attend to precision.
According to the Common Core's description of Math Practice 6, mathematically proficient students “try to communicate precisely with others” while they “examine claims and make explicit use of definitions.” In this lesson, as Kate and Christopher begin to create diagrams to solve more challenging same speed problems, they attend to precision in two ways. First, they attend to the precise meaning of a car going at the same speed as another car [3:06 in Episode 1]. Christopher’s language becomes more precise when he says, “They (the two cars) are going at the same speed, but they will arrive at different times.” Second, they attend to the key details in their diagram with precision. When Kate and Christopher redraw their diagram to find the time it should take a car to travel 60 miles so that it goes the same speed as a car traveling 12 miles in 9 minutes, they no longer include images of people or houses. They also alter their diagram so that the size of each representation of a little trip of 12 miles in 9 minutes is about the same size [3:15 in Episode 2].
