Kate and Christopher use diagrams to demonstrate why additive reasoning does not work to find a unit ratio.
For use in a classroom, pause the video and ask these questions:
1. [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?
[2. 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?
When engaging in the tasks in class, invite your students to consider features of mathematical diagrams by asking students to:
1. 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?
2. 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?”