Changing One Quantity at a Time
Kate and Christopher begin to make sense of proportional reasoning in a speed context. They use an applet called Races to explore how to make one car go slower or faster than another car.
Episode 1: Making Sense
Christopher and Kate make sense of an applet called Races by first entering different values of distance and time for two cars and then noticing what happens.
Episode 2: Exploring
Kate and Christopher use the Races applet to explore how to make the red car go slower than the blue car when both cars travel the same distance of 15 miles.
Episode 3: Reflecting
The students suggest a rule for choosing the number of minutes that the red car will travel if it is slower than the blue car, and the two cars travel the same number of miles.
Episode 4: Exploring
Kate and Christopher form and test a rule for choosing the number of miles for the red car to go if it is slower than the blue car, and the two cars both travel for 6 minutes.
Episode 5: Repeating Your Reasoning
The students figure out how to make the red car go faster than the blue car when the two cars both travel for 6 minutes.
Episode 6: Reflecting
By acting out races with their hands, Christopher and Kate explain why a car that goes a greater distance than another car in the same amount of time will be faster than that car.