Kate and Christopher use diagrams to demonstrate why additive reasoning does not work to find a unit ratio.
Mathematics in this Lesson
Common Core Math Standards
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.
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].