Proportional relationships are the major focus in the Common Core State Standards for grade 7 math. And this requires teachers to be intentional about setting the stage to make connections across the concepts included in the Ratios and Proportional Relationships domain.
The Desert Run team activity, adapted from a practice problem in the Math Course 2 textbook by
McDougal Littell, centers around three animals and their top speeds. When comparing the running distances provided in the activity, students may initially think the greyhound rules the desert. However, further investigation is required to compare distance per unit of time because the snapshot distances are collected in different time intervals. This activity prompts students to determine which animal is the fastest and how far each animal has traveled after 11 seconds.
- Students may calculate the unit rate for the speed of each animal to determine which one is fastest. And then they may continue to use the unit rates to determine the distance each animal travels in 11 seconds.
- Students may set up a proportion to determine the distance after 11 seconds and use those results to declare which animal is fastest.
- Students may use the unit rate to determine the fastest animal and then set up a proportion to determine the distances after 11 seconds.
An extension of representing rates graphically is included for teams who finish early. Be sure to share your favorite student-created scenario in the comment section.
This activity prompts rich discussion with an opportunity to critique the work of others and make connections between rates and proportions. A record sheet is included for convenient use with the Fan-N-Pick or Showdown structures for
Kagan cooperative learning.
The most popular proportional relationship is found in the formula d=rt. If your students are unfamiliar with the formula, lead them to it by asking them to create a table of values that model the relationship between the distance in feet that the greyhound travels over time in seconds and then write the equation that models the relationship. Extend their typical y=ax equation to better model the situation...let "y" be represented by "d" for distance in feet, let "a" be represented by "r" for rate, and let "x" be represented by "t" for time in seconds. Consider the following discussion path to help students connect equivalent rates to the equation for proportional relationships.
The concepts discussed in the Desert Run team activity build the foundation needed for multi-step ratio problems. Modeling the sample "
Reading Three Books" Type 1 task from
PARCC, this Solving Multi-Step Ratio Problems team activity uses the Simultaneous RoundTable structure for
Kagan cooperative learning. This activity assesses conceptual understanding of unit rates and its application in a multi-step ratio problem.
These activities highlight Common Core State Standards 7.RP.A.2b, 7.RP.A.2c, and 7.RP.A.3 included in MATH-7.
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