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Modeling Public Transportation

Grade Level:

Activity Overview: After identifying and looking at the capacity of different modes of transportation, this activity takes a more problem-solving approach to move individuals from one place to another. If you' and your class are beginning to explore algebraic representation, there is an opportunity to extend the procedure of this activity into mathematical expressions.

Materials: Pick one configuration from the list below or mix and match depending on what is available to you.

  • Toy models of different modes of transportation (car, bus, truck, train, subway car, etc.)
  • Common recyclable objects to represent each different category of transportation, such as a shoe box or egg carton for bus and steel cans or glass jars for private cars
  • Print and cut out images of each method of transportation


If using "stand in" objects, make a label or write directly on the object what it represents and also label the average capacity of each method of transportation from Modes of Transportation.

If you are using toys as models, consider placing a small sticky note or other marker showing the average capacity of each mode on these as well to make it easier to model transport patterns during the activity.

As this activity examines the relative efficiency of public transportation, it lends itself to collaborative work. You may consider working as a class or  in groups in order to follow the procedure. If working in multiple smaller groups, make sure each group has sufficient materials to model the below situations.

Working as a class or in groups, use numerical reasoning to "model" the following traffic patterns. Then answer the questions below. The questions are appropriate for both individual and group work. 

Use the different modes of transportation represented by the models before you to move the following number of people between two places. For the purpose of this simple exercise, the transit is a Point A to Point B movement, and everyone needs to leave Point A at the same time. Further, students can assume that each mode of transit will carry exactly its average capacity.

Configurations will vary for each group and each case below. Feel free to mix and match cases as you see fit or split the cases amongst different groups, keeping in mind that the larger cases are slightly more difficult. 

  • Case 1: 105 individuals need to move from the community center near their home in one town to a Civic Center in a neighboring city.
  • Case 2: 338 individuals who live in the same neighborhood need to go to work in the same building in the central business district.
  • Case 3: 1578 individuals travel from their suburban town to a school in an urban city. 


For each case or for comparing and contrasting between different cases, consider the following questions. Not all questions will apply depending on how you have configured this activity in your classroom.

  • How many vehicles (in total) were required to move the individuals required?
  • How many of those vehicles were using public roadways?
  • Which mode of transportation requires the most vehicles?
  • Which modes of transportation are better suited for which cases?

As time permits, relaunch the activity with the following challenges and answer the same questions.

  • Design a solution that only uses cars OR buses OR rail.
  • Design a solution that only uses cars and in which every car only holds one person.


MATH.2.6A, MATH.3.4E, MATH.3.4K, MATH.2.7C, MATH.3.5A

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