Modeling with Systems of Inequalities in Two Variables

10 min

Narrative

This Warm-up gives students a chance to get an idea of how to add subjective values to a modeling situation. In later activities for this lesson, students model planning a trip using different methods of transit. One consideration for the methods of transit is which method is generally preferred. Students should keep their values in the table for an activity later in the lesson.

Launch

Tell students that they are going to explore different methods of transit, such as riding the bus, renting an electric bike, or walking. 

Ask students whether they would prefer to take a bus or walk. Would a trip in which they take the bus halfway and walk the rest be as good as one in which they ride the bus 80% of the way and walk the rest?

Display the table, and give students 1–2 minutes to notice and wonder about what they see. Then, invite students to share their observations and questions.

Tell students, “Jada has assigned values to her level of enjoyment with different modes of transit. Walking is set at a baseline level of 1, and the other methods are given values relative to the baseline. For example, Jada enjoys riding a bike twice as much as walking and being in a bus half as much as walking.”

Ensure that students understand that greater numbers mean that those methods are preferred over methods with lower numbers.

Student Task

Complete the table with your own relative values, giving walk the same baseline value of 1.

Jada's enjoyment per mi your enjoyment per mi
bus 0.5
train 1.5
bike rental 2
scooter rental 0.8
walk 1 1
car 1.3

Sample Response

Answers vary.

Activity Synthesis (Teacher Notes)

Display a table with additional columns, and invite 2–4 students to share their responses. Clarify their understanding by asking questions such as:

  • “Why do you think this student gave this mode of transit a value greater than 1?” (They like using that mode of transit more than walking.)
  • “Did anyone use a value less than 1? What does that mean?” (Yes. It means that they like walking more than that mode of transit.)
  • “Could you rank Jada’s favorite methods of transit from least favorite to most?” (Yes. She likes riding the bus least, then riding a scooter a little more, then walking, then taking a car, then the train, and likes riding a bike the most.)
  • “What considerations did you use to rank your enjoyment riding a bus?” (On the one hand, it is better for the environment to use public transit, and it is easy to ride without having to pay attention. On the other hand, it doesn’t go directly where I want, and I’d prefer not to be around so many people.)
Standards
Addressing
  • HSN-Q.A.2·Define appropriate quantities for the purpose of descriptive modeling.
  • N-Q.2·Define appropriate quantities for the purpose of descriptive modeling.
  • N-Q.2·Define appropriate quantities for the purpose of descriptive modeling.
  • N-Q.2·Define appropriate quantities for the purpose of descriptive modeling.

20 min

20 min