Solving Problems about Proportional Relationships

10 min

Teacher Prep
Setup
1 minute of quiet think time, followed by whole-class discussion, followed by 2 minutes of quiet work time.

Narrative

The purpose of this Warm-up is to prepare students for the Info Gap activity that follows. First, students are given a problem with incomplete information. They are prompted to brainstorm what they need to know to solve a problem that involves constant speed. Next, they practice asking for information, explaining the rationale for their request, and persevering if their initial questions are unproductive (MP1). Once students have enough information, they solve the problem.

Launch

Display the first paragraph of the activity statement for all to see. Ask students to solve the problem. When they recognize that not enough information is given, display the second prompt and ask what they need to know to be able to solve the problem. Display the sentence frame “Can you tell me . . .” for all to see and invite students to use it to frame their information request. Give students 2 minutes of quiet think time.

Student Task

A person is running a distance race at a constant rate. What time will they finish the race?

What specific information do you need to be able to solve the problem?

Sample Response

Sample responses:

  • Can you tell me how long the race is?
  • Can you tell me how fast the person is running?
  • Can you tell me how far the person ran in 1 minute?
  • Can you tell me what time they started the race?
Activity Synthesis (Teacher Notes)

Tell students that the problem is a part of an Info Gap routine. In the routine, one person has a problem with incomplete information, and another person has data that can help with solving it. Explain that it is the job of the person with the problem to think about what is needed to answer the question, and then request it from the person with information.

Tell students they will try to solve the problem this way as a class to learn the routine. In this round, the students have the problem, and the teacher has the information needed to solve the problem.

  • Ask students, “What specific information do you need to find out what time they will finish the race?”
  • Select students to ask their questions. Encourage students to use the format of “Can you tell me . . . ?” Respond to each question with, “Why do you need to know _____?”
  • Once students justify their question, only answer questions if they can be answered using these data:
    • The race is 10,000 meters long.
    • The race started at 9:15 a.m.
    • In 1 minute, the person ran 15614156\frac14 meters.
    • An equation relating distance and time is given by d=15614td = 156\frac14 t, where dd represents distance in meters and tt represents time in minutes.
    • It takes 32 minutes for the person to run 5,000 meters.
    • The person runs at a pace of 6.4 minutes per kilometer (or 1,000 meters).
  • If students ask for information that is not on the data card, respond with, “I don’t have that information.”

When students think they have enough information, give them 2 minutes to solve the problem. (The person should finish the race at 10:19 a.m.)

Tell students they will work in small groups and use the routine to solve problems in the next activity.
 

Standards
Addressing
  • 7.RP.2·Recognize and represent proportional relationships between quantities.
  • 7.RP.A.2·Recognize and represent proportional relationships between quantities.

30 min