Solving Equivalent Ratio Problems

10 min

Teacher Prep
Setup
2 minutes of quiet think time, then a full-class discussion.

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

Give students 2 minutes of quiet think time.

Student Task

A red car and a blue car enter the highway at the same time and travel at a constant speed. How far apart are they after 4 hours?

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

Sample Response

Sample responses:

  • How fast is each car traveling?
  • Are the cars going the same direction?
  • Did the cars enter the highway at the same location?
  • What is the difference between the speeds of the two cars?
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 how far apart the cars will be after 4 hours?” 
  • 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 red car is traveling faster than the blue car.
    • One car is traveling 5 miles per hour faster than the other car.
    • The slower car is traveling at 60 miles per hour.
    • The blue car is traveling at 60 miles per hour.
    • The faster car is traveling at 65 miles per hour.
    • The red car is traveling at 65 miles per hour.
    • Both cars entered the highway at the same location.
    • Both cars are traveling in the same direction.
  • 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 cars will be 20 miles apart after 4 hours.)

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

Standards
Addressing
  • 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

25 min