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IM 7.2.9 Lesson: Solving Problems about Proportional Relationships

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race? What information would you need to be able to solve the problem?

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:If your teacher gives you the data card:

  1. ilently read your card and think about what information you need to be able to answer the question.
  2. Ask your partner for the specific information that you need.
  3. Explain how you are using the information to solve the problem. Continue to ask questions until you have enough information to solve the problem.
  4. Share the problem card and solve the problem independently.
  5. Read the data card and discuss your reasoning.
  1. Silently read your card.
  2. Ask your partner  “What specific information do you need?”  and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
  3. Before sharing the information, ask “Why do you need that information?” Listen to your partner’s reasoning and ask clarifying questions.
  4. Read the problem card and solve the problem independently.
  5. Share the data card and discuss your reasoning.

Pause here so your teacher can review your work. Ask your teacher for a new set of cards and repeat the activity, trading roles with your partner.

A company is hiring people to read through all the comments posted on their website to make sure they are appropriate. Four people applied for the job and were given one day to show how quickly they could check comments.

  • Person 1 worked for 210 minutes and checked a total of 50,000 comments.
  • Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes.
  • Person 3 worked for 120 minutes, at a rate represented by , where is the number of comments checked and is the time in minutes.
  • Person 4 worked for 150 minutes, at a rate represented by .
 Order the people from greatest to least in terms of total number of comments checked.

Order the people from greatest to least in terms of how fast they checked the comments.

Write equations for each job applicant that allow you to easily decide who is working the fastest.

Make a table that allows you to easily compare how many comments the four job applicants can check.

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