Lesson 3

Doubles

Est. Class Sessions: 2–3

Summarizing the Lesson

Solve John's Problem. Ask students to solve a similar problem using the John's Problem Assessment Master. Distribute and display the page.

Show or tell how you decided. After students have had a few minutes to read and work on the problem independently, discuss the expectations of the problem. Refer students to and display the Math Practices page in the Reference section of the Student Guide. Discuss Math Practices Expectations 1, 2, 5, and 6.

Ask:

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  • What does the problem ask? (To decide between two payment plans)
  • Describe the two plans. (Get paid $1 a day or get paid like the vizier did.)
  • Which strategies and tools would be helpful for this problem? (Possible response: Make a table.)
  • What might you include in your written work to show your work and your thinking? (Possible response: Show a table that shows the pay for the two plans for each day. Tell why I made my choice.)
  • What labels will you need to use? (days, $, ¢)

If students are having trouble getting started, help them set up a table with Days Worked (D) and pay for each option. See Figure 6. Some students might see that the basic problem is the same and use their completed Doubling Data Table to compare the two payment options.

After students have solved the problem, made their choices, and described their reasoning, ask them to exchange papers and to use the Student to Student section on the John's Problem Feedback Box to make comments to help their partners meet the Math Practices Expectations.

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Use the John's Problem Assessment Master with Feedback Box to assess students' abilities to make predictions and generalizations using patterns [E5], find a strategy [MPE2], show that strategy [MPE5], and label their work [MPE6].

As you refer to each of the related Math Practices Expectations, ask:

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  • What can you tell your partner about his or strategy? Was it efficient? Is the strategy appropriate?
  • How did your partner make his or her decision? Which option did he or she choose? Why? How did they decide?
  • Did your partner clearly label the numbers in their solution?

After partners have had a chance to provide feedback, have students discuss ways to improve their papers. Then ask students to revise their own work based on the feedback they received.

Ask a few students to share their decision and their reason. If John works all ten days, he would earn more money with option #2. If he works less than ten days, option #1 makes the most sense.

Use the Teacher-to-Students section on the Feedback Box to provide comments to students.

Student Guide:
Student Activity Book:
Master:
Complete data table for John's Problem
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