This activity offers students an opportunity to apply different strategies to solve part-part-whole ratio problems. Because of the large numbers involved, students need to reason flexibly and choose representations strategically. For example, for the first problem, students may choose to: 

• Use a double or triple number line diagram, but showing energy use for increments of 500 pounds (instead of 1 pound) of paper.

  

• Use a table and multiply 6 by different factors to get to 9,000. 

  paper produced (lb)	energy use, paper mill A, tree fiber (kWh)	energy use, paper mill B, recycled material (kWh)	energy use, total (kWh)
  1	4	2	6
  100	400	200	600
  500	2,000	1,000	3,000
  1,500	6,000	3,000	9,000

   
• Draw a tape diagram showing 4 units for one quantity and 2 for the other. They may then experiment with different values for each unit that would add up to 9,000, or divide 9,000 by 6 units.

  

In this partner activity, students take turns sharing their initial ideas and first drafts. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to “Should Mill A change to only recycled materials? Explain your reasoning.” In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help their partner clarify and strengthen their ideas and writing.

If time allows, display these prompts for feedback: 

• “ makes sense, but what do you mean when you say. . . ?”
• “Can you describe that another way?”
• “How do you know . . . ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer.

After Stronger and Clearer Each Time, invite students to share their responses and reasoning. Then, focus the discussion on whether or how the larger numbers in the problems affect the strategies or representations that students chose to use in solving the problems.