If students are unsure what it means to scale the photo by 80%, consider saying:

• “Tell me about a time when you or someone else had to change the size of a photo.”

• “Sketch and label the sides of a photo that is half the size, or 50%, of the original. What do you notice?“

Invite previously selected students to share their strategies for finding the values of the sequence. Sequence the discussion of the strategies in the order listed in the Activity Narrative. If possible, record and display the students’ work for all to see.

Connect the different responses to the learning goals. Ask questions such as these:

• “How is the 80% value used in each of the methods?”
• “Which method is most efficient for finding the next value of the sequence?”
• “Which method is most efficient for jumping ahead several positions in the sequence?”

If not mentioned by students, reinforce the fact that repeated multiplication can be expressed efficiently with an exponent.

If time permits, consider showing a graph to illustrate how the measurement in the image changes as a result of successive scaling, such as the graph shown here.

If students think the growth of algae is linear and conclude that the pond is half covered on May 18, halfway between May 12 and May 24, consider asking:

• “Can you explain how you knew when the pond would be half covered.”

• “If the pond is half covered on May 18th, what will the pond look like on May 19th?”

The goal of this discussion is to get students thinking about how to determine values of exponential functions when the input is not an integer. Invite previously identified students to share their responses to the questions, displaying any organization strategies used for all to see.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to why Clare may find the caretaker’s claim hard to believe. 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 clarify and strengthen their partner’s 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. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

After Stronger and Clearer Each Time, ask, “If 50% of the pond is covered at the start of May 23, how would you figure out how much of the pond is covered halfway through May 23?” After a brief quiet think time, select students to share their strategies. Some possible suggestions:

• Graph the percent coverage over time for the pond and use it to estimate.
• Make a table for days since May 12 and the percent of the pond covered, and use it to estimate.
• Write an exponential equation for the situation, where the input is days since May 12 and the output is the percent covered, and evaluate the equation for 11.5 days.

There is no need to discuss any of these strategies not brought up by students at this time.