In this activity, students apply what they have learned previously about surface area and volume to different situations (MP4). Students have to consider whether they are finding the surface area or volume before answering each question. In addition, students apply proportional reasoning to find the cost of the material that is needed. This is an opportunity for students to revisit this prior understanding in a geometry context.

As students work on the task, monitor for students who are using different methods to decompose or compose the base of the object to calculate the area.

For surface area, monitor for students who calculate the area of each face of the object, as well as those who use the perimeter of the base.

• “Tell me more about the unit price of the foam.”
• “How can we write the price of the foam to make it more clear?”

The purpose of this discussion is to highlight different approaches to this problem. Select previously identified students to share how they calculated the area of the base. 

Here are some questions for discussion:

• “Are there other ways to calculate the area of the base?”
• “How did you know when to calculate surface area or volume for this problem?”
• “If Kiran buys a big block of foam that is 36 inches wide, 20 inches deep, and 10 inches tall and cuts it into this shape, what shapes would he be cutting off?” (A rectangular prism for the step on the left side and a triangular prism for the slide part on the right.)
• “How much more would the big block of foam cost than your calculations?” (This method wastes a volume of cubic inches of foam. This would be an extra \$17.92 since .)
• If Kiran decides not to cover the bottom of the structure with vinyl, how much would he save?” (This reduces the area of vinyl needed by another square inches. This would save \$4.32 since .) 

This activity provides another opportunity for students to apply what they have previously learned about surface area and volume to different situations. Students will practice using proportions as they apply to volumes of prisms in a real-world application.

As students work on the task, monitor for students who use different strategies to answer the questions.

• “Exactly how many bags of sand were needed for each sandbox?”
• “How could the extra sand be used in this situation?”

Use Critique, Correct, Clarify to give students an opportunity to improve a sample written response to the last question by correcting errors, clarifying meaning, and adding details.

• Display this first draft:
  “It will cost $195.00. They need 10 bags of sand and .
  Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.
• Give students 2–4 minutes to work with a partner to revise the first draft.

• Select 1–2 groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each student shares, and then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Next, select previously identified students to share their methods for solving the problem. Consider asking the following questions:

• “Are there any other ways to solve this problem?”
• “Did you use any answers from one question (or multiple questions) to help you answer another question? If so, why?”
• “Did you use volume or surface area to help you answer any questions?” (yes, volume)
• “How did you calculate how much the daycare would spend on sand?”

In this partner activity, students take turns sorting cards and deciding if the context is better represented with surface area or volume. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

Here, students are asked to sort questions with a context to determine if it makes more sense to think about surface area or volume when answering the question. After sorting, students think about what information they need to answer a question and estimate reasonable measurements to calculate the answer to their question (MP2).

Once all groups have completed the Card Sort, discuss:

• “Which cards were tricky to sort? Explain why.”
• “Did you need to make adjustments in your choices? What might have caused an error? What adjustments were made?”