In this activity students are presented with a prism that was used in a previous lesson to calculate volume. Here, they calculate the surface area of the prism. This provides students with the opportunity to work,  within a given context, with complex shapes to find surface area.

Monitor for students who use these different strategies:

• Decomposing the heart into shapes to calculate the area.
• Calculating the area of a square around the heart and removing the negative space.

In each approach, students will be decomposing the figure into smaller areas to do calculations.

Students who are familiar with actual heart-shaped boxes of chocolate may want to double the lateral area to represent the way the top and bottom pieces nest together.

The goal of this discussion is to connect different methods of calculating the surface area of the box. Focus on connecting a few different strategies and how they arrive at the same answer.

Display, for all to see, 2–3 approaches/representations from previously selected students. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:

• “What do the approaches have in common? How are they different?”
• “Did anyone solve the problem the same way, but would explain it differently?”
• “Are there any benefits or drawbacks to one representation compared to another?”

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?”

This activity reinforces work that students have done in previous activities with regard to surface area and volume. Students work with a contextual problem to determine the surface area and volume of an object.

The purpose of this discussion is to clarify when to calculate volume and when to calculate surface area, as well as acknowledging that there are times that a partial surface area is needed. 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?”