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D: height 12 cm; area of base 32 cm2
For the pyramid with a triangular base, students may forget that the triangle area formula involves dividing by 2, resulting in a base area of 6 square units. Prompt them to draw and label the base prior to calculating its area.
The purpose of this discussion is to allow students to see multiple approaches to solving these multi-step problems. Ask students to share their strategies for volume calculations. For example, for the cone, did they calculate the area of the base first, and substitute it into the formula ? Or, perhaps they wrote out and performed the calculations all at once.
Select previously identified students to share their thought process on the “working backward” cone problem. If possible, find one student who solved an equation algebraically and another who used backward reasoning rather than formally solving an equation.
Math Community
Display the Math Community Chart for all to see. Give students a brief quiet think time to read the norms, or invite a student to read them out loud. Tell students that during this activity they are going to practice looking for their classmates putting the norms into action. At the end of the activity, students can share what norms they saw and how the norm supported the mathematical community during the activity.
Use Three Reads to support reading comprehension and sense-making about this problem. Display only the problem stem, without revealing the instructions in the last sentence.
A caterer is making an ice sculpture in the shape of a pyramid for a party. The caterer wants to use 11 liters of water, which makes about 720 cubic inches of ice. The sculpture must fit on a table with space around it for the food. The caterer needs to decide how large to make the base, which can be any shape. Draw and label the dimensions of 2 different pyramids that would work.
The purpose of this discussion is to highlight aspects of modeling that students used during the activity. Ask previously selected students to share their strategies. Here are some questions for discussion:
Math Community
Conclude the discussion by inviting 2–3 students to share a norm they identified in action. Provide this sentence frame to help students organize their thoughts in a clear, precise way:
Students may not know how to get started because this problem has few constraints. Ask students to choose a shape for the base first, then to consider what information from the problem could help them choose a size for that base.