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Session 10, Part B:
Reasoning About Measurement
In This Part: Exploring Standards | Analyzing a Case Study
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To continue the exploration of what measurement topics look like in a classroom at your grade level, you will watch a video segment of a teacher who took the Measurement course and then adapted the mathematics to his own teaching situation. We will begin by looking at some of the content addressed in the videotaped lesson. Note 3
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Problem B1 |  |
In the videotaped lesson, Mr. Cellucci challenges students to construct a rectangular prism with a volume of 72 cm3. Students must find a prism with this volume that has the smallest and largest surface area. Generate a list of dimensions for rectangular solids that have a volume of 72 cm3, and then calculate the surface area for each of the different solids. What do you notice about the relationship between the dimensions of a prism and its resulting surface area?
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Problem B2 | |
Mr. Cellucci chose the volume of the rectangular prism to be 72 cm3 as compared to 71 or 73 cm3. What might be the purpose of using 72 cm3 as the volume?
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Problem B3 | |
a. | Students use different methods to discover the dimensions that result in a solid with a volume of 72 cm3. What problem-solving strategies are students using to find the shape with the smallest surface area? |
b. | Having found the shape with the smallest surface area, the students draw the net of the solid on a white board and build the solid from paper. What are the instructional benefits of examining this solid as a two-dimensional net and a three-dimensional solid? |
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Problem B4 | |
Mr. Cellucci also asks his students to find the rectangular solid with the largest surface area. How does this task support the NCTM Measurement Standards? |
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Problem B5 | |
This lesson focuses on the fact that if volume remains constant (in this case, 72 cm3), the surface area of shapes constructed with that volume can vary. Do you think the mathematical purpose of the lesson is clear? What other factors make a lesson successful? |
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Join the discussion! Post your answer to Problem B5 on Channel Talk; then read and respond to answers posted by others. |
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Problem B6 | |
Often we want students to generalize what they have learned. How did Mr. Cellucci use a summary discussion to move students toward generalizing? What generalizations did his students mention? |
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