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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 begin 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
Mr. Belber uses pentominoes to explore area and perimeter relationships with his class. A pentomino is made from five squares arranged so that each square shares at least one adjacent side with at least one other square. There are 12 unique pentominoes.
On graph paper, draw the 12 pentominoes, or print out the prepared set (PDF). Cut them out so that you can use the 12 pentominoes in the next problem.
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Problem B1 |  |
Put any two pentominoes together and determine both the perimeter and the area of the new shape. What is the largest perimeter possible, and what is the smallest perimeter possible?
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Problem B2 | |
As students discover different perimeters, Mr. Belber has them record their findings on grid paper. What are the advantages and disadvantages of this recording scheme? What problem-solving strategies are students using to find the possible perimeters?
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Problem B3 | |
Mr. Belber wanted his students not only to use a guess-and-check strategy to find the possible perimeters, but also to analyze how the placement of the pentominoes next to each other affected the perimeter. How can the perimeter of a new shape made from two pentominoes be determined without counting? How did Mr. Belber help students understand this analytic method? What additional questions could you ask to confirm that the students understand the method? |
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Problem B4 | |
This lesson focuses on the fact that if area remains constant (in this case, 10 in2), the perimeter of shapes constructed with that area 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 B4 on Channel Talk; then read and respond to answers posted by others. |
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Problem B5 | |
Sometimes we want students to generalize what they have learned. How did Mr. Belber extend the learning from this lesson? What generalizations might he expect students to mention? |
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