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Reflect on each of the following questions about the 3D Figures/Isometric Dot Paper problem you've just explored, and then select "Show Answer" to reveal our commentary.
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Question: How are these problems an extension of the Pentomino problem you completed in Part B of Session 3?
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Our Answer:
In the Pentomino problem, we worked with rearranging the shapes on a two-dimensional plane, and we needed to consider how the shapes were alike or different. In this section, we now consider a third dimension of depth as we look for the various possibilities.
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Question: What mathematical concepts are developed in these problems?
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Our Answer:
The mathematical concepts include visualizing the relationship between the angles of an actual cube and an isometric drawing of a cube, recognizing the possible views of a three-dimensional figure, using two-dimensional drawings to record three-dimensional figures, and using reflections and rotations.
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Question: How do these activities connect to subjects other than mathematics?
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Our Answer:
Here are some examples:
Art: perspective, three-dimensional drawing, model building
Science: chemical structure, robotics
Social Studies: archeology, that is, the study of structures and buildings of early cultures
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Question: What are some ways that these activities connect to real-world applications?
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Our Answer:
Real-world applications include architecture, modeling, robotics, computer graphics, and molecular structure.
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Question: How do these problems connect to the other Process Standards?
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Our Answer:
In solving these problems, it is helpful for you to communicate the process(es) used in analyzing the various viewpoints. Working in a group or with partners will help you find various strategies for reaching the solution. Looking at the three-dimensional model from different views and recording those views on isometric models are means of representation. Reasoning about the relationships between the views will help you eliminate duplicates. Several problem-solving strategies are useful in exploring these problems, including (1) solve a simpler problem, (2) account for all possibilities systematically, (3) make a model, and (4) change your point of view.
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 Summing up
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