Outline: "constructing three-dimensional objects through parallel translation s of planes"
... Learning activities 
... Teacher's instructions/guide 
... Evaluation (expected student responses)
Regarding the necessary software data for using "Cabri 3D File" and "Flash Movie" on the pages, please review[Installing necessary software] .
... Learning activities ... Teacher's instructions/guide ... Evaluation (expected student responses) Regarding the necessary software data for using "Cabri 3D File" and "Flash Movie" on the pages, please review[Installing necessary software] .
Learning content
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Of the figures submitted last time, select and present one which doesn't form a cube. (If there was no such corresponding figure, the teacher should display a figure he or she has prepared.)
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First, encourage students to think about it in their minds only. |
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By detaching (1) and (2), connecting (2) and (4), and any other way, point out the five regular squares end up forming a line. |
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Verify what he or she thought about while actually building a cube using the polyhedrons. |
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Lead the students to the fact that, by rotating one or more regular squares around any vertex, it becomes easier to explain why different developments can be created or not. |
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Based on how the surfaces connect and how they are placed, explain that the presented figure cannot be a cube. [Note] This class shows implicitly that, while the proposition, "When five (or more) regular squares form a line, a cube cannot be created," is true, the converse that says, "If a cube is not created, five (or more) regular squares form a line" is not true. This means, "The correct proposition's converse has not necessarily been established," and offers the opportunity for demonstration. |
Expected responses from the students
| A | The figure follows the characteristics of those capable of creating a cube, because the surfaces of the same color do not connect with each other, and because the number of the regular squares forming one line is less than five. |
| B | In reality, the figure can not become a cube. What is a good way of explain ing why a cube cannot be created? |
| C | The explanation appears possible if the way the regular squares are placed is changed while he or she thinks about how the sides will connect with each other when it is built. |
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| E | When confirmation has been carried out using the polyhedrons, it can be understood that surface (1) ends up overlapping surface (6). |
| F | When (2) is detached from (3) and the figure is created by connecting (2) to the top of (4), which are to connect with each other, the five regular squares form a line. This goes against the characteristic of figures capable of creating cubes . |
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By rotating the surfaces around any vertex, a new development is brought about, and it becomes possible to explain why the development cannot become a cube.
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