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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With the scenario of a game that uses a die provide the situation where the creat ion of a die is necessary. |
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Describe how to build it with the development shown below and ask: "Is it possible to use other paper pattern s (development s )?" 
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Distribute a total of six regular square polyhedrons in three colors (two squares per color) to all the students, and instruct them to c onstruct a cube where regular squares of the same color face each other. |
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Discover a development capable of creating a cube while building it by connecting the polyhedrons and opening it up.
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Describe the discovered cubic developments in a worksheet. |
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Present the discovered developments o n the blackboard as needed.
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Ask: "What characteristics do developments capable of creating a cube have?" |
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Look for the common characteristics of developments capable of creating a cube while confirming whether there are a ny development s that have not been discovered. |
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Describe the common characteristics of the developments, for example, "Regular squares of the same color are not adjacent to each other," or "Five regular squares do not form a line." |
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If an y incorrect development for creating a cube, as shown below, is submitted, suggest comparing it to the listed characteristics or actually building it.
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Expected responses from the students
| A | A cube can be created from six regular square sheets of paper being cut up. |
| B | It is more convenient to not cut the parts that will connect in the end. |
| C |
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| D | It is more convenient, because it is eas ier to build by connecting and opening it up. |
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The cubes are the same, but many kinds of developments can be produced according to different cutting methods (development methods). |
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When the surfaces facing each other have the same color, regular squares of the same color are never adjacent to each other when the cube is developed.
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| G | I did not notice that myself and I was surprised that there are so many possible developments. |
| H | A development does not exist when five or more regular squares form a line. |
| I | If I think about how the sides will connect with each other when the cube is built, it appears possible to derive another development from another. |
| J | There are cases where a cube cannot be created even when regular squares of the same color are not adjacent to each other and even when five or more regular squares do not form a line. |
| K | I would like to further research the positional relation ships of a cube's surfaces, sides, and vertexes. |
