Outline: "explanation of the reason why a cube's cut surface can not be a regular pentagon.
... 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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Present again the sketch submitted the previous time, and confirm that it seemed to be possible to create a "regular triangle," a "rhombus," and a "regular hexagon" when the cube was cut through a plane. | ||||||||||||
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Regarding the case where a cut surface become a "regular triangle," a "rhombus," or a "regular hexagon," observe them from various directions using Cabri 3D.
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Based on the content learned the previous time, confirm that it seemed to be impossible to create a regular pentagon when the cube was cut through a plane. | ||||||||||||
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Ask: "Is it true that a regular pentagon cannot be created no matter what cutting method is used?" | ||||||||||||
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Present a sketch that looks like a regular pentagon, and request observation of an actual cubic object created from Sty r ofoam. | ||||||||||||
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 With operations in mind regarding the question, "Is it true that a regular pentagon cannot be created?" set learning as observation of the cut area when the cube was cut.
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Observe while individually operating Cabri 3D. | ||||||||||||
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Think about why a regular pentagon cannot be created. | ||||||||||||
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Ask if there is a common point that can be said regarding pentagons appearing on the cut surface. | ||||||||||||
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Through various cut s and observation, describe inductively that it seems to be impossible to create a regular pentagon. |
Expected responses from the students
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| B | It appears to be an isosceles triangle according to the observation direction. However, when viewed from the anterior, it can be understood that a regular triangle is created. |
| C | It is difficult to know the actual shape of the cut surface when they are not viewed from the anterior. It is important to make observ ations from various directions . |
| D | A regular triangle, regular square and regular hexagon were definitely created. But is it true that a regular pentagon cannot be created? |
| E | When the sketch drawn by the teacher is seen , it appears to be a regular pentagon, but it is probably necessary to observe it from various directions. |
| F |
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| G | It appears to be a regular pentagon. |
| H |
Even when the same cutting method is used, the cut surface look s different according to the observation direction. Thus, it is necessary to observe it by changing observation direction even though it does appear to be a regular pentagon.
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| I |
 Even though it appears to be a regular pentagon, it can be understood that it is indeed not a regular pentagon when the observation direction is changed. |
