Outline: "constructing the sides of three-dimensional figures by moving segments"
... 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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Think about the types of three-dimensional figures that can be constructed with segment's and moving them . | ||||||||
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Ask if there are any methods of creating a column and conic solid other than the already confirmed methods. | ||||||||
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Show a model created by erecting a bamboo skewer on the perimeter of a plane. | ||||||||
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Set learning as observation while moving a line segment and imaging the side of a cylinder.
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Observe while individually operating Cabri 3D. | ||||||||
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Respond to any students puzzled using the computer. | ||||||||
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Show how to create the side of a cylinder using a line segment.
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線分を動かして、円錐の側面をイメージしながら観察する学習を位置付ける。
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Observe while individually operating Cabri 3D. | ||||||||
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Respond to any students puzzled using the computer. | ||||||||
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Show how to create the side of a cone using a line segment.
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Set learning as observation while moving line segments and imaging the sides of a quadrangular prism and of a quadrangular pyramid.
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ompare the structures of each side of the cylinder, cone, quadrangular prism, and quadrangular pyramid, and ask about their "common points" and "different points." | ||||||||
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Summarize that the sides of any of the three-dimensional figures can be created by moving (a) line segment(s) and by a set of line segments. | ||||||||
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Summarize the differences between the "quadrangular pyramid" and "cylinder/cone/quadrangular prism." | ||||||||
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Describe that it is possible to view the column and conic solid as sets of line segments and as three-dimensional figures created by moving (a) line segments. | ||||||||
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Describe that only the length of the line segments of the "quadrangular pyramid" is not constant. | ||||||||
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Ask about the differences that can be found between the three-dimensional figures created by parallel translations or rotation of the plane surface(s) and the three-dimensional figures constructed with a set of line segments. Then confirm that a difference exists whether the inside is full or not. | ||||||||
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Concretely confirm using the models shown below. |
Expected responses from the students
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| B | When the bamboo skewer is viewed as a line segment, a column appears to be created by aligning line segments. |
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 When the segment line is moved around the circumference, it seems that a cylinder can be created. |
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The side of a cone is created when one end of a line segment is fixed in place while the other rotates .
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| H |
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| I |
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| J | However, the length of the line segments is constant in the case of the column and cone, but the length of the line segments of quadrangular pyramids is different in places and not constant. |
| K | The three dimensional figures created by parallel translations and rotation of the plane surface(s) are solid inside, but the three-dimensional figures created with a set of line segments are not. |
| L | Creating three-dimensional figures with a set of line segments means that only the shell is created. They appear to be like bird cages. |
