Outline: "cutting cylinder s and cone s , and observation of the cut surfaces"
... 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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Ask: "What kinds of three-dimensional figures need to be cut in order to create stamps that includ e a curved line?" | ||||||||||||||
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Think about the three-dimensional figures that include a curved line, and realize that a sphere, cylinder, or cone need s to be used. | ||||||||||||||
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Demonstrate how to cut a sphere. | ||||||||||||||
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Set learning as observation of the cut area when a sphere is cut.
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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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Describe that, no matter how the sphere is cut, the cut surface will always be a circle. | ||||||||||||||
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Observe similarly in the case of cutting a cylinder.
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Describe that there are cases when a cut surface will be a shape such as a circles, ellipse, and rectangle. | ||||||||||||||
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Observe similarly in the case of cutting a cone.
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Describe that there are cases when the cut surface will be a shape s uch as a circle, ellipse, parabola, hyperbola, or isosceles. |
Expected responses from the students
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| B |
The size of the cut surface vari es but the shape always seem s to be a circle.
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| C | Many seal impressions are cylinder-shaped. If a cylinder is cut through a plane parallel to the rotation axis, the cut surface will be a circle. |
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| E |
When it is cut through a plane unparallel to the rotation axis, an ellipse is created.
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| F | There are cases where the ellipse will be broken at the upper or lower base, but it becomes an unbroken ellipse if the cylinder is considered to be longer. |
| G | When it is cut through a plane parallel to the rotation axis, a rectangle is created. |
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| I |
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| J |
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| K |
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| L |
 In the case of cutting a cone, an isosceles is created when it is cut through a plane that includes the vertex and that is vertical to the base surface. |
| J | In the case of cutting a cone, a smooth curved line (hyperbola/parabola) appears. |
