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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Using the worksheet and Cabri 3D File from the previous time, confirm the shape of the cut surface when a cone is cut through a plane parallel to the symmetrical axis. | ||
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Introduce the "hyperbol ic triangle," and provide the opportunity to observe the case where two cones are cut.
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Observe the cut surfaces while freely moving the plane used to cut it . | ||
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Take up the case of cutting them through a plane parallel to the rotation axis, and discuss the appropriateness of the name "hyperbol ic (triangle)." | ||
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After showing the hyperbola created using Flash Movie, take time to confirm it while observation is freely carried out using Cabri 3D File.
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Regarding the case of cutting them through a plane parallel to the base line, discuss the difference when cutting them through a plane parallel to the rotation axis. | ||
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After showing that a parabola is created using Flash Movie, take time to confirm it while freely observing it using Cabri 3D File.
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Using Flash Movie, show how the shape of the cut surface changes from "a circle --- an ellipse --- a parabola --- a hyperbola," and summarize that all the figures are included in the "conic al curve" group.
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Observe again using the file showing the cutting from free directions. | ||
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The students will be convinced that there are the cut surfaces in the form of a circle, an ellipse, a parabola, and a hyperbola (and an isosceles), and that the figures can be summarized as the conic al curve group . |
Expected responses from the students
| A | When they are cut by a plane parallel to the rotation axis, a mountain-like shape was created. |
| B |
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| C | When how two cones can be cut is observed, it definitely appears to be a hyperbola, because similar curved lines appear both above and at the bottom. |
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| E |
I was surprised that it was actually a hyperbola in the case of
cutting through a plane parallel to the rotation axis. |
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| G | They are similar curved lines, but they seem to be different. |
| H | A smooth curved line appear s in both cases . |
| I |
Until now, a curved cut surface has always appeared except in the cases of isosceles-shaped cut surfaces.
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| J | I underst an d that various figures can appear when cones are cut. |
| K | All the figures differ from each other, but it can be said that they all belong to the same group when consideration is given to " what appear s when a cone is cut." |
| L | I feel, "It is understandable," when viewed again using Cabri 3D. |
