Outline: "constructing three-dimensional figures with 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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Promote students' reflecting three-dimensional figures constructed by translating a plane figure respectively. | ||||||||||||||||
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Recognize that it was difficult to draw sketches of those and ask "How can you draw them well?" to students. | ||||||||||||||||
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Set the learning task.
Let's think about ways of drawing the sketch es better by referring to the way a column is created when moving planes around with Cabri 3D.
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Using Flash Movie, show the figure that is created when a vertical move is made relative to a plane figure, in addition to confirm the operational methods.
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Think about how to draw the sketches better by individually operating Cabri 3D, and then draw ing the sketch.
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Respond to any students puzzled by operating the computer. | ||||||||||||||||
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As the sketch is drawn, instruct students to focus on the positional relation ships of the "sides," "sides and surfaces," and "surfaces," and to list what can (or cannot) be said. | ||||||||||||||||
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Ask: "Is there anything that any of the columns have in common?" | ||||||||||||||||
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Discuss approximately the following from what the students thought about. [Sides] . The longitudinal sides created through moving the figures are all parallel to each other. . The sides of the moved figures are all vertical relative to the created longitudinal sides where are cross. . Some of the sides of the moved figure and the created longitudinal sides are not parallel and do not cross. (Twist) [Sides and Surfaces] [Surfaces] ... Details omitted |
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Ask what happens to the relation ships that were discussed when a diagonal move is carried out relative to the plane, and show how a given square moves diagonally .
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While moving a given square and circle in diagonal directions, observe the positional relation ships among the sides and surfaces.
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Let the students observe closely the positional relation ships of the sides and surfaces while operating Cabri 3D. (Drawing a sketch is unnecessary .) | ||||||||||||||||
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Observe with emphasison the Cabri 3D operations. |
Expected responses from the students
| A | Figures such as a triangular prism, quadrangular prism, and cylinder were created . |
| B | It was very difficult to draw the sketch. |
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It seems that I can draw the sketch well when referring to how the plane figure moves .
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| F | All the line segments are of the same length, because the height coincides with the distance created by moving the plane. |
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| H |
In the case of moving a circle, draw perpendicular lines from the circumference.
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| I | All the longitudinal sides are of the same length. |
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When it is moved diagonally relative to the plane, a skewed column is created.
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| L | The upper and lower bases are parallel in all cases. |
| M | Regarding the created longitudinal sides, the same thing can be said in the case when moving the figure vertically. |
