Observe a three-dimensional figure while drawing a cone with Cabri3D.
Outline: "constructing three-dimensional figures through parallel translation s of planes"

Learning activities ... Learning activities     Teacher's instructions/guide ... Teacher's instructions/guide     Evaluation (expected student responses)   ... 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]
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Learning content

Teacher's instructions/guide Present a conical model, and request observation from different directions.
Teacher's instructions/guide Ask: "What is a good way to draw a three-dimensional figure in order to show it on a plane?"
Learning activities Think about showing it by means of a development based on content already learned.
Learning activities Apart from the development, think about drawing the observed condition as is.
Teacher's instructions/guide Explain that a figure drawn to approximate the observed condition is called a "sketch."
Teacher's instructions/guide Introduce the dynamic geometry soft "Cabri 3D," and outline it.
Teacher's instructions/guide Set sketch ing a cone using Cabri 3D as a task.
[Task]
Let's draw and observe a cone using Cabri 3D.
Learning activities Draw a cone using Cabri 3D.
Teacher's instructions/guide To denote a point in a given space, the concept of space itself is necessary, and rather difficult. Ensure sufficient time while teaching it carefully and taking your time.
Learning activities Move and rotate the drawn apex of the cone, and observe it from various directions.
Evaluation (expected student responses) Draw a cone using Cabri 3D.

[Note]
Since this class aims at understanding the characteristics and basic operations of Cabri 3D, ensure time where free operations can be carried out as much as possible, and emphasize the importance of instructions in according with students' needs.

Expected responses from the students

A It looks like a triangle when seen from the side.
B It looks like a circle when seen from above (or the bottom).
C There is a development for showing three-dimensional figures in the plane.
D
Explanation of the sketch is given .
Other than a development, there should be a way of expressing it as a picture and showing the observed condition as it is.
E
Cabri 3D is explained .
Let's show a cone with a sketch.
F It seems possible to draw a cone using Cabri 3D.
[Task]
Let's draw and observe a cone using Cabri 3D.
G I understood how to draw a circle on a plane, but I do not understand how to decide the apex.
H
Explain operational methods according to individual student.
I thought that I had set the apex, but the point seems to be located in the same plane as the base.
I cabri3D I was able to draw a cone.
J cabri3D When the point is moved to the side, the whole figure is modified.
K It is possible to modify the size of the circle.
L It is very convenient, because it is possible to observe it while freely rotating it.


In addition, all copy rights of the unit structure, Class development, and worksheets belong to Hitoshi Arai (affiliation: Nagano City Yanagimachi junior high school).

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