Let's sketch the three-dimensional figures that can be created by moving plane figures in parallel.
Outline: "constructing three-dimensional figures with 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 Promote students' reflecting three-dimensional figures constructed by translating a plane figure respectively.
Teacher's instructions/guide Recognize that it was difficult to draw sketches of those and ask "How can you draw them well?" to students.
Teacher's instructions/guide 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.
Teacher's instructions/guide 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.
Vertical move of a quadrangle with trace Flash
Learning activities Think about how to draw the sketches better by individually operating Cabri 3D, and then draw ing the sketch.
Vertical move of a triangle Flash cabri
Vertical move of a triangle with trace Flash cabri
Vertical move of a rectangle Flash cabri
Vertical move of a rectangle with trace Flash cabri
Vertical move of a quadrangle Flash cabri
Vertical move of a quadrangle with trace Flash cabri
Vertical move of a circle Flash cabri
Vertical move of a circle with trace Flash cabri
Teacher's instructions/guide Respond to any students puzzled by operating the computer.
Teacher's instructions/guide 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.
Teacher's instructions/guide Ask: "Is there anything that any of the columns have in common?"
Teacher's instructions/guide 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
Teacher's instructions/guide 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 .
Diagonal move of a quadrangle with trace Flash
Learning activities While moving a given square and circle in diagonal directions, observe the positional relation ships among the sides and surfaces.
Diagonal move of a rectangle Flash cabri
Diagonal move of a rectangle with trace Flash cabri
Diagonal move of a quadrangle Flash cabri
Diagonal move of a quadrangle with trace Flash cabri
Diagonal move of a circle Flash cabri
Diagonal move of a circle with trace Flash cabri
Diagonal move of an ellipse Flash
Diagonal move of an ellipse with trace Flash
Teacher's instructions/guide Let the students observe closely the positional relation ships of the sides and surfaces while operating Cabri 3D. (Drawing a sketch is unnecessary .)
Evaluation (expected student responses) 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.
C
cabri3D It seems that I can draw the sketch well when referring to how the plane figure moves .
D
It seems possible to draw it well if an upper surface's position is determined by drawing a perpendicular line from the three vertexes of the triangle of the base surface.
E
The rectangle can also be done in a similar way .
F All the line segments are of the same length, because the height coincides with the distance created by moving the plane.
G
The way is the same regardless of the type of square created and moved.
H
cabri3D In the case of moving a circle, draw perpendicular lines from the circumference.
I All the longitudinal sides are of the same length.
J
Since the created longitudinal sides do not cross each other, they are also parallel.
K
cabri3D When it is moved diagonally relative to the plane, a skewed column is created.
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.

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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