ENJOY MATHEMATICS in 3D

Lesson7

Set a learning activity of creating stamps by cutting the cubes.
Arrange the learning environments to ensure that the observation can be carried out while the cubes are freely cut with Cabri 3D.

Take up polygons that can and cannot be created on the cut surfaces, and think about why.

Set up a situation to take up the challenge of creating a stamp in the form of a regular pentagon.
Let the students focus on the outlines created by crossing two planes and on the positional relationships among the surfaces making up the cubes.

Based on the characteristics of a regular pentagon and a regular hexagon, set the learning activity of thinking about why a regular pentagon does not appear on a cut surface of a cube.
Prepare the contents facilitating the observation of the cases where a cut surface becomes a regular hexagon and where a cut surface becomes a pentagon.
* The situation provides an opportunity to actually see that a contrasting proposition B of a true proposition A is also true (true and false coincide). It is considered as the learning of fostering a basis for demonstration.

Cut three-dimensional figures other than a cube, and observe figures appearing the cut surfaces.

Set a learning activity of creating stamps by cutting the three-dimensional figures other than a cube.
Set learning environments to ensure that the three-dimensional figures such as a sphere, cylinder, and cone can be observed as they are cut with Cabri 3D.

Observe the figures that appear when a cone is cut by various planes, and summarize the characteristics.

Prepare two congruent three-dimensional figures whose vertexes are connected and which are symmetrically placed with respect to the point. Set learning activities of cutting the figures with a plane parallel to the generating line and with a plane parallel to the rotation axis, and of summarizing the characteristics.
Use Flash Movie, and prepare the contents facilitating understanding of existence of a hyperbola.
* A parabola also appears. But do not deal with the further details. However, when the figures are cut by a plane parallel to the rotation axis and with a place parallel to the generating line, expect that there are students who notice their differences.