ENJOY MATHEMATICS in 3D

Lesson1

Create a cube and observe the positional relationships among the surfaces, sides, and vertexes.

Set the learning activity of creating the cube for the purpose of using it as a die in a game.
By using polyhedrons, set up the time of observing the positional relations among such matters as the development types and surfaces while students open them up and close them again.

Clarify a difference between the developments capable of creating a cube (correct developments) and those incapable of doing so (incorrect developments).

Clarify the common characteristics of the developments capable of creating a die, and set the learning activity of explaining why some developments are incapable of creating a die.
* The situation provides an opportunity to see a converse proposition B of a true proposition A is not necessarily true. It is considered as the learning of fostering a basis for demonstration.

While a cone is drawn with Cabri 3D, understand the basic operations of Cabri 3D through observation of three-dimensional figures.

Set a learning of drawing the cone by using Cabri 3D.
Deal carefully with the method of taking a point in a given space.
* By dealing with such methods as changing a radius of a circle, changing a point's position, and observing from various directions, this hour aims at ensuring that subsequent learning activities are smoothly carried out.

Expand perspective regarding the method of constructing three-dimensional figures. (Part 1)
* Columns and oblique prisms are seen as the three-dimensional figures constructed by movements of planes.

Present a thick book and a stack of paper, and expand images.
Prepare simulation of constructing a quadrangular prism from a square.
Arrange the learning environments to ensure that the observation can be carried out while Cabri 3D is used to create the columns and oblique prisms by moving planes parallel.

Expand perspective regarding the method of constructing three-dimensional figures. (Part 2)
* Such figures as spheres, cylinders, and cones are seen as the three-dimensional figures constructed by rotating a plane.

Present the model of a rotating body, and confirm that it is a three-dimensional figure that can always be seen as a circle from a certain direction.
Show simulation of a cylinder as a rotation body example.
Arrange the learning environments to ensure that three dimensional figures are created by rotating various figures around the rotation axes by using Cabri 3D.

Expand perspective regarding the method of constructing three-dimensional figures. (Part 3)
* Columns and oblique prisms are seen as the three-dimensional figures constructed by moving line segments.

Arrange the learning environments to ensure that the columns and conic solids are seen as a set of line segments (generating lines) of the same length.
Arrange the learning environments to ensure that a column can be created by rotating, for one time, a line segment vertical to the base, along the circumference of the base, and that a conic solid can be created by fixing one tip of a line segment while rotating another tip along the circumference of the base.
Prepare a model allowing students to see that something is inside of the three-dimensional figures in order to facilitate their understanding: "The insides are not stuffed." This is one of the differences from three-dimensional figures created by rotation or parallel translation of (a) plane(s).