ENJOY MATHEMATICS in 3D

Lesson 12

Introduce products that effectively use the methods of cutting a cylinder and a cone.
Introduce situations where designs are contrived in terms of functionality.
Introduce situations where various three-dimensional figures can be observed (for example, a photo of the head office of Fuji Television Network, Inc.), and set a learning of drawing it with Cabri 3D.
* The hour is to freely use Cabri 3D.

Take up a cylinder-shaped container and a cone-shaped container which have the same base area and height, and set a learning situation where the volumes are compared.
Through actually creating each three-dimensional figure, emphasize the relationship of the actual measurements and calculation methods.
Through the comparison of the volumes of the cylinder and a cone, summarize inductively how to obtain volumes of prisms and of conic solids.

Regarding the cylinder and the cone created during the previous hour, set a learning situation to think which container can be created with smaller paper.
Confirm that the areas of the developments coincide with the surface areas of the figures.
Summarize how to obtain the area of the sector.
Confirm the meanings of “surface area,” “base area,” and “lateral area.”
Through the comparison of the volumes of the cylinder and the cone, summarize inductively that the surface areas of the three-dimensional figures coincide with the areas of the developments.
* When the areas of the developments are obtained, the areas of the known figures need to be obtained and totaled. Thus, it is considered that this point can be summarized as the matter common to all three-dimensional figures.