Lesson14 - ENJOY MATHEMATICS in 3D

Outline: "cutting cylinder s and cone s , and observation of the cut surfaces"

... Learning activities

... Teacher's instructions/guide

... 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] .

[Task]

Let's compare which has the smaller paper pattern when creating containers A and B.

Learning content

	Regarding container A (column) and container B (conic solid) used the previous time, provide the opportunity to think about which can be created with the smalle st paper.
	Observe while picking up with his or her own hands the three-dimensional figures that he or she created.
	By developing them again, think about how to obtain their surface area.
	Request confirmation of the type of the figures that mak e up the developments.
	Regarding how to obtain the surface area of the sector figure, request th at students think about its percentage relative to a full circle whose radius is 10cm.
	By using such ma terial as the circular graphs learned at elementary schools, confirm that the percentage of the part relative to the whole figure can be obtained by using the center angle.
	Teach "base area," "lateral area," and "surface area , " respectively.
	Confirm that the surface area is the area of the development and can be obtained by totaling the area of each part (such as base and side surfaces).
	Summarize that, in addition to columns and cones, the same thing can be said of other three-dimensional figures.
	Obtain the surface area of the column and cone through calculations. [Note] Volume and surface area are not limited to cylinder s and cone s , but can be learned using the column and cone as the opportuni ty for discussion . If there is any spare time, provide the opportunity to learn about other three-dimensional figures through effective us e of actual objects.

Expected responses from the students

A	Waste can be reduced if containers can be created using the minimum material.
B	Since one cup of container A (cylinder) was equivalent to three cups of container B (cone), there is probably a similar difference in the size of the paper patterns.
C	It seems that the size of the surface area is not that different.
D	Since the cylinder's development consists of circles and a rectangle, the surface area can be obtained by calculating and totaling each surface area.
E	Since the cone's development consists of a circle and a sector, the surface area can also be obtained by calculating and totaling each surface area. How does the surface area of the sector need to be obtained?
F	The center angle of the sector is 216 degrees. Since a full circle's circumference is 360 degrees, according to the following calculation, "216 / 360 = 0.6," the sector's surface area accounts for 60% of a full circle whose radius is 10cm.
G	The percentage is the same as that of the radius of the base surface accounting for the radius of the sector (when the side surface is developed).
H	The cylinder's surface area is 132 B cm2 and the cone's surface area is 96 B cm2; therefore, the difference is not that big al though the cylinder does ha ve the larger surface area.