Topicmdf034be27cc747a6_1528449000663_0Topic

The surface area of the prism

Levelmdf034be27cc747a6_1528449084556_0Level

Second

Core curriculummdf034be27cc747a6_1528449076687_0Core curriculum

XI Solid geometry. The student:

1) recognizes prisms and pyramids – including right regular and regular,

2) calculates the volumes and the surface area of right regular and regular prisms and also the ones that are not right at the level of difficulty not higher than the example task: The base of the right regular prism is an isosceles triangle, whose two equal angles are 45° each, and the longest side has the length of $6\sqrt{2}$ dm. One of the sides of a rectangle, which is the face with the largest area, is 4 dm long. Calculate the volume and the total surface area of this prism.

Timingmdf034be27cc747a6_1528449068082_0Timing

45 minutes

General objectivemdf034be27cc747a6_1528449523725_0General objective

Using simple, well‑known mathematical objects, interpretation of mathematical concepts and operating mathematical objects.

Specific objectivesmdf034be27cc747a6_1528449552113_0Specific objectives

1. Calculating the surface area of the prism.

2. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

Learning outcomesmdf034be27cc747a6_1528450430307_0Learning outcomes

The student:

- calculates the surface area of the prism.

Methodsmdf034be27cc747a6_1528449534267_0Methods

1. Discussion.

2. Thematic competition.

Forms of workmdf034be27cc747a6_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmdf034be27cc747a6_1528450127855_0Introduction

The teacher informs the students that during this class they will calculate the surface area of the prism.

Proceduremdf034be27cc747a6_1528446435040_0Procedure

Task

The students work individually, using their computer. Their task is to observe how to draw the net of the prism.

[Geogebra applet]

Discussion – how to calculate the area of the prism, having its net.

The conclusion that should be drawn by the students:

- The surface area of the prism equals the area of the net of this prism.
P - the surface area of the prism equals:

where:
PIndeks dolny p  Indeks dolny koniec_p - the base area,
PIndeks dolny b_b - the lateral surface area.

The students use the information to solve the tasks.

The problem competition – students work in groups of 4 or 5. Each group solves the same set of tasks prepared by the teacher. The teacher gives marks as the prize in the competition.

Task

Draw the net of the regular hexagonal prism.mdf034be27cc747a6_1527752263647_0Draw the net of the regular hexagonal prism.

Task

Calculate the surface area of the right regular prism, whose altitude is 10 cm. The polygon illustrated below is the base of the prism.mdf034be27cc747a6_1527752256679_0Calculate the surface area of the right regular prism, whose altitude is 10 cm. The polygon illustrated below is the base of the prism.

[Ilustration 1]

Task

The base of the prism is a rectangle whose perimeter is 34. Two lateral faces are squares whose areas are 144 each. Calculate the lateral surface of this prism if its altitude equals 8.mdf034be27cc747a6_1527712094602_0The base of the prism is a rectangle whose perimeter is 34. Two lateral faces are squares whose areas are 144 each. Calculate the lateral surface of this prism if its altitude equals 8.

Task

The rhombus with altitude 5 cm and acute angle 60° is the base of the prism. Calculate the altitude and the total surface area of the prism if the lateral surface area equals 180 cmIndeks górny 2².

Having finished all the tasks, the fastest group presents their solutions. If the solutions are correct and the group also solved the additional task, the students get marks from the teacher.

An extra task:

Decide if the sentences are correct.

1. If the edges of one prism are identical to the edges of another prism, both prisms have identical surface area.

2. If all the edges of the regular prism will become three times longer, the total surface area will be three times larger.

Lesson summarymdf034be27cc747a6_1528450119332_0Lesson summary

The students do additional tasks.

Next, they summarize the class and formulate the conclusions that they need to remember.

P - the surface area of the prism equals:

where:
PIndeks dolny p_p - the base area,
PIndeks dolny b_b - the lateral surface area.

Selected words and expressions used in the lesson plan

the base surface of the prismthe base surface of the prismthe base surface of the prism

the lateral surface area of the prismthe lateral surface area of the prismthe lateral surface area of the prism

the net of the prismthe net of the prismthe net of the prism

the prismthe prismthe prism

the total surface area of the prismthe total surface area of the prismthe total surface area of the prism