Topicma091af722f76defb_1528449000663_0Topic

The prism – description

Levelma091af722f76defb_1528449084556_0Level

Second

Core curriculumma091af722f76defb_1528449076687_0Core curriculum

XI Solid geometry. The student:

recognizes prisms and pyramids – including right regular and regular,

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 √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.

Timingma091af722f76defb_1528449068082_0Timing

45 minutes

General objectivema091af722f76defb_1528449523725_0General objective

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

Specific objectivesma091af722f76defb_1528449552113_0Specific objectives

1. Discussing the structure of the prism.

2. Drawing prisms.

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

Learning outcomesma091af722f76defb_1528450430307_0Learning outcomes

The student:

- knows the structure of the prism,

- draws prisms.

Methodsma091af722f76defb_1528449534267_0Methods

1. Discussion.

2. Association chain.

Forms of workma091af722f76defb_1528449514617_0Forms of work

1. Group work.

2. Whole class.

Lesson stages

Introductionma091af722f76defb_1528450127855_0Introduction

The teacher informs the students that during the class they will recognize and draw prisms.

Procedurema091af722f76defb_1528446435040_0Procedure

Group work

The teacher gives the students models of: the cuboid, the oblique prism and the right triangular prism. The students’ task is to notice the similarities in the structure of prisms and finding the differences between them. The students make an association chain, where links illustrate information connected with the prism. They add the names and properties of the solids to their notes.

The students’ conclusions

The right regular prism – has two bases with the shape of congruent polygons on parallel planes. The lateral faces are rectangles perpendicular to the bases.

The right prism – is the right regular prism whose base is an equilateral polygon (e.g. the right triangle, the square, the regular pentagon, the regular hexagon).

The oblique prism – its lateral faces are parallelograms. They are usually on planes, which are not perpendicular to their bases.

Geogebra1

The students work individually, using their computers. Their task is to observe the method of drawing a model of a prism and the changes of the location of the prism on a plane.

Task

Draw the right triangular prism and the right hexagonal prism.ma091af722f76defb_1527752263647_0Draw the right triangular prism and the right hexagonal prism.

Task

Draw the oblique prism, whose base is the isosceles trapezoidma091af722f76defb_1527752256679_0Draw the oblique prism, whose base is the isosceles trapezoid.

Task

The base of the right triangular prism is a triangle whose area is $36\sqrt{3}\mathrm{}{\mathrm{cm}}^2$. Calculate how many centimetres of wooden slat you need to build a model of the prism whose altitude is 9 cm.

Task

Calculate the diagonal length of the right hexagonal prism whose base is 3 cm long and the altitude 8.ma091af722f76defb_1527712094602_0Calculate the diagonal length of the right hexagonal prism whose base is 3 cm long and the altitude 8.

Task

The n‑gonal prism is given.

Find:

a) the number of bases,

b) the number of base edges,

c) the number of lateral faces,

d) the number of lateral edges,

e) the number of all faces,

f) the number of all edges,

g) the number of vertices.

Extra task

What is the number of diagonals in:

a) the hexagonal prism,

b) the 100‑gonal prism,

c) then‑gonal prism?

Lesson summaryma091af722f76defb_1528450119332_0Lesson summary

The students do the additional tasks.

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

The right regular prism – has two bases with the shape of congruent polygons on parallel planes. The lateral faces are rectangles perpendicular to the bases.

The right prism – is the right regular prism whose base is an equilateral polygon (e.g. the right triangle, the square, the regular pentagon, the regular hexagon).

The oblique prism – its lateral faces are parallelograms. They are usually on planes, which are not perpendicular to their bases.

Selected words and expressions used in the lesson plan

oblique prismoblique prismoblique prism

prismprismprism

right prismright prismright prism

right regular prismright regular prismright regular prism