Topicma9005c96737520b0_1528449000663_0Topic

The pyramid – the description of the solid

Levelma9005c96737520b0_1528449084556_0Level

Second

Core curriculumma9005c96737520b0_1528449076687_0Core curriculum

XI. Solid geometry. The student:

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

Timingma9005c96737520b0_1528449068082_0Timing

45 minutes

General objectivema9005c96737520b0_1528449523725_0General objective

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

Specific objectivesma9005c96737520b0_1528449552113_0Specific objectives

1. Discussing the structure of the pyramid.

2. Drawing pyramids.

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

Learning outcomesma9005c96737520b0_1528450430307_0Learning outcomes

The student:

- knows the structure of the pyramid,

- draws pyramids.

Methodsma9005c96737520b0_1528449534267_0Methods

1. Discussion.

2. Individual problem competition.

Forms of workma9005c96737520b0_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionma9005c96737520b0_1528450127855_0Introduction

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

Procedurema9005c96737520b0_1528446435040_0Procedure

The students make the definition of the pyramid and defines various types of pyramids on the basis of the models presented by the teacher.

Definition

- The pyramid is a type of a polyhedron, whose base is any polygon and the lateral faces are triangles which meet at one mutual vertex.

Types of pyramids:

- The right regular pyramid – the pyramid whose all lateral edges are equal.

- The oblique pyramid – the pyramid which is not straight.

- The regular pyramid – the right regular pyramid whose base is a regular polygon.

- The regular tetrahedron – the pyramid whose all faces are equilateral triangles.

Task

The students work individually, using their computer. Their task is to indicate the elements of the pyramid in the diagram.

[Geogebra applet]

Individual problem competition.

The students solve the competition tasks. They can look for the needed information in any available sources, e.g. on the Internet. The students can start another level of the competition if they have the correct results confirmed. Three fastest students get excellent marks, the consecutive three get very good marks.

Competition task

Draw an oblique triangular pyramid and indicate its altitude in the diagram.ma9005c96737520b0_1527752263647_0Draw an oblique triangular pyramid and indicate its altitude in the diagram.

Competition task

Draw a right regular pyramid whose altitude is 7 cm and the base is a rhombus.ma9005c96737520b0_1527752256679_0Draw a right regular pyramid whose altitude is 7 cm and the base is a rhombus.

Competition task

The base of the regular triangular pyramid is a triangle whose area is
$16\sqrt{3}$ cmIndeks górny 2². Calculate how many centimeters of wooden slat you need to build a model of the pyramid if its lateral edge equals 9 cm.ma9005c96737520b0_1527712094602_0The base of the regular triangular pyramid is a triangle whose area is
$16\sqrt{3}$ cmIndeks górny 2². Calculate how many centimeters of wooden slat you need to build a model of the pyramid if its lateral edge equals 9 cm.

Competition task

The sum of lengths of all edges of the pentagonal pyramid equals 40. Calculate the length of the lateral edge of this pyramid, knowing that the base edge equals 3.

Competition task

Does a pyramid with 21 edges exist?

Extra competition task:

The 100‑gonal pyramid 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.

Lesson summaryma9005c96737520b0_1528450119332_0Lesson summary

The students do additional tasks.

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

- The pyramid is a type of a polyhedron, whose base is any polygon and the lateral faces are triangles which meet at one mutual vertex.

Types of pyramids:

- The right regular pyramid – the pyramid whose all lateral edges are equal.

- The oblique pyramid – the pyramid which is not straight.

- The regular pyramid – the right regular pyramid whose base is a regular polygon.

- The regular tetrahedron – the pyramid whose all faces are equilateral triangles.

Selected words and expressions used in the lesson plan

the pyramidthe pyramidthe pyramid

the right regular pyramidthe right regular pyramidthe right regular pyramid

the regular pyramidthe regular pyramidthe regular pyramid

the oblique pyramidthe oblique pyramidthe oblique pyramid