Topicm43e01c70eb8cdac7_1528449000663_0Topic

Pyramids

Levelm43e01c70eb8cdac7_1528449084556_0Level

Second

Core curriculumm43e01c70eb8cdac7_1528449076687_0Core curriculum

X. The solids. The student:

1) identifies the right prisms, the pyramids, the cylinders, the cones, the spheres in practical situations and differentiates them from other solid models.

Timingm43e01c70eb8cdac7_1528449068082_0Timing

45 minutes

General learning objectivesm43e01c70eb8cdac7_1528449523725_0General learning objectives

Creating and interpreting mathematical texts, presenting data graphically.

Key competencesm43e01c70eb8cdac7_1528449552113_0Key competences

1. Identifying pyramids as well as the relevant terminology in English.

2. Describing the construction and the elements of pyramids.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Operational (detailed) goalsm43e01c70eb8cdac7_1528450430307_0Operational (detailed) goals

The student:

- identifies pyramids,

- identifies and describes the basic elements of pyramids in English.

Methodsm43e01c70eb8cdac7_1528449534267_0Methods

1. Practical exercises.

2. Situational analysis.

Forms of workm43e01c70eb8cdac7_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm43e01c70eb8cdac7_1528450127855_0Introduction

Students point at the the vertices, thy edges, the faces and the bases in the models of polyhedrons.

Revision of the elements of the prisms.

The teacher introduces the topic of the lesson: learning about pyramids and about their properties.

Procedurem43e01c70eb8cdac7_1528446435040_0Procedure

Egyptian pyramids are well‑known examples of pyramids in architecture. The basebasebase of the pyramidpyramidpyramid is a squaresquaresquare and all its lateral faces are identical isosceles triangles.

[Illustration 1]

Many buildings and objects are not the pyramids (types of buildings) but they are spatial figures called pyramids.m43e01c70eb8cdac7_1527752263647_0Many buildings and objects are not the pyramids (types of buildings) but they are spatial figures called pyramids.

[Ilustration 2]

[Ilustration 3]

The teacher presents the models or the drawings of the solids.

The solids presented below

[Illustration 4]

are called pyramids.

On the basis of the drawing teacher introduces the notions related to the pyramid: the vertexvertexvertex, the edgeedgeedge, the facefaceface.

The drawing below presents the elements of the pyramidpyramidpyramid.

[Illustration 5]

The student can answer the question:

How many bases, vertices and edges does this pyramid have?

The students watch what kind of figures the faces of pyramids are and what the name of the pyramid depends on.

[Slideshow]

Task 1

Watch the slideshow and answer the following questions:

What is the shape of the lateral faces of the pyramids?
What does the name of the pyramid depend on?m43e01c70eb8cdac7_1527752256679_0What is the shape of the lateral faces of the pyramids?
What does the name of the pyramid depend on?

Students should come up with the following conclusions:

- all lateral faces of the pyramids are in the shape of the triangletriangletriangle,

- the name of the pyramid depends on the type of its polygonal basebasebase.

Students point at the:

- pyramids among other models of solids which are in the classroom,

- classroom objects in the shape of the pyramid,

- the examples of other objects in the shape of pyramid which can be found around.

The students and the teacher draw the following conclusion:

The pyramidpyramidpyramid is a spatial figurespatial figurespatial figure which has:

- one polygonpolygonpolygon base,

- lateral faces of triangles.

The name of the pyramid depends on the type of polygon of the base.

Students identify the pyramids presented in the drawing.

Task 2

Identify the pyramids shown in the drawings below. Give the number of:

a) lateral edges,

b) basebasebase edges,

c) lateral faces,

d) vertices

of each of these pyramids.

[Illustration6]

Students describe the construction of the pyramid and its elements.

Task 3

Look at the model of the pyramid below and complete the sentences to make them correct.

[Illustration 7]

The pyramidpyramidpyramid with the base of:

a) triangletriangletriangle,

b) quadrangle,

c) pentagon,

d) hexagon.

The pyramid has:

a) 5, 6, 7, 8 vertices,

b) 8, 10, 12, 14 edges,

c) 4, 5, 6, 7 lateral faces.

The lateral faces are:

a) the isosceles triangles,

b) the right–angled triangles,

c) the squares,

d) the trapeziums.

An extra task:

Find on the Internet examples of the pyramids in architecture.

Lesson summarym43e01c70eb8cdac7_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

Then, together they sum up the classes, drawing the conclusions to memorise:

- The pyramidpyramidpyramid is a spatial figurespatial figurespatial figure which has one polygonal base and lateral faces of triangles.

- The right pyramid with the base of a regular polygonpolygonpolygon is called the regular pyramid. Its lateral faces are congruent isosceles triangles.

- The name of the pyramid depends on the type of the polygon of the base, e.g. a pyramid with the base of pentagon is called the pentagonal pyramid.

The students discuss what they have learned during the lesson. 

Homework:

Use the available sources of information to find out what the tetrahedron is.

Selected words and expressions used in the lesson plan

basebasebase

edgeedgeedge

facefaceface

lateral facelateral facelateral face

polygonpolygonpolygon

pyramidpyramidpyramid

spatial figurespatial figurespatial figure

squaresquaresquare

triangletriangletriangle

vertexvertexvertex