Topicmad5c50de7f751b8b_1528449000663_0Topic

Cylinders, cones and spheres in practical situations

Levelmad5c50de7f751b8b_1528449084556_0Level

Second

Core curriculummad5c50de7f751b8b_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.

Timingmad5c50de7f751b8b_1528449068082_0Timing

45 minutes

General objectivemad5c50de7f751b8b_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts.

Specific objectivesmad5c50de7f751b8b_1528449552113_0Specific objectives

1. Recognising the cylinders, the cones and the spheres.

2. Describing the elements of the cylindercylindercylinder and the coneconecone.

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

Learning outcomesmad5c50de7f751b8b_1528450430307_0Learning outcomes

Student:

- recognises the cylindercylindercylinder, the coneconecone and the spherespheresphere,

- describes the elements of the cylinder and the cone.

Methodsmad5c50de7f751b8b_1528449534267_0Methods

1. Brainstorming.

2. Situational analysis.

Forms of workmad5c50de7f751b8b_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmad5c50de7f751b8b_1528450127855_0Introduction

Discussion about the shape of the objects in our surroundings. The students should notice that apart from the prisms and the pyramids there are other models of the solids. Such models are for example the flower pot, a can, a birthday cap or a ball.

The teacher explains that such shapes are characteristic for the solids if revolution. The sample solids are: cylinders, cones and spheres.

Proceduremad5c50de7f751b8b_1528446435040_0Procedure

Task 1

The students work individually using their computers. They are going to watch how cylindercylindercylinder is constructed and what element is it made of.

After completing the task the students form the definition of the cylinder and some of its elements.

The cylindercylindercylinder is a solid, which was made as a result of rotating a rectangle about one of its sides.

The generating linegenerating linegenerating line is every segment whose endings belong to the bases of cylinder included in the lateral surface of the cylinder.

The altitude of the cylinder is the every perpendicular segment between the bases. In particular the generating line of a cylinder is its altitude.

Task  2

The students work individually using their computers. They are going to watch how the right triangle was rotated to make the coneconecone and what elements is a cone made of.

[Illutration 1]

After completing the task they form the definition of the cone. The cone is the solid made by rotating the right triangle about the line including one of its legs.

The cone is a solid, which was made as a result of rotating a right triangle about the line including one of its legs.

Task 3

Students cut out a circle. They cut it in such a way to get half a circle and two quarters . Next, they stick the lateral surfaces of two cones: half a circle and a quarter of the circle. (one quarter is still left). They trace the bases of both cones and they discuss which of the base of the cone has a greater diameter. They compare the altitude of both cones.mad5c50de7f751b8b_1527752256679_0Students cut out a circle. They cut it in such a way to get half a circle and two quarters . Next, they stick the lateral surfaces of two cones: half a circle and a quarter of the circle. (one quarter is still left). They trace the bases of both cones and they discuss which of the base of the cone has a greater diameter. They compare the altitude of both cones.

Conclusion:

The basebasebase of the coneconecone whose lateral surface was the half a circle has larger diameter .

The cone whose lateral surface was the quarter of circle has larger altitude.

The teacher shows an orange and explains it is in a shape of the spherespheresphere.

The students are going to find out some information about the sphere, what  it is made of.

An extra task:

Construct a model of an object of everyday use made of the elements of the cylinders,  the cones and the spheres.

Lesson summarymad5c50de7f751b8b_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

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

- The cylinder is a solid, which was made as a result of rotating a rectangle about one of its sides.
- The generating line is every segment whose endings belong to the bases of cylinder included in the lateral surface of the cylinder.
- The altitude of the cylinder is the every perpendicular segment between the bases. In particular the generating line of a cylinder is its altitude.
- The cone is a solid, which was made as a result of rotating a right triangle about the line including one of its legs.mad5c50de7f751b8b_1527752263647_0- The cylinder is a solid, which was made as a result of rotating a rectangle about one of its sides.
- The generating line is every segment whose endings belong to the bases of cylinder included in the lateral surface of the cylinder.
- The altitude of the cylinder is the every perpendicular segment between the bases. In particular the generating line of a cylinder is its altitude.
- The cone is a solid, which was made as a result of rotating a right triangle about the line including one of its legs.

Selected words and expressions used in the lesson plan

cylindercylindercylinder

coneconecone

spherespheresphere

basebasebase

solid of revolutionsolid of revolutionsolid of revolution

generating linegenerating linegenerating line