Topicmbad0a57acf5d85b1_1528449000663_0Topic

Angles and their types

Levelmbad0a57acf5d85b1_1528449084556_0Level

Second

Core curriculummbad0a57acf5d85b1_1528449076687_0Core curriculum

VIII. The angles. The student:

1) identifies the arms and the vertexvertexvertex in any angleangleangle;

4) identifies the acute, right and obtuse angles.

Timingmbad0a57acf5d85b1_1528449068082_0Timing

45 minutes

General objectivembad0a57acf5d85b1_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts, including practical one.

Specific objectivesmbad0a57acf5d85b1_1528449552113_0Specific objectives

1. Indicating the arms and the vertexvertexvertex in an angleangleangle.

2. Identifying the types of angles on the basis of the drawings and their measuremeasuremeasure.

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

Learning outcomesmbad0a57acf5d85b1_1528450430307_0Learning outcomes

The student:

- indicates and describes the elements of the angleangleangle,

- identifies and describes the acute, the right and the obtuse angles.

Methodsmbad0a57acf5d85b1_1528449534267_0Methods

1. Practical exercises.

2. Situational analysis.

Forms of workmbad0a57acf5d85b1_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionmbad0a57acf5d85b1_1528450127855_0Introduction

The teacher introduces the topic of the lesson: the students are going to learn the notion of the angleangleangle and its types.

The angle is not only a mathematical term but mostly the geometric figure which is present in our everyday life.

The teacher presents the drawing of the angleangleangle to the students .Then, they define the angle together.

[Illustration 1]

Two half‑lines with a common beginning cut the plane into two parts. Each of these parts with half‑lines is called the angle.mbad0a57acf5d85b1_1527752263647_0Two half‑lines with a common beginning cut the plane into two parts. Each of these parts with half‑lines is called the angle.

The vertex is a common beginning of two half‑lines which are called the arms of the angle.
The measurement unit of the angle is a degree. The angle of 20 degrees is indicated with the symbol 20°.
Students point out the models of the angles in the classroom.mbad0a57acf5d85b1_1527752256679_0The vertex is a common beginning of two half‑lines which are called the arms of the angle.
The measurement unit of the angle is a degree. The angle of 20 degrees is indicated with the symbol 20°.
Students point out the models of the angles in the classroom.

What elements is an angleangleangle made of?

Give some examples of the angles.

Procedurembad0a57acf5d85b1_1528446435040_0Procedure

Task

Students work individually using their computers. They are going to watch how the name of the angleangleangle changes according to its measuremeasuremeasure.

[Geogebra applet]

After completing the task students should draw the following conclusions:

- the angleangleangle which is greater than 0 and smaller than 90 degrees is called the acute angleacute angleacute angle,

- the angle with the measuremeasuremeasure of 90 degrees is called the right angleright angleright angle,

- the angleangleangle greater than 90 and smaller than 180 degrees is called the obtuse angleobtuse angleobtuse angle.

Task

Students draw in their notebooks:

- the right angleright angleright angle,

- three acute angles,

- three obtuse angles.

Task

Students answer the following questions:

Is every acute angleacute angleacute angle smaller than the right angleright angleright angle?

Is the measuremeasuremeasure of the obtuse angleobtuse angleobtuse angle smaller than the acute angle?

Does the acute angleacute angleacute angle greater than 45° exist?

Is the angleangleangle 20° greater than the 75° an acute angle?

An extra task

Using various sources of information, the literature or the Internet answer the following questions:

What is the measuremeasuremeasure of the zero angle, the straight angleangleangle, the round angle? What do such angles look like?

What angles are called convex angles? Give the examples.

What angles are called concave? Give the examples.

Lesson summarymbad0a57acf5d85b1_1528450119332_0Lesson summary

Students do the exercises summarising the class.

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

The angleangleangle is a part of a planeplaneplane cut out by the two half‑lines with a common beginning. These half‑lines are called the arms of the angle and the beginning is called the vertexvertexvertex of an angleangleangle.

There are three main types of the angles:
- acute angles from 0 to 90 degrees,
- right angles of 90 degrees,
- obtuse angles from 90 to 180 degrees.mbad0a57acf5d85b1_1527712094602_0There are three main types of the angles:
- acute angles from 0 to 90 degrees,
- right angles of 90 degrees,
- obtuse angles from 90 to 180 degrees.

Selected words and expressions used in the lesson plan

acute angleacute angleacute angle

angleangleangle

armarmarm

half‑linehalf‑linehalf‑line

measuremeasuremeasure

obtuse angleobtuse angleobtuse angle

planeplaneplane

pointpointpoint

right angleright angleright angle

vertexvertexvertex