Topicmb2e38aa538066c6e_1528449000663_0Topic

Adjacent and apex anglesapex anglesapex angles

Levelmb2e38aa538066c6e_1528449084556_0Level

Second

Core curriculummb2e38aa538066c6e_1528449076687_0Core curriculum

VIII. The angles. The student:

6) identifies apex and adjacent anglesadjacent anglesadjacent angles and uses their properties.

Timingmb2e38aa538066c6e_1528449068082_0Timing

45 minutes

General objectivemb2e38aa538066c6e_1528449523725_0General objective

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

Specific objectivesmb2e38aa538066c6e_1528449552113_0Specific objectives

1. Identifying adjacent and apex anglesapex anglesapex angles.

2. Using the properties of adjacent and apex anglesapex anglesapex angles.

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

Learning outcomesmb2e38aa538066c6e_1528450430307_0Learning outcomes

The student:

- identifies the adjacent and the apex anglesapex anglesapex angles,

- calculates the measuremeasuremeasure of adjacent and apex angles.

Methodsmb2e38aa538066c6e_1528449534267_0Methods

1. Snowball sampling.

2. Situational analysis.

Forms of workmb2e38aa538066c6e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmb2e38aa538066c6e_1528450127855_0Introduction

The students bring the protractor and the drawings of:

- two acute angles,

- two obtuse angles.

The teacher revises the notion of the angle:
The angle is a part of a plane cut out by two half‑lines with a common beginning including the half‑lines.
Then the teacher explains that if we extend the arms of the angle to the straight lines we will get pairs of angles having many properties. Today the students are going to discover such properties.mb2e38aa538066c6e_1527752263647_0revises the notion of the angle:
The angle is a part of a plane cut out by two half‑lines with a common beginning including the half‑lines.
Then the teacher explains that if we extend the arms of the angle to the straight lines we will get pairs of angles having many properties. Today the students are going to discover such properties.

Proceduremb2e38aa538066c6e_1528446435040_0Procedure

The teacher introduces the drawings of adjacent and apex anglesapex anglesapex angles to the students.

[Illustration 1]

[Illustration 2]

The students work carrying out the snowball sampling method. They are going to arrive at the definition of adjacent and apex angles. The students formulate the definitions on their own, then in pairs and in the groups of 4. Every group presents their own definitions. Finally, the students define and write down the correct definition of adjacent and apex anglesapex anglesapex angles:

Two convex angles are adjacent when they have a common arm and the other arm forms a straight line.
Convex angles whose arms form two straight lines are called apex angles.mb2e38aa538066c6e_1527752256679_0Two convex angles are adjacent when they have a common arm and the other arm forms a straight line.
Convex angles whose arms form two straight lines are called apex angles.

Task

Students work individually using their computers. They are going to watch how the measuremeasuremeasure of adjacent and apex anglesapex anglesapex angles change depending on the position of their arms.

[Geogebra applet]

Students should draw the following conclusions:

- The sum of adjacent angles equals 180°.
- The apex angles are of the same measure.mb2e38aa538066c6e_1527712094602_0- The sum of adjacent angles equals 180°.
- The apex angles are of the same measure.

Task

Students compare the properties of adjacent and apex anglesapex anglesapex angles.

They discuss how they can calculate the measuremeasuremeasure of one angle having the value of the other angle.

Task

Calculate the measuremeasuremeasure of the angles:

- adjacent to the angle of 30°,

- apex to the angle of 120°.

An extra task

Here are adjacent anglesadjacent anglesadjacent angles. One of them is five times larger than the other one. Calculate the measuremeasuremeasure of the angles.

Lesson summarymb2e38aa538066c6e_1528450119332_0Lesson summary

Students do the exercises summarising the class.

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

- Two angles are adjacent when they have a common armarmarm and the other arms form the straight linestraight linestraight line. The sum of the measures of the adjacent anglesadjacent anglesadjacent angles is 180°.

- Convex angles which arms form two straight lines are called apex anglesapex anglesapex angles. Apex angles are the same size.

Selected words and expressions used in the lesson plan

acute angleacute angleacute angle

adjacent anglesadjacent anglesadjacent angles

angleangleangle

apex anglesapex anglesapex angles

armarmarm

half‑linehalf‑linehalf‑line

measuremeasuremeasure

obtuse angleobtuse angleobtuse angle

planeplaneplane

straight linestraight linestraight line