Objectives

(5 - 7 minutes)

1. Understanding the angular classification of triangles: The main objective of this topic is for students to become familiar with the different types of triangles based on their internal angles. They should be able to identify and differentiate between acute-angled, right-angled, and obtuse-angled triangles.

2. Applying the Pythagorean Theorem: The Pythagorean Theorem is essential for classifying triangles according to their internal angles. Students should understand how to apply this theorem to determine the angular classification of a triangle.

3. Solving related problems: Students should be able to apply the acquired knowledge to solve problems involving the angular classification of triangles and the Pythagorean Theorem.

Secondary Objectives:

• Encouraging active student participation: The teacher should encourage active student participation during the lesson, promoting discussions and clarifying doubts.

• Developing critical thinking and problem-solving skills: By solving problems related to the angular classification of triangles, students will have the opportunity to develop their critical thinking and problem-solving skills.

Introduction

(10 - 12 minutes)

1. Review of previous concepts: The teacher starts the lesson by reviewing the concepts of angles and triangles, briefly explaining the types of triangles according to their sides (equilateral, isosceles, and scalene). This review is essential for understanding the lesson topic, as knowing angles well is necessary to classify a triangle according to its angles.

2. Problem-solving situations: The teacher presents two problem-solving situations to stimulate students' thinking. The first one could be: 'If a triangle has an angle of 90 degrees, what can we say about the other two angles?' The second one could be: 'If a triangle has an angle of 30 degrees and another of 120 degrees, how can we classify it?'

3. Contextualization: The teacher explains the importance of the angular classification of triangles in solving practical problems, such as in building construction, maritime and aerial navigation, and object modeling in computer programs.

4. Introduction to the topic: To spark students' interest, the teacher presents two curiosities related to the topic. The first one is about the Pythagorean Theorem: 'Did you know that the Pythagorean Theorem was proven in Babylon, almost 2000 years before Pythagoras was born?' The second curiosity is about right-angled triangles: 'Did you know that the number of different right-angled triangles that can be formed with whole number sides is infinite?'

5. Capturing students' attention: To conclude the Introduction, the teacher shares a math joke related to the topic: 'Why did the triangle go to the doctor? Because it had an angle!' This joke, although funny, serves to reinforce the importance of angles in geometry.

Development

(20 - 25 minutes)

1. Theory presentation:

   • Definition of triangles classified by angles (acute-angled, right-angled, and obtuse-angled): The teacher reviews the concepts of acute, right, and obtuse angles. Then, explains that the angular classification of triangles is based on the measurement of their internal angles. Acute-angled triangles are those that have all internal angles smaller than 90°. Right-angled triangles are those that have an internal angle of 90°. And obtuse-angled triangles are those that have an internal angle greater than 90°.
   • Application of the Pythagorean Theorem: The teacher reminds students about the Pythagorean Theorem, which applies only to right-angled triangles. Explains the formula of the theorem (a² = b² + c²) and how it can be used to find the measurement of a side of a right-angled triangle when the measurements of the other two sides are known.
   • Practical examples of applying angular classification and the Pythagorean Theorem: The teacher presents practical examples of how angular classification and the Pythagorean Theorem are used in solving everyday problems, such as measuring angles for building construction and determining distances on maps.

2. Demonstration of theory application:

   • Solving problems of angular classification of triangles: The teacher proposes problems for students to classify triangles according to their internal angles. The problems should involve identifying acute-angled, right-angled, and obtuse-angled triangles based on their measurements of internal angles.
   • Solving problems using the Pythagorean Theorem: The teacher proposes problems that require the application of the Pythagorean Theorem for resolution. The problems should involve determining the measurement of a side of a right-angled triangle from the measurements of the other two sides.

3. Practical activity:

   • Construction of homemade protractor and square: The teacher proposes a practical activity in which students will build a homemade protractor and square to measure angles. This activity will reinforce the concept of angle and the importance of precise angle measurement in the angular classification of triangles.
   • Angle measurement and triangle classification: After constructing the instruments, students will measure the angles of different triangles and classify them according to their internal angles.

Throughout the lesson Development, the teacher should encourage students to participate actively, asking questions, proposing solutions to problems, and sharing their ideas. The teacher should also monitor students' progress, providing feedback and guidance as necessary.

Return

(10 - 12 minutes)

1. Review of learned concepts: The teacher starts the Return phase by reviewing the main concepts that were addressed during the lesson. He reaffirms the definition of acute-angled, right-angled, and obtuse-angled triangles and the application of the Pythagorean Theorem. He can do this by asking students direct questions, requesting them to explain the concepts in their own words.

2. Connection between theory and practice: The teacher then reviews the practical activities carried out. He asks students to share their experiences in building homemade measuring instruments and measuring the angles of triangles. He highlights how these activities helped visualize and better understand the theoretical concepts.

3. Reflection on the importance of learned concepts: The teacher suggests that students reflect on the importance of the learned concepts. He can do this by asking questions like: 'How can the angular classification of triangles and the Pythagorean Theorem be useful in everyday situations?' or 'Which professions or fields of study can benefit from knowledge about triangles and their angles?'

4. Identification of doubts and difficulties: The teacher opens a space for students to share any doubts or difficulties that may have arisen during the lesson. He encourages students to ask and answer each other's questions, promoting an open and collaborative discussion.

5. Teacher's feedback: The teacher provides feedback on the class's performance. He praises students' efforts, highlights strengths, and offers suggestions for improvement. He also answers any unanswered questions and clarifies any misunderstandings that may have arisen.

6. Preparation for the next lesson: Finally, the teacher gives a preview of the topic of the next lesson, encouraging students to prepare and read in advance about the subject. He may suggest reading materials, videos, or websites that can help in understanding the next topic.

Throughout the Return process, the teacher should create a safe and welcoming learning environment where students feel comfortable sharing their doubts and difficulties. He should value students' contributions, promote self-confidence, and motivation to learn.

Conclusion

(5 - 7 minutes)

1. Summary of covered contents: The teacher starts the Conclusion of the lesson by summarizing the main points that were addressed. He reaffirms the definition of acute-angled, right-angled, and obtuse-angled triangles, the Pythagorean Theorem, and how to apply it in problem-solving.

2. Connection between theory, practice, and applications: Next, the teacher highlights how the lesson connected theory, practice, and applications. He recalls the practical activities carried out, such as building homemade measuring instruments and measuring the angles of triangles, and how they helped visualize and better understand the theoretical concepts. He also reaffirms the importance of the learned concepts, showing examples of how they can be applied in everyday life and in different professions or fields of study.

3. Suggestion of extra materials: The teacher suggests extra materials for students who wish to further deepen their knowledge. He may recommend math books, educational websites, explanatory videos, and online games that address the topic of triangles and their angles in a playful and didactic way.

4. Importance of the topic for daily life: Finally, the teacher emphasizes the importance of the topic for daily life, reinforcing how knowledge about triangles and their angles is useful in practical everyday situations. He can give examples of situations where the angular classification of triangles and the Pythagorean Theorem are used, such as in solving construction problems, navigation, and object modeling in computer programs.

5. Closure: The teacher concludes the lesson by thanking students for their participation and effort. He reinforces that mathematics is a discipline that requires practice and patience, but that with time and effort, students will be able to master the concepts and solve complex problems. He encourages students to continue studying and striving, reminding them that the knowledge gained in mathematics can be applied in various areas of life.