Lesson plan of Triangles: Classification by Sides

Objectives (5 minutes)

1. Understanding the classification of triangles by sides: Students should be able to identify and differentiate between equilateral, isosceles, and scalene triangles based on the measure of their sides. They should have a clear understanding of the characteristics of each of these types of triangles.

2. Applying acquired knowledge: Students should be able to apply the acquired knowledge to solve problems that involve identifying and classifying triangles based on the measure of their sides.

3. Encouraging curiosity and critical thinking: In addition to learning about the classification of triangles, students should be encouraged to think about the importance and practical use of this knowledge, both in mathematical contexts and in everyday applications.

Secondary objectives:

• Developing logical reasoning skills: Through the study of triangles and their classification, students will have the opportunity to improve their logical reasoning skills, a fundamental skill in mathematics and in many other aspects of life.

• Encouraging active participation and collaboration: The proposed flipped classroom strategy should promote students' active participation and collaboration among them, encouraging discussion and exchange of ideas.

Introduction (10 - 15 minutes)

1. Review of previous concepts: Start the lesson by recalling the basic concepts about triangles, such as the fact that it is a figure with three sides and that the sum of its internal measurements is always equal to 180 degrees. This review can be done through a short interactive quiz or a crossword puzzle, for example. (3-5 minutes)

2. Problem situation 1: The mysterious triangle challenge: Present students with a drawing of a triangle with no measurements indicated. The challenge is to try to classify the triangle as equilateral, isosceles, or scalene, without taking any measurements. Encourage students to share their strategies and justifications. (3-5 minutes)

3. Contextualizing the importance of the content: Explain to students that the classification of triangles is a tool widely used in various areas, such as architecture, engineering, natural sciences, and even in board games, where geometry plays an important role. (2-3 minutes)

4. Curiosity 1: The pyramids of Egypt: Talk about the pyramids of Egypt, which are actually a set of stacked triangles. Explain that to build the pyramids, the ancient Egyptians needed to have a very good understanding of the geometry of triangles, including their classification. (2-3 minutes)

5. Curiosity 2: Triangles in nature: Show images of animals and plants that have body parts or structures in the shape of a triangle, such as the wings of a butterfly or the leaves of a sunflower. Explain that nature uses the triangular shape because it is an efficient and stable way to build structures. (2-3 minutes)

Development (20 - 25 minutes)

1. Activity 1: "Create Your Triangle" (10 - 15 minutes)

   • Description: In this activity, students will be divided into groups of five. Each group will receive a sheet of paper, a ruler, and a compass. The goal is for them to draw three different triangles (one equilateral, one isosceles, and one scalene) and classify each one of them.

   • Step by step:

     1. Each group should draw a circle on the sheet of paper using the compass.
     2. Then, they should use the ruler to connect three points on the circle, forming a triangle.
     3. For an equilateral triangle, the points should be equally spaced.
     4. For an isosceles triangle, two points should be close together and the third farther apart.
     5. For a scalene triangle, the three points should be in different locations.
     6. After drawing and classifying the triangles, the groups should present their creations to the class and justify why they classified each one that way.

   • Importance: This activity will allow students to visualize and manipulate real triangles, which can help solidify their understanding of the classification of sides. In addition, the group discussion will encourage collaboration and critical thinking.

2. Activity 2: "Triangle Hunt" (10 - 15 minutes)

   • Description: In this activity, students will continue in their groups. They will receive a sheet with several drawings of geometric figures, including triangles. The challenge is to identify and classify the triangles present on the sheet.

   • Step by step:

     1. Distribute the activity sheet to each group.
     2. Explain that the triangles on the sheet are of different types (equilateral, isosceles, and scalene), but without indicating which is which.
     3. Students should work together to identify and classify the triangles.
     4. After completing the activity, each group should present their answers and justify their classifications.

   • Importance: This activity will help students develop their observation and classification skills. In addition, the group discussion will stimulate collaboration and the exchange of ideas.

3. Activity 3: "Triangle Quiz" (5 - 10 minutes)

   • Description: To finish the development stage, students will participate in a triangle quiz. They will answer a series of multiple-choice and true/false questions about the classification of triangles.

   • Step by step:

     1. Students will answer the quiz individually, but they will be able to discuss the answers with their classmates.
     2. The questions should address the main concepts learned in class, such as the characteristics of equilateral, isosceles, and scalene triangles, and how to identify them.
     3. After everyone has answered the quiz, the answers will be corrected and discussed together.

   • Importance: This quiz will serve as a formative assessment tool, allowing the teacher to check students' understanding of the topic. In addition, the discussion after the quiz will help clarify any remaining doubts.

Debrief (10 - 15 minutes)

1. Group discussion (5 - 7 minutes):

   • Description: After concluding the activities, it is time to gather all the students and promote a group discussion. Each group will have up to 3 minutes to share their solutions and conclusions from the activities. The teacher should ensure that all students have the opportunity to speak and that the environment is welcoming for the exchange of ideas.

   • Step by step:

     1. The teacher calls each group to share their findings, starting with Group A.
     2. Group A students share their conclusions while the other groups listen attentively.
     3. After Group A's presentation, the other groups have the opportunity to ask questions or make comments.
     4. The teacher repeats the process for Groups B, C, D, and E, until everyone has shared their findings.
     5. During the presentations, the teacher should intervene to correct any misunderstandings and to reinforce the key concepts.

   • Importance: This group discussion will allow students to see different approaches to the same problem, which can help them expand their way of thinking. In addition, by listening to their classmates' ideas, students may realize that they are not alone in their difficulties or confusions, which can increase their confidence and motivation.

2. Connection to the theory (3 - 5 minutes):

   • Description: After listening to the groups' presentations, the teacher should make the connection to the theory, reinforcing the key concepts and clarifying any misunderstandings. The teacher can use practical examples or drawings to illustrate the most important points.

   • Step by step:

     1. The teacher briefly reviews the concepts of equilateral, isosceles, and scalene triangles, and how they can be identified.
     2. Then, the teacher refers to the solutions presented by the groups, highlighting the positive points and correcting any errors.
     3. The teacher can use practical examples or drawings to illustrate the concepts, if necessary.
     4. The teacher ends the discussion by reinforcing the importance of understanding the classification of triangles and how it can be applied in everyday situations.

   • Importance: This stage is crucial for consolidating students' learning, as it allows them to see the relevance and practical application of theoretical concepts. In addition, by correcting any misunderstandings, the teacher helps to prevent the formation of misconceptions.

3. Final reflection (2 - 3 minutes):

   • Description: To end the class, the teacher suggests that students reflect silently for a minute on the answers to the following questions: "What was the most important concept you learned today?" and "What questions have not yet been answered?".

   • Step by step:

     1. The teacher asks students to focus and reflect silently on the questions.
     2. After a minute, the teacher asks students to share their reflections. They can answer orally or write their answers on a piece of paper.
     3. The teacher listens attentively to the students' answers and, if necessary, can offer feedback or additional clarifications.

   • Importance: This final reflection helps students consolidate their learning and identify any areas where they may need more practice or clarification. In addition, by listening to students' answers, the teacher can get valuable feedback on the effectiveness of the class.

Conclusion (5 - 7 minutes)

1. Summary of the content (2 - 3 minutes):

   • Description: The teacher should summarize the main points covered during the class, reiterating the concepts of equilateral, isosceles, and scalene triangles, and how they are classified. It is also important to mention the practical activities carried out by the students and how they helped reinforce the theoretical understanding.

   • Step by step:

     1. The teacher begins the summary by recalling the definition of a triangle and the importance of its classification.
     2. Then, he reinforces the characteristics of an equilateral triangle (all sides equal), isosceles (two equal sides), and scalene (all sides different).
     3. The teacher mentions the practical activities carried out, highlighting how they allowed students to visualize and manipulate the different types of triangles.
     4. To conclude, the teacher emphasizes the applicability of the content learned in everyday situations and in various professional fields.

   • Importance: The summary is an opportunity to consolidate students' learning, reinforcing the most important concepts. In addition, by reviewing the practical activities, the teacher can highlight students' strengths and identify any areas that may need additional review.

2. Connection between theory, practice, and applications (1 - 2 minutes):

   • Description: The teacher should explain how the class connected the theory (the classification of triangles), the practice (the activities of drawing and identifying triangles), and real applications (the importance of the classification of triangles in different areas).

   • Step by step:

     1. The teacher begins by highlighting the theory learned and how it applies to the classification of triangles.
     2. Then, he mentions the practical activities carried out and how they allowed students to apply the theory in a concrete way.
     3. Finally, the teacher reiterates the practical applications of the classification of triangles, mentioning examples of real situations where this knowledge is useful.

   • Importance: This explanation helps students understand the relevance of what they have learned and see the connection between theory, practice, and real applications. This can increase their motivation to learn and their confidence in applying what they have learned.

3. Extra materials (1 - 2 minutes):

   • Description: The teacher should suggest extra materials for students who wish to deepen their understanding of the classification of triangles. This could include additional readings, explanatory videos, interactive online games, among others.

   • Step by step:

     1. The teacher lists the extra materials, briefly explaining what each of them offers.
     2. He suggests that students explore these materials in their own time, as a way to review and consolidate what they have learned.

   • Importance: Extra materials can be a valuable tool for students who want to review the content, deepen their understanding, or simply explore the topic more autonomously. In addition, by offering these materials, the teacher is encouraging continuous and self-directed learning.

4. Relevance of the topic (1 minute):

   • Description: To end the class, the teacher should highlight the relevance of the topic presented, explaining how the classification of triangles is a useful and important skill in various situations, from solving mathematical problems to understanding natural phenomena and applying it in different careers.

   • Step by step:

     1. The teacher briefly reiterates the main points of the class, highlighting the importance and practical application of the classification of triangles.
     2. He encourages students to think about how this knowledge can be useful in their daily lives and in their future careers.

   • Importance: By emphasizing the relevance of the topic, the teacher is helping students understand that what they are learning is not just abstract theory, but a set of practical tools and skills that can be applied in many aspects of their lives.