Objectives (5 - 10 minutes)

1. Understand the concept of the area of a triangle and its importance in solving mathematical problems.
2. Learn to use the formula for the area of a triangle in various ways and in different situations.
3. Develop skills in calculating the area of a triangle by applying the formula in practical exercises.

Secondary objectives:

1. Reinforce students' understanding of the concept of area and its application in different geometric shapes.
2. Stimulate students' logical reasoning and problem-solving skills through the practice of triangle area exercises.
3. Promote interaction among students, encouraging discussion and the exchange of ideas during the resolution of exercises.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts: The teacher should begin the class by briefly reviewing the concepts of geometry and, in particular, the properties of the triangle (sides, angles, etc.) that are relevant to calculating its area. This can be done through direct questions to students to check if they remember the concepts learned previously. (3-5 minutes)

2. Problem Situations: Next, the teacher should present two problem situations that involve calculating the area of the triangle. For example, the first situation could involve calculating the area of a right triangle, while the second could be more complex, involving a triangle with sides of different lengths. The objective here is to arouse students' interest in the topic and show the practical applicability of the concept that will be studied. (5 - 7 minutes)

3. Contextualization: The teacher should then contextualize the importance of calculating the area of the triangle, explaining that it is a fundamental concept in various areas of knowledge, including architecture, engineering, physics, among others. Examples can be given of how the calculation of the area of the triangle is used in practice, such as in the construction of bridges, in determining the force of a wind on the sail of a boat, etc. (2 - 3 minutes)

4. Introduction to the Topic: Finally, the teacher should introduce the topic of the class, which is the formula for calculating the area of the triangle. One can start by telling the story of how the formula was discovered or developed, or by discussing the application of the formula in a real problem. The teacher should also mention that there are different ways to calculate the area of the triangle, depending on the information one has about the triangle. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Presentation of the Theory (10 - 15 minutes)

1.1. Formula for Calculating the Area of a Triangle: The teacher should begin the presentation of the theory by explaining the general formula for calculating the area of a triangle: Area = (base x height) / 2. The teacher should draw a triangle on the board and show how to identify the base and height of the triangle. The teacher should also explain that the base can be any of the sides of the triangle, as long as the height is measured from the side opposite the base.

1.2. Different Ways to Calculate the Area of a Triangle: The teacher should then explain that, in addition to the general formula, there are other ways to calculate the area of the triangle, depending on the information one has about the triangle. For example, if the triangle is a right triangle, one can use the formula Area = (leg1 x leg2) / 2, where the legs are the sides that form the right angle. If the triangle is equilateral, one can use the formula Area = (side x side x √3) / 4, where the side is the length of one of the sides of the triangle.

1.3. Application of the Formula in Examples: The teacher should then solve examples of calculating the area of the triangle, showing step by step how to apply the formula. The teacher should start with simple examples and gradually increase the difficulty of the examples to challenge the students.

2. Guided Practice (5 - 10 minutes)

2.1. Exercises on Applying the Formula: The teacher should then move on to guided practice, where the students will have the opportunity to solve exercises on calculating the area of the triangle on their own, while the teacher circulates through the room, offering help and clarifying doubts. The teacher should start with simple exercises and gradually increase the difficulty to challenge the students. The exercises should involve different types of triangles (right, equilateral, isosceles, etc.) and different ways of calculating the area of the triangle.

3. Discussion and Resolution of Doubts (5 - 10 minutes)

3.1. Discussion of Results: After the students finish the exercises, the teacher should promote a classroom discussion about the results obtained. The teacher should ask the students how they arrived at their answers and if they encountered any difficulties. The teacher should use this discussion as an opportunity to reinforce the concepts learned and clarify any remaining doubts.

3.2. Resolution of Doubts: The teacher should then give the students the opportunity to ask questions and clarify any doubts they may have. The teacher should be prepared to answer a variety of questions and be able to explain the concepts clearly and concisely. If there is time, the teacher can review some of the more difficult examples or exercises, explaining them again step by step to ensure that all students have understood the material.

Feedback (5 - 10 minutes)

1. Review of Concepts (2 - 3 minutes)

1.1. The teacher should begin by briefly reviewing the key concepts of the class, such as the formula for calculating the area of the triangle, the importance of correctly identifying the base and height of the triangle, and the different ways to calculate the area of the triangle, depending on the information one has about the triangle. 1.2. The teacher should ask the students to share their definitions or explanations of the concepts, encouraging them to use their own words to demonstrate their understanding. The teacher should be attentive to any misunderstandings or misconceptions that may arise during this review, and correct them immediately.

2. Connection between Theory and Practice (2 - 3 minutes)

2.1. The teacher should then make the connection between the theory learned and the practice of the exercises. For example, one can discuss how the formula for the area of the triangle is applied to solve practical problems, such as calculating the area of a triangular plot of land to build a house, or calculating the force needed to lift a triangular object. 2.2. The teacher should ask the students to share their perceptions of how theory and practice connect, and how the application of the formula for the area of the triangle helps to solve real problems. This can be done through direct questions to the students, or by asking them to reflect on the connection between theory and practice for one minute.

3. Reflection on Learning (1 - 2 minutes)

3.1. The teacher should then ask the students to reflect on what they learned in class. The teacher can ask open-ended questions, such as "What was the most important concept you learned today?" or "What questions do you still have about the area of the triangle?" This allows the students to express their own perceptions about what they learned and helps the teacher to evaluate the effectiveness of the class. 3.2. The teacher should encourage all students to participate in this reflection, creating a safe and inclusive classroom environment where everyone feels comfortable sharing their ideas and doubts.

4. Homework Assignment (optional) (1 minute)

4.1. If there is time, the teacher can suggest one or two problems for calculating the area of the triangle for the students to solve at home. This allows the students to practice what they learned in class and helps to reinforce the material. 4.2. The teacher should provide clear instructions on how the problems should be solved and be available to clarify any doubts that the students may have.