Lesson plan of Triangle Area

Objectives (5 - 7 minutes)

1. Understanding the Concept of Triangle Area: Students should be able to understand what the area of a triangle is and how it is calculated. This includes understanding that the area is the measurement of the region occupied by a triangle in the plane, and that the formula for calculating the area depends on the base and height.

2. Applying the Triangle Area Formula: Students should be able to apply the triangle area formula (A = (base * height)/2) to solve practical problems. This includes the ability to identify the base and height of a triangle in different situations and to substitute these values into the formula to obtain the area.

3. Solving Problems Involving Triangle Area: Students should be able to solve problems that involve calculating the area of a triangle. This includes the ability to interpret the problem statement, to identify the relevant information, to decide on the best strategy to solve the problem, and to carry out the necessary calculations.

Secondary Objectives

• Developing Critical and Logical Thinking: Through solving problems involving triangle area, students will have the opportunity to develop their critical and logical thinking skills. They will practice the ability to analyze a problem, to think of possible solutions, and to make decisions based on logic.

• Promoting Active Learning: The use of the flipped classroom methodology will encourage active participation of students in the learning process. They will be responsible for studying the content beforehand and for bringing their doubts and difficulties to class, where they will have the opportunity to discuss and clarify these issues.

Introduction (10 - 12 minutes)

1. Recalling Basic Concepts: The teacher begins the class by recalling basic concepts that are fundamental to understanding the topic of the day. He can review what a triangle is, its properties, and how to identify the base and height. This can be done through directed questions to students to activate prior knowledge. (3 - 4 minutes)

2. Presenting Problem Situations: The teacher then presents two problem situations that involve calculating the area of a triangle. The first could be the area of a soccer field that is in the shape of a triangle and the second could be calculating the area of a roof that is in the shape of a triangle. The teacher can ask students how they would solve these problems, even if they do not yet have the necessary knowledge to do so. (3 - 4 minutes)

3. Contextualizing the Importance of the Topic: The teacher then contextualizes the importance of the subject, highlighting that calculating the area is a fundamental skill in various fields, such as architecture, engineering, physics and economics. He can mention that often, to solve real problems, it is necessary to divide the area into simpler shapes, such as triangles. (2 - 3 minutes)

4. Introducing the Theory with a Curiosity: To arouse students' interest, the teacher can introduce the theory with a curiosity. He can mention that the formula for calculating the area of a triangle has been the same since the time of the ancient Egyptians, who used it to calculate the area of their lands. This can serve as an introduction to the explanation of the triangle area formula. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity "Building the Area of a Triangle" (10 - 12 minutes)

   • Preparation of Materials: The teacher should prepare beforehand triangles of different sizes (two bases and two heights for each triangle). It can be made of cardboard, EVA, cardboard, etc. and a meter or ruler to measure the base and height. Each group of students will receive a set of these triangles.
   • Carrying out the Activity: Students, divided into groups, should calculate the area of the triangles provided using the formula A = (base * height)/2 and then check the accuracy of their calculation by measuring the area of the triangles with the meter or ruler. Students should be encouraged to discuss in their groups how they will perform the measurements and calculations.
   • Discussion and Reflection: After the activity, the teacher should lead a classroom discussion where each group will present their triangles, the formula they used to calculate the area and the results obtained. The teacher should reinforce that, even though the triangles are of different sizes, the ratio between the base and the height and, consequently, the area, remains the same.

2. Activity "Triangle Area in Practice" (10 - 12 minutes)

   • Preparation of Materials: The teacher should prepare beforehand card stock cut into triangle shapes and pictures of different constructions (such as bridges, roofs, etc.) that have the shape of a triangle. Each group of students will receive a piece of card stock and a picture.
   • Carrying out the Activity: Students, divided into groups, should calculate the area of the triangles on the card stock using the formula A = (base * height)/2 and then compare the calculated area with the actual area of the picture (which can be provided by the teacher or researched on the internet). Students should be encouraged to discuss in their groups how they will perform the calculations and comparison.
   • Discussion and Reflection: After the activity, the teacher should lead a classroom discussion where each group will present the picture they chose, the formula they used to calculate the area of the triangle and the comparison between the calculated area and the actual area. The teacher should reinforce that the triangle area formula can be used to solve real problems, such as calculating the area of a roof, a soccer field, etc.

3. Activity "Triangle Area Challenge" (5 - 6 minutes)

   • Preparation of Materials: The teacher should prepare beforehand a list of problems that involve calculating the area of a triangle. The problems can be of varying difficulty and can involve applying the formula in different ways. Each group of students will receive a copy of the list of problems.
   • Carrying out the Activity: Students, divided into groups, should solve the problems on the list using the triangle area formula. They should be encouraged to discuss in their groups how they will solve the problems.
   • Discussion and Reflection: After the activity, the teacher should lead a classroom discussion where each group will present the problems they solved, the strategy they used to solve them and the difficulties they encountered. The teacher should reinforce that problem solving is an important part of the learning process and that it is normal to encounter difficulties, but that the important thing is to persist and seek help when necessary.

These activities have been designed to allow students to explore the concept of triangle area in a practical and fun way, and to be able to discuss and reflect on what they have learned. In addition, the activities promote interaction between students, which is important for the development of social skills.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • Each group will have a maximum of 3 minutes to present the solutions found during the activities. The teacher should guide the students to make a brief presentation, highlighting the strategy used to solve the problem and the reasoning behind the solution.
   • During the presentations, the teacher should encourage other students to ask questions and express their opinions on the solutions presented. This will promote a collaborative learning environment where students can learn from each other.
   • The teacher should make specific interventions, reinforcing correct concepts and correcting possible misunderstandings, always in a respectful and constructive manner.

2. Connection with Theory (2 - 3 minutes)

   • After the presentations, the teacher should lead a classroom discussion, connecting the solutions presented by the groups with the theoretical concepts covered in class, such as the triangle area formula and the importance of the base and height.
   • The teacher should highlight how students applied these concepts to solve the proposed problems and how they can be applied in other situations. This will help students to consolidate their learning and to realize the relevance of what they have learned.

3. Individual Reflection (2 - 3 minutes)

   • To finish, the teacher should ask students to reflect individually on what they learned in class. They should think about what the most important concepts were, what questions have not yet been answered and what they would like to learn in the next lessons.
   • The teacher can facilitate this reflection by asking questions such as: "What was the most important concept you learned today?" and "What questions have not yet been answered?".
   • Students should be encouraged to write down their reflections, as this can help them review the content and prepare for the next classes.

4. Teacher Feedback (1 minute)

   • The teacher should give general feedback on the students' participation, highlighting the positive points and pointing out areas that need improvement. He should encourage students to continue making an effort and not to give up in the face of difficulties, remembering that the learning process is gradual and that everyone is progressing.

This Return moment is essential for the teacher to evaluate students' understanding of the content and to identify possible difficulties. In addition, it promotes reflection and metacognition, which are fundamental processes for meaningful learning.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes)

   • The teacher should begin the Conclusion by recapitulating the main points covered during the class. This includes the definition of triangle area, the formula for calculating the area (A = (base * height)/2), and the strategies for solving problems that involve calculating the area of a triangle.
   • The teacher can ask students to share what they consider to be the most important concepts they learned in class. This will allow the teacher to confirm whether the key points have been understood correctly.

2. Connection between Theory, Practice and Applications (1 - 2 minutes)

   • The teacher should highlight how the class connected theory, practice and applications. He can mention that, through the practical activities, students were able to apply the theory to solving real problems, such as calculating the area of a soccer field or a roof.
   • The teacher should reinforce that the ability to calculate the area of a triangle is an important tool in various fields, such as architecture, engineering, physics and economics, and that what students learned in class can be useful in solving problems in these areas.

3. Complementary Materials (1 - 2 minutes)

   • The teacher should suggest complementary materials for students to deepen their knowledge of triangle area. These materials may include explanatory videos, additional exercises, math games and educational websites.
   • For example, the teacher could suggest that students watch a video that explains the triangle area formula in a different way, so that they can see the concept from different angles and approaches.

4. Importance of the Topic (1 minute)

   • To conclude, the teacher should reinforce the importance of the topic presented in class. He can mention that calculating the area is a fundamental skill that will be needed in many life situations, and that learning to calculate the area of a triangle is an important step in that process.
   • The teacher should encourage students to continue practicing and not to give up, even if they encounter difficulties, because practice is essential to becoming proficient in solving problems involving the area of a triangle.

The Conclusion is a crucial time to consolidate learning, reinforce the relevance of the topic and motivate students to continue studying. By suggesting complementary materials, the teacher provides students with the opportunity to deepen their knowledge according to their own pace and interest.