Lesson plan of Triangle Area

Objectives (5 - 7 minutes)

1. Understand the concept of the area of a triangle and how it is calculated from the base and the height.
2. Apply the formula of the triangle area in practical and real situations, using different types of triangles.
3. Develop problem-solving skills, logical reasoning, and application of mathematical formulas.

Secondary objectives:

• Encourage active student participation, promoting discussions and exchanges of ideas during the resolution of problems.
• Develop critical thinking skills, encouraging students to question and justify their answers.
• Promote teamwork through group activities that encourage collaboration and communication between students.

Introduction (10 - 15 minutes)

1. Review: The teacher begins the lesson by reviewing the basic concepts of geometry, especially those related to triangles. He or she may ask questions to check students' understanding of topics such as the sides, vertices, and angles of a triangle. (3 - 5 minutes)

2. Problem situation: Next, the teacher presents two problem situations that involve calculating the area of a triangle. For example, the teacher can draw two different triangles on the board and ask students how they could determine the area of each one. These problem situations serve to arouse the students' interest and prepare them for the lesson topic. (2 - 3 minutes)

3. Contextualization: The teacher contextualizes the importance of calculating the area of a triangle by showing real-world applications. For example, the teacher may mention how the area of a triangle is used in construction to calculate the amount of material needed to build a triangular roof or how it is used in cartography to calculate the area of land. These examples help students understand the relevance of the topic and motivate them to learn it. (2 - 3 minutes)

4. Presentation of the topic: Finally, the teacher introduces the topic of the lesson - the area of the triangle. The teacher explains that the area is a measure of how much space an object occupies and that for the triangle, the area can be calculated in a specific way. The teacher may use the example of a soccer field to illustrate the idea of area. (1 - 2 minutes)

5. Curiosities: To finish the introduction and capture the students' attention even more, the teacher presents two interesting facts about the area of the triangle. For example, the teacher can mention that the formula to calculate the area of a triangle is the same, regardless of the size of the triangle, or that the area of a triangle is always half the product of the base and the height. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity "Building Triangles" (10 - 12 minutes)

   • The teacher divides the class into groups of 3-4 students and gives each group a set of popsicle sticks or straws and string.
   • The teacher instructs the students to form different types of triangles (scalene, isosceles, equilateral) using the materials available.
   • After building the triangles, the teacher asks the students to measure the base and height of each of the triangles and record these measurements.
   • Next, the teacher guides the students to apply the formula of the triangle area (Area = 1/2 * base * height) and calculate the area of each triangle.
   • Finally, the teacher asks the students to compare the areas of the triangles and discuss their observations in relation to the different types of triangles.

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

   • The teacher poses the following situation: "Imagine that you are an engineer at a construction company and need to calculate the amount of flooring needed to cover the floor of a triangular room. How could you use the concept of triangle area to solve this problem?"
   • Each group should draw a plan of the room on paper, identifying the base and height of the triangle.
   • Next, the students should calculate the area of the triangle and, using the measurements of the flooring provided by the teacher, determine the quantity of flooring needed.
   • The teacher circulates around the room, assisting the groups as needed, and encouraging the students' discussion and reasoning.

3. Activity "Triangle Area Problems" (5 - 8 minutes)

   • The teacher distributes a sheet with triangle area problems to each group.
   • Students should work together to solve the problems, applying the triangle area formula.
   • The problems may involve determining the area of triangles with given measurements, solving equations to find the height or base, or solving application problems of the triangle area in different contexts.
   • The teacher guides students to discuss their solving strategies and justify their answers.

These activities allow the students not only to understand the concept of the triangle area, but also to apply this knowledge in a practical and contextualized way. In addition, they promote collaboration between the students, logical reasoning, and the ability to solve problems, which are important skills in the study of mathematics.

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher gathers all the students and starts a group discussion. Each group has up to 3 minutes to share the solutions or conclusions they found during the activities.
   • The teacher can ask a representative from each group to explain briefly what they discussed and how they applied the triangle area formula in their activities.
   • As the groups present, the teacher should ask questions to stimulate the students' reflection and ensure that the content was understood correctly and deeply.

2. Connection with the Theory (2 - 3 minutes)

   • After all the presentations, the teacher makes a summary of the main ideas and connections with the theory. The teacher reviews the concepts of the triangle area, the formula used, and how it applies in different situations.
   • The teacher may also highlight the main difficulties encountered by the students and reinforce the most important points. The teacher should emphasize the importance of using the formula, but also of understanding the concept behind it.

3. Final Reflection (2 - 3 minutes)

   • To finalize the lesson, the teacher asks the students to reflect individually on what they have learned. The teacher formulates some questions to guide this reflection, such as:
     1. What was the most important concept learned today?
     2. What questions have not yet been answered?
     3. How can you apply what you have learned about the area of the triangle in everyday situations?
   • The teacher encourages students to write down their answers and questions, as they may be useful for future lessons.

4. Teacher Feedback (1 minute)

   • Finally, the teacher provides general feedback on the lesson, praising the students' effort and participation and highlighting the positive points. The teacher also mentions the areas that can be improved and makes suggestions for the students' individual study.
   • The teacher reinforces the importance of practicing the calculation of the triangle area and reviewing the formula and concept at home.

Feedback is a crucial stage of the lesson plan, as it allows the teacher to evaluate the students' progress, correct possible misconceptions, and consolidate learning. In addition, by promoting reflection and self-assessment, Feedback contributes to the development of metacognitive skills and to the students' autonomy.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher begins the Conclusion of the lesson by summarizing the main points covered. The teacher reinforces the concept of the triangle area, the formula used (Area = 1/2 * base * height), and how it applies in different contexts.
   • The teacher also goes over the hands-on activities done, highlighting the students' main findings and reflections, and how they applied the triangle area formula to solve real problems.

2. Theory-Practice Connection (1 - 2 minutes)

   • The teacher then makes the connection between theory and practice, reinforcing how the activities performed helped to illustrate and apply the concept of the triangle area.
   • For example, the teacher may mention how the "Building Triangles" activity allowed students to visualize the base and height of a triangle and how the "Triangle Area in Practice" activity demonstrated a real-world application of calculating the triangle area.

3. Supplementary Materials (1 minute)

   • The teacher suggests supplementary materials for the students to use to explore the triangle area further. These materials may include explanatory videos, interactive online tutorials, math games related to the topic, and additional exercises.
   • For example, the teacher may indicate a video that explains the origin of the triangle area formula, an online tutorial that allows students to practice calculating the triangle area interactively, and a game that challenges students to apply the triangle area concept to solve math puzzles.

4. Practical Applications (1 minute)

   • To finish, the teacher highlights the importance of calculating the triangle area in various areas of everyday and professional life. For example, the teacher may mention that the triangle area is used in architecture and engineering to calculate the amount of material needed to build a triangular structure, in cartography to measure the area of a triangular piece of land, and even in art and design to create visual shapes and patterns.
   • The teacher encourages students to be aware of the presence and application of the triangle area concept in their everyday lives and to share with the class any new discoveries or applications they find.

Conclusion is an essential step in the lesson plan, as it allows the teacher to consolidate the students' learning, reinforce the most important concepts, make connections with practice and the real world, and motivate the students to continue studying and exploring the topic. In addition, by proposing supplementary materials and highlighting the practical applications of the concept, the Conclusion contributes to meaningful learning and to the students' motivation.