Lesson plan of Area: Triangle

Objectives (5 - 10 minutes)

1. Understanding the concept of the area of a triangle: Students should be able to understand and explain what the area of a triangle is, using the formula A = (b * h) / 2, where b is the base of the triangle and h is the height.

2. Applying the formula for the area of a triangle to practical problems: Students should be able to apply the formula for the area of a triangle to practical situations, such as calculating the area of a triangular plot of land or the area of a figure composed of several triangles.

3. Developing logical thinking and problem-solving skills: Through solving problems related to the area of triangles, students should improve their logical thinking and problem-solving skills, contributing to the development of their mathematical skills in general.

Secondary objectives:

• Stimulating students' active participation: In addition to achieving the learning objectives, the lesson should also seek to stimulate students' active participation, encouraging them to ask questions, discuss problem solutions, and share their own approaches to problem-solving.

• Promoting collaborative learning: Through group activities, students should be encouraged to work together, sharing ideas and helping each other solve problems. This not only promotes collaborative learning but also enhances students' communication and collaboration skills.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should begin the lesson by briefly reviewing related concepts that were covered in previous lessons and are fundamental to understanding the topic of the current lesson. In this case, it is important to review the concepts of a triangle (definition, types, and properties), base, and height of a triangle. The teacher can do this by asking targeted questions to the students, promoting their active participation, and helping to reinforce prior knowledge. (3 - 5 minutes)

2. Problem situations for contextualization: To arouse students' interest and show the relevance of the subject, the teacher can propose two problem situations. The first could be to calculate the area of a triangular plot of land, and the second, to calculate the area of a triangle that is part of a larger figure, such as a rhombus. The teacher can encourage students to think about how they would solve these situations before starting the theoretical explanation. (3 - 5 minutes)

3. Contextualization of the importance of the subject: The teacher should then explain how the calculation of the area of a triangle is applied in various everyday situations and in other disciplines, such as architecture, engineering, physics, and geography. For example, in architecture and engineering, calculating the area of a triangle is essential for determining the amount of material needed to build a triangular structure. In physics, the area of a triangle can be used to calculate the pressure exerted by a triangular object. In geography, the area of a triangle can be used to calculate the area of a plot of land or an island. (2 - 3 minutes)

4. Introduction of the topic with curiosities and practical applications: To gain the attention of the students, the teacher can share some interesting curiosities and applications of the area of the triangle. For example, the teacher can talk about Heron's theorem, which allows to calculate the area of any triangle from the lengths of its sides, without the need to know the height. Another curiosity is that the area of a triangle is always positive, regardless of the orientation of the vertices. For practical applications, the teacher can talk about how the area of a triangle is used in computer games to render 3D images, or in GPS to calculate the distance between two points on the map. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity "Building and Measuring Triangles" (10 - 15 minutes)

   • Objective: Allow students to have a practical and visual experience in constructing triangles and measuring their bases and heights, so that they can better understand how these measurements are related to the area of the triangle.

   • Materials needed:

     • Ruler
     • Pencil
     • Cardstock or cardboard
     • Scissors

   • Description of the activity:

     • The teacher should divide the class into groups of 3 to 4 students.
     • Each group will receive a piece of cardboard, a ruler, a pencil, and a pair of scissors.
     • The teacher should explain that they will construct different triangles on the cardboard and measure their bases and heights.
     • The students should then construct at least 5 triangles of different types (e.g., equilateral, isosceles, scalene) on the cardboard, using the ruler and pencil.
     • After constructing each triangle, the students should measure the base and height of the triangle with the ruler, and record the values in a table.
     • After constructing and measuring all the triangles, the students should calculate the area of each triangle using the formula A = (b * h) / 2, and record the values in the table.
     • The teacher should circulate around the room, assisting the groups as needed, and encouraging discussion and sharing of ideas among the students.

2. Activity "Area of a Triangular Plot of Land" (10 - 15 minutes)

   • Objective: Apply the concept of the area of a triangle to a practical and realistic context, allowing students to see how mathematics can be used to solve real-world problems.

   • Materials needed:

     • Sheet of graph paper
     • Pencil and eraser

   • Description of the activity:

     • The teacher should present the students with a drawing of a triangular plot of land on the sheet of graph paper.
     • The teacher should explain that the students' task is to calculate the area of this plot of land, which is a triangle.
     • The students should then measure the base and height of the plot of land (represented by the drawing on the sheet of paper), and record the values.
     • Next, the students should use the formula A = (b * h) / 2 to calculate the area of the plot of land, and record the result.
     • The teacher should circulate around the room, assisting the groups as needed, and encouraging discussion and sharing of ideas among the students.
     • After all the groups are finished, the teacher should ask one or two groups to share their solutions with the class, and discuss the different approaches to solving the problem.

3. Activity "Area of a Composite Figure" (5 - 10 minutes)

   • Objective: Apply the concept of the area of a triangle to a context of a composite figure, allowing students to see how mathematics can be used to solve more complex problems.

   • Materials needed:

     • Sheet of graph paper
     • Pencil and eraser

   • Description of the activity:

     • The teacher should present the students with a drawing of a figure composed of several triangles on the sheet of graph paper.
     • The teacher should explain that the students' task is to calculate the area of this figure.
     • The students should then divide the figure into triangles that they can identify and calculate the area of each triangle.
     • Then, they should add the areas of all the triangles to obtain the total area of the figure.
     • The teacher should circulate around the room, assisting the groups as needed, and encouraging discussion and sharing of ideas among the students.
     • After all the groups are finished, the teacher should ask one or two groups to share their solutions with the class, and discuss the different approaches to solving the problem.

Debrief (10 - 15 minutes)

1. Group discussion (5 - 7 minutes):

   • Objective: Allow students to share their findings and solutions with the class, promoting discussion and debate on the concepts learned.
   • Description: The teacher should ask each group to share their answers and solutions to the activities carried out. Each group will have a maximum of 3 minutes to make their presentation. During the presentations, the teacher should encourage the other students to ask questions and express their opinions. The teacher should also take the opportunity to correct any conceptual errors and reinforce the key points of the lesson.

2. Connection with theory (2 - 3 minutes):

   • Objective: Allow students to relate the practical activities to the theory presented, reinforcing the understanding of the concepts.
   • Description: After the presentations, the teacher should summarize the main ideas presented, highlighting how they connect with the theory. For example, the teacher can show how the formula for the area of the triangle was used to solve the practical problems, and how the construction and measurement of the triangles helped to visualize the relationship between the base, the height, and the area of a triangle.

3. Individual reflection (2 - 3 minutes):

   • Objective: Allow students to reflect on what they have learned and identify possible doubts or difficulties.
   • Description: The teacher should propose that the students do a brief individual reflection on the lesson. To do this, the teacher can ask questions such as:
     1. What was the most important concept you learned today?
     2. What questions have not yet been answered?
   • Students should write their answers on a piece of paper or in their notebooks. The teacher should collect these notes to assess students' understanding and identify any difficulties that will need to be worked on in future lessons.

4. Feedback and closing (1 - 2 minutes):

   • Objective: Provide feedback to students on their performance and understanding, and end the lesson in a clear and organized manner.
   • Description: The teacher should thank the students for their participation and commend their effort and dedication during the lesson. The teacher should then provide general feedback on the class's performance, highlighting the strengths and areas that need more practice. Finally, the teacher should reinforce the main concepts and tasks of the lesson, and announce the topic of the next lesson.

Conclusion (5 - 10 minutes)

1. Summary of Key Content (2 - 3 minutes):

   • The teacher should recap the main points covered during the lesson, reinforcing the definition of the area of a triangle and the formula A = (b * h) / 2.
   • The different types of triangles and their characteristics, such as base and height, which are essential for calculating the area, should be recalled.
   • The teacher should also reinforce the importance of understanding the application of the formula for the area of the triangle to practical problems, such as calculating the area of a composite figure or the area of a triangular plot of land.

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

   • The teacher should highlight how the lesson connected the theory, practice, and applications of calculating the area of the triangle.
   • It can be mentioned how the students were able to visualize the relationship between the base, the height, and the area of a triangle through the activity "Building and Measuring Triangles".
   • In addition, it can be emphasized how the activities "Area of a Triangular Plot of Land" and "Area of a Composite Figure" allowed students to apply this concept in practical and real-world contexts.

3. Supplementary Materials (1 - 2 minutes):

   • The teacher should suggest complementary study materials for students who wish to deepen their knowledge of calculating the area of the triangle.
   • These materials may include math books, educational websites, explanatory videos, and math apps.
   • For example, the teacher could suggest that students watch a video about Heron's theorem, or that they solve more triangle area problems in a math app.

4. Importance of the Topic for Everyday Life (1 - 2 minutes):

   • To conclude, the teacher should reinforce the relevance of calculating the area of the triangle to students' everyday lives.
   • It can be mentioned again how this concept is applied in various areas, such as architecture, engineering, physics, and geography.
   • The teacher can also remind students that developing mathematical skills, such as logical thinking and problem-solving, is essential not only for mathematics but also for many other areas of life.