Lesson Plan | Active Learning | Triangle Area

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is crucial for establishing clear learning goals that students must achieve by the end of the lesson. By defining the main objectives, the teacher guides the students on what is expected of them and how the knowledge acquired will be applied. This clarity helps to direct classroom activities and focus on the most important points of the study of the area of the triangle, ensuring a deep and practical understanding of the subject.

Main Objectives:

1. Empower students to calculate the area of triangles using the standard formula and alternative methods, promoting a deep understanding of the mathematical concept involved.

2. Develop students' ability to apply the calculation of the area of triangles in practical situations, such as calculating areas of land and irregular surfaces.

Side Objectives:

1. Encourage logical reasoning and problem-solving skills in mathematics through practical and contextualized exercises.

Introduction

Duration: (15 - 20 minutes)

The Introduction stage serves to engage students and connect the content they studied at home with real-world situations and historical curiosities, demonstrating the relevance of studying the area of a triangle. The proposed problem situations encourage students to apply their prior knowledge in a practical and contextualized manner, setting the stage for more in-depth application in the classroom. The contextualization, in turn, broadens students' views on the importance of the topic, motivating the study and application of the content.

Problem-Based Situations

1. Imagine you are an architect and need to calculate the amount of tiles required to cover the floor of a house with several triangular rooms. How would you proceed to calculate the area of each of these triangles?

2. A farm has a triangular-shaped pond and the owner wants to fence this area to protect the animals. Knowing that the pond has sides measuring 100 meters, 150 meters, and 200 meters, how can the owner calculate the amount of material needed for the fence, knowing that it will be placed 1 meter from the edge of the pond?

Contextualization

The area of a triangle is a fundamental measure in practical contexts, from technical and architectural drawing to urban and agricultural planning. Interestingly, the formula for calculating the area of a triangle was discovered by Indian mathematicians Bhaskara I and Aryabhata I thousands of years ago, and has since been an essential tool in various fields. This technique enabled, for example, the development of methods for measuring areas of land for taxation and equitable distribution purposes, an important aspect of the history of mathematics.

Development

Duration: (70 - 75 minutes)

The Development stage is designed to allow students to practically and contextually apply the concepts studied at home about the area of triangles. Working in groups, students will face challenges that simulate real situations where area calculation is essential, promoting logical reasoning, collaboration, and the application of mathematical formulas in everyday scenarios. Moreover, the activity aims to reinforce learning through experimentation and error, crucial elements for the retention of mathematical content.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Architects in Action

> Duration: (60 - 70 minutes)

- Objective: Apply theoretical knowledge about the area of triangles in a practical context, developing calculation and presentation skills.

- Description: In this activity, students will be divided into groups of up to 5 members, and each group will represent a team of architects tasked with designing and calculating the area of classrooms in a fictional school. The classrooms will have varied shapes, including rectangles and triangles. Each group will receive floor plans to analyze and calculate the total area of each room, with a special focus on calculations for the triangles present.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the floor plans of the classrooms to each group.

• Guide students to calculate the total area of each room, identifying the triangles present and applying the area formula for triangles.

• Ask each group to present their findings, explaining the calculations performed and the strategies used.

Activity 2 - Geometric Treasure Hunt

> Duration: (60 - 70 minutes)

- Objective: Develop problem-solving skills and practical application of area concepts, especially the area of triangles, in a playful and collaborative manner.

- Description: Students, in groups, will participate in a treasure hunt within the school, where they will have to find and measure areas of specific locations, such as the soccer field (which can be approximated as a rectangle) and the garden, which has several triangular areas. Each group will receive a map with clues and mathematical challenges to solve.

- Instructions:

• Organize the classroom into groups of up to 5 students.

• Provide a map with clues and mathematical challenges to each group.

• The groups must follow the clues to find the locations and calculate the areas, using measuring tapes and calculators.

• The first group to solve all the challenges and present the correct answers wins the treasure hunt.

Activity 3 - Kite Festival

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of the area of a triangle in a practical project, encouraging creativity and teamwork.

- Description: Students will design and build kites in groups, where the shape of the kite must be a triangle. After building, they must calculate the area of each kite. The activity will culminate in a kite flying event in the school field, where the kites will be evaluated not only for their flying ability but also for the accuracy of the area calculation.

- Instructions:

• Divide students into groups of up to 5.

• Provide materials for building kites, such as paper, bamboo sticks, and strings.

• Guide students to design their kites in the shape of triangles.

• After construction, each group must calculate the area of the kite.

• Hold the kite festival in the school field, where students will present their kites and the area calculations.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage of the lesson plan is to consolidate the learning acquired by students during practical activities. Through group discussion, students have the opportunity to verbalize and reflect on what they learned, consolidating knowledge. Furthermore, by hearing their peers' experiences, students can gain new perspectives and insights, enriching their understanding of calculating the area of a triangle and its practical application.

Group Discussion

To start the group discussion, the teacher should gather all students and ask each group to share their findings and learnings from the activities. It is important that the teacher encourages students to reflect on the challenges encountered and the strategies adopted to overcome them. This is an opportunity for students to express the difficulties they faced and how they managed to overcome them, promoting an environment of collaborative learning and exchange of experiences.

Key Questions

1. What were the main difficulties encountered when calculating the area of the triangles in the activities and how did you overcome them?

2. How did the practical application of calculating the area of the triangle in projects like architecture or kite building alter or reinforce your theoretical understanding of the subject?

3. Was there any surprise or interesting discovery during the activities that you would like to share?

Conclusion

Duration: (10 - 15 minutes)

The Conclusion stage is designed to consolidate the knowledge acquired by students during the lesson, summarizing the main points discussed and reinforcing the practical applicability of the content. This moment is crucial to ensure that students leave the lesson with a clear and integrated understanding of the subject, able to recognize the relevance of studying the area of the triangle in various contexts. Additionally, by highlighting the connection between theory and practice, the Conclusion helps to reinforce learning and students' motivation for future applications of mathematical knowledge.

Summary

Today's lesson focused on calculating the area of the triangle, covering the classic formula, its derivatives, and various practical applications. Students were able to review and deepen their theoretical knowledge through practical activities that simulated real situations, such as the work of architects and kite building. This practical approach allowed for a deeper understanding of the concept of area and its importance in various contexts.

Theory Connection

Today's lesson effectively connected theory and practice. Students were able to directly apply the formulas and methods discussed at home in solving practical problems, such as calculating the areas of classrooms and land, and in building kites. This approach not only reinforced theoretical learning but also demonstrated the relevance and applicability of mathematical concepts in daily life and specific professions.

Closing

Understanding and knowing how to calculate the area of the triangle is fundamental not only for mathematics but also in various areas of practical life, from engineering and architecture to everyday situations such as interior decoration and event planning. This knowledge allows students a greater ability to solve problems and make informed decisions, reinforcing the importance of studying mathematics.