Lesson Plan | Active Learning | Area: Composite Figures

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)

This stage of the lesson plan is crucial to establish the foundations that will guide the students' exploration of the theme 'Composite Figures'. By clearly outlining the objectives, students will be better prepared to engage in the proposed practical activities, understanding the importance and applicability of area calculations in real and mathematical situations.

Main Objectives:

1. Empower students to calculate the area of composite figures made up of triangles and rectangles.

2. Develop the ability to solve practical problems involving the calculation of the total area of structures, such as, for example, a house.

Side Objectives:

1. Encourage logical reasoning and the spatial visualization ability of students.

Introduction

Duration: (15 - 20 minutes)

The Introduction stage serves to engage students with the content they have previously studied, using problem situations that make them think critically about the practical applicability of area calculations. Furthermore, the contextualization of the theme with real and historical examples helps to perceive the importance and relevance of studying composite figures in the real world, increasing students' motivation and interest in the subject.

Problem-Based Situations

1. Imagine that you are an architect tasked with designing a new school. The total area of the land is a large rectangle, but the school itself includes a triangular inner courtyard. How would you calculate the total area of the land and the usable area for construction?

2. Think of a park that has a main rectangular area, with a triangular fountain in the center. If the area of the park is 800 square meters and the base of the fountain measures 10 meters, how do you calculate the total area occupied by the fountain and the remaining area of the park?

Contextualization

The ability to calculate areas of composite figures is not just a mathematical tool, but a practical necessity in various professions and everyday situations. From architects who design house plans to gardeners who plan garden layouts, understanding how areas add and subtract in different shapes is essential. Additionally, the history of geometry reveals how ancient architects and engineers used area concepts to design complex structures that endure to this day.

Development

Duration: (70 - 75 minutes)

The Development phase is designed to allow students to apply the studied concepts practically and interactively. By working in groups, they not only solidify their understanding of the area calculations of composite figures but also develop essential skills such as collaboration, communication, and problem-solving. The activities are structured to be challenging and engaging, ensuring that students are actively engaged and motivated.

Activity Suggestions

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

Activity 1 - The Junior Architect Challenge

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of area calculation in a practical and realistic context, developing teamwork and presentation skills.

- Description: Students, divided into groups of up to 5, take on the role of junior architects to design the layout of a new school. The land is a rectangular area, but the school must include a triangular inner courtyard. Students need to calculate the total area of the land and the area available for construction.

- Instructions:

• Form groups of up to 5 students.

• Use graph paper and pencils to draw the floor plan of the school.

• Calculate the total area of the land (rectangle) and the area of the inner courtyard (triangle).

• Present the project, showing how the areas were calculated and discuss possible uses for the inner courtyard.

• Prepare a brief presentation to share with the class.

Activity 2 - Geometry in the Park: A Mathematical Amusement Park

> Duration: (60 - 70 minutes)

- Objective: Develop area calculation skills in varied contexts and promote creativity in solving space optimization problems.

- Description: In this activity, students, organized into groups, are challenged to design an amusement park in a rectangular area that already contains a triangular fountain. They must calculate the total area of the park and the area occupied by the fountain to optimize space for attractions.

- Instructions:

• Divide into groups of up to 5 students.

• Use grid paper to draw the layout of the park.

• Calculate the total area of the park and the area occupied by the fountain.

• Plan the location of the attractions to optimize the remaining space.

• Prepare a report explaining the decisions made in planning the park.

Activity 3 - Garden Party: Planning the Layout

> Duration: (60 - 70 minutes)

- Objective: Use area calculation to plan events and develop spatial reasoning and teamwork skills.

- Description: Students, in groups, are invited to plan the layout of a garden party. They must calculate the total area available for the event, considering that the garden has a rectangular pool and a triangular flower bed.

- Instructions:

• Organize into groups of up to 5 students.

• Draw the layout of the garden on grid paper, including the pool and the flower bed.

• Calculate the total area of the garden, the pool, and the flower bed.

• Decide where to place the buffet table, chairs, and dance floor, considering the available space.

• Present the final layout, justifying the placement choices based on area calculations.

Feedback

Duration: (15 - 20 minutes)

This stage of the lesson plan is essential to consolidate students' learning. By discussing in groups, students have the opportunity to verbalize what they have learned, hear different perspectives, and reflect on the learning process. This helps to reinforce knowledge and identify areas that may still need clarification, ensuring a deeper understanding of area calculation in composite figures and their applicability.

Group Discussion

At the end of the activities, organize a group discussion with all students. Start by asking each group to share their findings and challenges faced during the activities. Encourage them to discuss the strategies used to calculate areas and how these strategies can be applied in everyday situations. Use guiding questions such as 'What were the biggest challenges your group faced when calculating areas?' and 'How did you solve the space optimization problems?' to guide the conversation and ensure that all students actively participate.

Key Questions

1. What are the main differences between calculating the area of simple figures and composite figures?

2. How does area calculation help in solving practical problems like those you faced in the activities?

3. Was there any mathematical concept that you found particularly challenging? How did you overcome those challenges?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is designed to reinforce students' learning by summarizing the main points discussed during the lesson and highlighting the connection between mathematical theory and its practical application. Additionally, it emphasizes the importance of studying areas in daily life, motivating students to value and utilize the knowledge gained in various real and professional situations. This final reflection helps solidify understanding and prepare students for future applications of the concepts learned.

Summary

Lesson Summary: In this lesson, we explored the calculation of areas in composite figures, emphasizing the composition of triangles and rectangles. Students applied theoretical knowledge in practical situations, such as planning a school, an amusement park, and a party layout. This practical exercise allowed them to see the relevance of mathematical concepts in the real world.

Theory Connection

Connection between Theory and Practice: During the activities, students could directly perceive how mathematical concepts can be applied to solve real problems, such as space planning. From the studied theory, they calculated areas of composite figures and used these calculations to optimize space usage and understand the importance of area calculations in various professions.

Closing

Importance of Mathematics in Daily Life: The study of areas is not only an essential part of mathematics but also a crucial tool in many aspects of daily life. From urban planning to furniture arrangement in a house, area calculation is fundamental to ensuring efficiency and functionality. Understanding and applying these concepts helps students prepare for future practical and professional challenges.