Lesson Plan | Active Learning | Basic Area Formula

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 to clearly establish what is expected from students at the end of the lesson. In this context, the aim is to guide students' learning so that they can not only understand but also actively apply the concepts of area in basic figures, which are essential for their mathematical education. By clearly detailing the objectives, students can focus their efforts on the necessary skills to achieve these goals during the lesson's practical activities.

Main Objectives:

1. Empower students to calculate the area of basic geometric figures, such as triangles, squares, and rectangles.

2. Develop students' ability to solve practical problems involving the calculation of areas of triangles, squares, and rectangles.

Side Objectives:

1. Promote the use of logical and mathematical reasoning in problem-solving.
2. Encourage collaboration and discussion among students during practical activities.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to connect students' prior knowledge with the practical application of area calculation, using problem situations that stimulate critical thinking and the direct application of the concepts studied. Additionally, the contextualization helps to show the relevance of the topic in daily life, increasing interest and perception of the usefulness of what is being learned.

Problem-Based Situations

1. Present a scenario in which a construction company needs to calculate the amount of material necessary to cover the floor of a rectangular area and another of a triangular shape. Ask students to calculate the areas of each floor and compare the results to decide which floor requires more material.

2. Imagine a farmer has two fields, one square and the other triangular, of different sizes. He wants to know which field can accommodate more crops. Ask students to calculate the areas of both fields to help the farmer make his decision.

Contextualization

Explain the importance of understanding and calculating areas in everyday life, using examples such as interior design, where the choice of rugs and furniture depends on the room's area; or in agriculture, where farmers need to calculate the area of their fields to determine the amount of seeds needed. Highlight how knowledge of areas can be critical in various professions and practical activities.

Development

Duration: (65 - 75 minutes)

The development stage is designed to allow students to practically and engagingly apply the area calculation concepts they studied previously. The proposed activities aim to solidify learning by promoting the application of concepts in real and playful scenarios that encourage creativity, logical reasoning, and collaboration. This approach reinforces theoretical understanding and also develops important teamwork and presentation skills.

Activity Suggestions

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

Activity 1 - The Math Garden

> Duration: (60 - 70 minutes)

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

- Description: In this activity, students will be challenged to design a garden in a defined area, using only simple geometric shapes: squares, rectangles, and triangles. They should calculate the total area of the garden, the area occupied by each type of plant (represented by geometric figures), and the area of paths or empty spaces.

- Instructions:

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

• Distribute graph paper and rulers to each group.

• Present a defined area on paper that symbolizes the garden.

• Each group should draw a plan for the garden, using only squares, rectangles, and triangles.

• Ask them to calculate the total area of the garden and the area occupied by each 'plant'.

• Students must present their project, explaining their choices based on area calculations.

Activity 2 - City Builders

> Duration: (60 - 70 minutes)

- Objective: Develop skills in area calculations and proportions, as well as promote creativity and teamwork.

- Description: Students will plan a small city on a given land, using geometric figures to represent buildings, streets, and public spaces. They will need to calculate areas to ensure that all elements fit adequately on the land.

- Instructions:

• Organize students into groups of no more than 5 people.

• Provide each group with a blank city map and geometric figures to represent elements such as buildings (squares), parks (rectangles), and squares (triangles).

• Explain that each figure must be proportional to the real area it represents within the city.

• Students must calculate the areas of each figure and then assemble the city on the map, ensuring that everything fits correctly.

• At the end, each group presents their city, explaining the choices and calculations made.

Activity 3 - The Magic Carpet Challenge

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of areas in a practical and three-dimensional context, developing spatial reasoning and collaboration.

- Description: In this activity, students will be challenged to 'dress' different areas with carpets of various shapes, such as squares, rectangles, and triangles. They will need to calculate the areas of the carpets and decide how to position them to cover as much area as possible.

- Instructions:

• Divide the students into groups of up to 5.

• Give each group several carpets of different shapes and sizes.

• Present a marked area on the floor where the carpets should be placed.

• Groups must calculate the areas of each carpet and decide how to position them to cover as much of the marked area as possible.

• Discuss each group's strategies and check the solutions during the activity.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate the learning acquired during the practical activities, allowing students to articulate what they learned and reflect on the application of mathematical concepts in various contexts. Group discussion helps develop communication and argumentation skills, while reflecting on the challenges faced and successful strategies promotes a deeper understanding of the content.

Group Discussion

To start the group discussion, ask each group to share their experiences and discoveries. Use the following questions to guide the discussion: 'What were the biggest challenges in applying area calculations in the activities? How did you solve those challenges? Which area calculation strategies worked best for the group and why?' Encourage students to explain the reasoning behind their choices and reflect on the importance of area calculation in real and theoretical situations.

Key Questions

1. How can knowledge about area calculation be applied in everyday situations?

2. Which mathematical skills were most important to complete the proposed activities?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage is to ensure that students have understood and internalized the concepts presented, relating them to real and everyday situations. By summarizing and reinforcing learning, the conclusion helps solidify the knowledge acquired and highlight the applicability of mathematics in students' daily lives, encouraging greater appreciation and use of the concepts learned.

Summary

In the conclusion, recap the main concepts addressed regarding the calculation of areas of basic figures such as triangles, squares, and rectangles. Emphasize the formulas used and how they apply in different contexts, from interior design to agriculture.

Theory Connection

Explain how practical activities, such as the garden design and city building, connected theory with practice. Highlight the importance of understanding mathematics in real contexts and how area concepts are essential for solving everyday problems.

Closing

Finally, emphasize the relevance of area calculation in various professions and practical situations, reinforcing the idea that mathematics is present in many decisions we make daily, from choosing the best configuration for a space to optimizing resources in larger projects.