Contextualization

Introduction

The area is an essential concept in mathematics that we utilize in various aspects of our lives, from determining the square footage of a room to calculating the amount of fabric needed for a curtain. In this project, we will explore the concepts of area, with a specific focus on parallelograms and squares. These geometric shapes have distinct properties that make their area calculations unique and interesting.

A parallelogram is a four-sided polygon with opposite sides that are parallel and of equal length. The formula to calculate the area of a parallelogram is base times height, where the base is any of the sides, and the height is the distance between the base and its parallel side.

On the other hand, a square is a special type of parallelogram where all four sides are equal in length and all four angles are right angles (90 degrees). The formula to calculate the area of a square is simply the length of one side squared.

Understanding the area of these shapes not only helps us solve mathematical problems but also has practical applications in various fields such as architecture, design, and engineering.

Relevance and Real-World Application

The area of parallelograms and squares has numerous real-world applications. For instance, architects and engineers use the area of a parallelogram to calculate the space required for certain structures or for determining the material needed to build them. Similarly, the area of a square is used to determine the size of a room or the amount of land needed for a building.

In the field of design, the knowledge of area is fundamental. Graphic designers determine the amount of space needed for certain elements in a design, such as images or text, based on their areas. In gardening, understanding the area is crucial for planning the layout of a garden or determining the amount of soil and fertilizer needed.

Resources and References

Students can refer to the following resources to deepen their understanding of the area of parallelograms and squares:

1. Khan Academy: Area of a parallelogram
2. Khan Academy: Area of a square
3. Math is Fun: Area of a parallelogram
4. Math is Fun: Area of a square
5. Book: Mathematics for the Nonmathematician by Morris Kline. Chapters 10 and 11 cover the area of parallelograms and squares respectively.

Practical Activity

Activity Title: "Area Explorers: Parallelograms and Squares in the Real World"

Objective of the Project

The aim of this project is to deepen your understanding of the concepts of area, particularly in relation to parallelograms and squares, and to apply this knowledge to real-world scenarios. By the end of this project, you should be able to calculate the area of a parallelogram and a square confidently, and understand their real-world applications.

Detailed Description of the Project

In this project, you will work in groups of 3 to 5. Each group will be given a set of 5 real-world scenarios where the area of parallelograms and squares are involved. Your task is to analyze each scenario, identify the key elements (parallelogram or square), calculate their respective areas, and provide a detailed explanation of your calculations.

After completing the calculations, your group should create a presentation (using PowerPoint, Google Slides, or any other suitable software) that includes:

• A brief description of each scenario.
• The identified shape(s) (parallelogram or square) within each scenario.
• Calculations of the area for each identified shape.
• Detailed step-by-step explanations of the calculations, including the use of the relevant formula(s).
• Discussion of how the knowledge of the area of parallelograms and squares was applicable to each scenario.
• A conclusion that summarizes the main learnings from the project.

The resources that can be used in this project include textbooks, the internet, and other relevant books or articles about geometry and real-world applications of area.

Necessary Materials

• A set of 5 real-world scenarios involving areas of parallelograms and squares (provided by the teacher).
• Geometrical tools: ruler, protractor, and compass.
• Notebooks for making calculations and taking notes.
• A computer with internet access and presentation software (e.g., PowerPoint, Google Slides).

Detailed Step-by-Step for Carrying Out the Activity

1. Formation of Groups (15 minutes): The teacher will divide the class into groups of 3-5 students. Each group will receive a set of 5 real-world scenarios involving areas of parallelograms and squares.

2. Scenario Analysis (30 minutes): Each group will analyze their given scenarios, identifying the key shapes (parallelograms and/or squares) within each scenario.

3. Calculations and Note Taking (1 hour): For each identified shape, the group will calculate its area, using the appropriate formula(s). They will also note down the steps of their calculations and discuss their findings among the group members.

4. Presentation Creation (1 hour): Using the gathered information, each group will create a presentation that includes all the required components (as stated in the detailed description of the project section). The presentation should be structured, clear, and concise.

5. Presentation (30 minutes): Each group will present their findings to the class. The presentation should be interactive, engaging, and informative.

6. Discussion and Reflection (15 minutes): After each presentation, there will be a short discussion and reflection session. The other students and the teacher will ask questions about the presented scenarios, calculations, and findings.

7. Report Writing (1 hour): After the presentations, each group will write a detailed report about their project, following the given structure: Introduction, Development, Conclusion, and Used Bibliography.

The project is expected to take around four to five hours per participating student to complete. This includes the time spent on research, discussion, calculations, presentation creation, and report writing.

Project Deliverables

The deliverables for this project are:

1. A presentation (PowerPoint, Google Slides, or any other suitable software) that includes all the required components (as stated in the detailed description of the project section).

2. A detailed report following the given structure: Introduction, Development, Conclusion, and Used Bibliography.

   • Introduction: Contextualize the theme, its relevance, real-world application, and the objective of this project.

   • Development: Detail the theory behind the area of parallelograms and squares, explain the activity in detail, indicate the methodology used, and present and discuss the obtained results.

   • Conclusion: Revisit the main points of the project, explicitly state the learnings obtained, and the conclusions drawn about the project.

   • Bibliography: Indicate the sources (books, web pages, videos, etc.) that you used to work on the project.

At the end of this project, you will not only have a deeper understanding of the area of parallelograms and squares but also have enhanced your collaborative and problem-solving skills. Good luck, and have fun exploring the fascinating world of geometry!