Contextualization

Area is a mathematical concept that describes the size of a surface. This concept is fundamental and applied in various areas of knowledge, from geometry to physics. In particular, rectangles and parallelograms are geometric figures that have specific properties very useful for area calculation.

In a rectangle, the area is given by the product of its base by the height, meaning all its parallel lines have the same measure, which simplifies the calculation. In a parallelogram, even if the parallel lines have different measures, the area can still be calculated by the product of the base by the height.

Understanding these concepts and the ability to calculate areas are essential not only for mathematics but also for other areas such as architecture, engineering, and even interior design. Knowing how to calculate the area of a rectangle or parallelogram can help you solve practical problems, such as determining the amount of paint needed to paint a wall or the amount of fabric needed to make a curtain.

Importance

Studying the areas of geometric figures, such as the rectangle and parallelogram, is a fundamental mathematical skill taught from elementary school. The calculation of areas is often used in many fields, including physical sciences, engineering, construction, agriculture, and many other professions.

Furthermore, understanding area is vital for intuitive understanding of space and for developing logical thinking and problem-solving skills. In this sense, area calculation also helps develop the ability to think creatively and solve complex problems effectively.

Practical Activity

Activity Title: "Measuring Surfaces: Exploring the Area of Rectangles and Parallelograms in Our School"

Project Objective

The objective of this project is to allow students to exercise their mathematical and collaborative skills through the practical application of the knowledge acquired about the area of rectangles and parallelograms. They will be able to visualize and understand the importance of these geometric figures in the real world.

Project Description

Students, divided into groups of 3 to 5, will be challenged to calculate the area of different rectangles and parallelograms present in the school environment, such as boards, doors, windows, tables, etc.

Each group will need to choose at least 5 different objects to measure and calculate their areas. They will also need to photograph each object. Then, they can calculate the areas based on the collected measurements and explain why they chose these objects.

Each group should complete this project in one week. The work should take between two to four hours for each student.

Necessary Materials

• Tape measure.
• Camera (can be a cellphone camera).
• Notebook and pen for notes.
• Calculator (optional).

Step by Step

1. Divide into groups.
2. Choose 5 different objects that are rectangles or parallelograms to calculate their areas.
3. Measure and write down the dimensions (base and height) of each chosen object.
4. Take a photograph of each object.
5. Calculate the area of each object using the area formulas for rectangles and parallelograms.
6. Write down the calculations and the areas obtained.
7. Discuss and write down why each object was chosen and the importance of knowing the areas of these objects in the real world.
8. Prepare a report following the guidelines below.

Report

Each group should prepare a report that includes the following points:

1. Introduction: Provide context on the topic, the relevance of learning this skill, and the project's objective. Include a brief description of the practical activity carried out.

2. Development: Explain the theory about calculating the areas of rectangles and parallelograms. Detail the activity performed, the method used to select the objects, how the measurements were taken, and the calculations were done. Discuss the results obtained.

3. Conclusions: Conclude the work by summarizing the main points. Comment on the learnings obtained and the conclusions about the project. What would they have done differently? What were the difficulties? How were they overcome?

4. Bibliography: List the sources consulted for the project.

5. Attachments: Include photos of the selected objects as well as the notes and calculations made.

This project will result not only in the development of technical skills, such as area calculation and understanding of geometric figures, but also in socio-emotional skills, such as time management, communication, problem-solving, creative thinking, and proactivity.