Contextualization

Mathematics is a universal language, used to understand and interpret the world around us. Among the various tools that mathematics offers us, plane geometry stands out for its practical application and visibility in everyday life. Within this theme, we will focus on the study of two geometric shapes, the rectangle and the parallelogram, and how to calculate their areas.

Area is a measure of the interior space of a closed figure, calculated in square length units. For a rectangle, the area is calculated as the product of its two dimensions, length and width. Similarly, the area of a parallelogram is given by the product of its base and its height. These are basic but essential rules to delve into the study of mathematics and geometry.

One of the main objectives of mathematics is to develop logical reasoning and problem-solving skills, which will be explored in this project. In addition to the basic mathematical concepts mentioned, we will also introduce notions of analytical geometry and trigonometry, which are fundamental to understand, in a more in-depth way, how we calculate the area of geometric figures.

Mathematics is present in all aspects of our lives, and calculating area is no exception. When we think about designing a house, or even arranging furniture in a room, we need to understand the area to optimize the space. Farmers can use area calculations to plan the irrigation of their crops, while engineers can use them to design structures and buildings. Calculating the area is essential in a multitude of professions, such as architecture, agronomy, civil engineering, and more.

Furthermore, calculating the area is also crucial in various fields of science. For example, biologists can use the concept of area to study animal behavior and the ecosystem, while physicists can use it to calculate the properties of an object.

Practical Activity

Activity Title: "Building and Calculating Areas"

Project Objective

• Understand the concepts of area through a practical project.
• Develop communication and teamwork skills.
• Apply mathematical knowledge to solve practical problems.

Detailed Project Description

This project is designed for groups of 3 to 5 students and aims to engage students in a practical mathematical modeling activity to calculate the areas of rectangles and parallelograms.

Students will design and simulate a "Mini Territory" on the classroom floor or schoolyard, using adhesive tape to mark the boundaries of the figures. The territories will contain various figures, including rectangles and parallelograms, representing different sections of the territory such as houses, sports fields, parks, and schools.

For each figure represented, students will need to calculate the area using the appropriate mathematical formulas. Additionally, they should analyze the calculated areas and discuss how changes in the dimensions of the figures could affect them.

Required Materials

• Sturdy adhesive tape.
• Long tape measure or ruler.
• Paper and pens for drawing the projects and making calculations.
• Computer with internet access for research.

Detailed Step-by-Step Guide for the Activity:

1. Planning: Each group should draw a sketch of their "Mini Territory" on paper, clearly dividing it into sections (houses, schools, parks, etc.) that will be represented by rectangles and parallelograms.

2. Measurement: Using the tape measure or ruler, students should measure the sides of each figure in their territory and record the measurements.

3. Area Calculation: Use the relevant formulas to calculate the area of each figure in the territory.

4. Simulation: Using adhesive tape, students will simulate their territory on the floor, faithfully reproducing its measurements and proportions.

5. Analysis: Students should discuss and reflect on the results obtained, such as the variation in area if the sides of the figure were altered.

6. Report Writing: After completing the practical activities, students should gather to write the final project report, including each of the detailed topics above.

Project Deliverables

The deliverables of this project are:

1. The sketch of the "Mini Territory" drawn on paper.
2. The record of measurements taken for each figure.
3. The calculations performed to determine the area of each figure.
4. The simulation of the territory with adhesive tape on the floor.
5. The discussion and analysis of the results obtained.
6. The written project report.

The report should follow the indicated format: Introduction, Development, Conclusions, and Bibliography.

• In the introduction, students should contextualize the theme, explain its relevance and real-world application, and also the objective of this project.
• In the development, students should explain the theory behind area calculation, describe the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.
• In the conclusion, students should revisit their main points, explain the learnings obtained, and the conclusions drawn about the project.
• In the bibliography, students should indicate the sources consulted to carry out the project.