Contextualization

A fundamental topic in the discipline of Mathematics is the study of areas. In particular, the area of a square is a simple yet incredibly powerful concept that serves as the foundation for studying other geometric shapes. The area of a figure is the measure of the extent of a surface. To calculate the area of most shapes, we need to rely on the calculation of the area of the square, which has all equal sides.

By studying the area of the square, you will learn how to apply a simple formula to calculate the extent of a surface. This is an essential process that has applications in many disciplines and real-world activities, from engineering and architecture to art and design.

The importance of studying area

The ability to calculate area is extremely valuable. For example, if you want to paint a wall, you will need to know the area of the wall to determine the amount of paint needed. If you are planning a garden, calculating the area will let you know how much space you have for planting. In engineering and architecture, calculating the area is a crucial step in creating projects and structures.

This skill is also useful in less obvious professions. For example, geographers use area calculations to create accurate maps, while artists use notions of area to create balanced and visually appealing artwork.

Hands-on Activity: "Building Squares of Our Own"

Project Goal

The goal of this project is to provide students with a practical and fun experience with the concept of "area of a square", where each group will build their own squares of different sizes and calculate their respective areas.

Project Description

Students, divided into groups of 3 to 5 people, will create a series of squares of different sizes using colored paper. They will measure the sides of these squares and calculate their areas using the formula A = side * side. After building the squares and calculating the areas, the groups will hold an exhibition in the classroom, where each group will present their squares and explain the process of calculating the area.

Necessary Materials

1. Colored paper or cardstock of different colors.
2. Ruler for measuring.
3. Scissors.
4. Pencils and erasers.
5. Calculator.
6. Flip chart or board for displaying the squares.

Project Step-by-Step

Step 1: Planning

Each group should decide how many and what sizes of squares they want to build. Remember that all sides of the square must be of the same length. After deciding, the groups should make a sketch of each planned square.

Step 2: Creating the Squares

Using the decided measurements, students should draw the squares on the colored paper and cut them out.

Step 3: Calculating the Area

Students need to carefully measure the sides of their squares and calculate the area of each one using the formula A=side*side. They should write down the area of each square.

Step 4: Preparing for the Exhibition

The groups should prepare a presentation, explaining how they built their squares, how they calculated the areas, and what they learned from the process. They can organize their squares on the flip chart or board for the exhibition.

Step 5: Exhibition and Presentation

On the scheduled date, the groups will present their work to the class.

Project Deliverables

Report

After the conclusion of the hands-on project, each group should write a report containing:

1. Introduction: Contextualize the project, its relevance and usefulness, as well as the objective of this work.
2. Development: Detail the theory of calculating the square's area, explain the work's execution method, present the methodology used, and discuss the obtained results.
3. Conclusion: Review the work's main points, discuss what was learned, and reflect on the project experience.
4. Bibliography: Include all sources used to carry out the work, such as books, websites, videos, etc.

This report should be submitted together with the exhibition and practical demonstration of the squares. Students should explain how the report fits and complements what was done in practice, presenting other relevant concepts and discussions that were learned during the project's research and implementation.