Contextualization

Theoretical Introduction

Geometry is a branch of mathematics that studies the shapes and dimensions of flat and spatial figures. One of the most basic figures found in plane geometry is the square. A square is a four-sided figure (quadrilateral) that has all sides of equal length and all angles equal to 90 degrees.

The area of a geometric figure is the space it occupies on a flat surface and is measured in square units. The area of a square is calculated as the product of its base by its height, and thanks to the symmetry of the square, both are equal. Therefore, the formula to calculate the area of a square is l x l, where "l" is the length of one side of the square.

Furthermore, the concept of area is present in many branches of exact sciences, such as physics, engineering, and architecture, as well as in some social sciences, such as geography and urban planning.

Theme Contextualization

Understanding the concept of area and calculating the area of a square are fundamental in everyday life. For example, you will need this knowledge when decorating a room and needing to know the amount of paint that will be necessary to paint the walls, or when choosing the correct size of a rug.

Moreover, in more advanced areas of study and work, the ability to calculate the area of various figures becomes even more crucial. For example, engineers need to calculate the area of cross-sections when designing structures, and agronomists need to calculate the area of fields when planning plantations.

Practical Activity

"Building and Measuring Squares"

Project Objectives:

• Understand the concept of area
• Be able to calculate the area of the square
• Develop teamwork skills

Project Description:

In this task, students will be divided into groups of 3 to 5 members. Each group will have to build and calculate the area of five different squares. The idea is for students to materialize theoretical concepts through a practical and playful activity.

Necessary Materials:

• Cardboard paper
• Ruler
• Pencil
• Scissors
• Tape

Step by Step:

1. Each group will receive five sheets of cardboard paper.
2. The group must then draw a square on each sheet, with the sides measuring respectively 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm. These measurements must be strictly respected.
3. After drawing the squares, the group must cut them out with scissors.
4. Now, each group must calculate the area of each square using the formula provided in the theoretical introduction (l x l).
5. The groups must then compare the calculated areas for each square and observe the behavior of the area as the size of the square's side increases.
6. Finally, based on the concepts learned and the activity carried out, each group must write a report.

Project Deliverables:

• Five cut-out squares, with the sides measuring respectively 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm.
• Calculation of the area for each square.
• Comparison of the calculated areas.

Students must also submit a report containing the following sections:

1. Introduction: Explain the relevance of the concept of area and calculating the area of a square. Describe the project's objective.
2. Development: Explain the theory behind the calculation of the square's area (l x l). Describe in detail the activity carried out, from drawing the squares to calculating their areas, and the methodology used (materials and process). Present and discuss the results of the calculations and the comparison between them.
3. Conclusion: Summarize the main points of the project and explain what was learned about the square's area. Indicate the conclusions about the project.
4. Bibliography: List the sources consulted for the project.