Contextualization

The study of plane geometric figures is a fundamental topic in Geometry, a branch of Mathematics. The area is a scalar quantity (ie, a number) that measures the extent of a flat surface. The square, one of the most basic and common shapes in geometry, is a regular polygon with four sides of equal length and four right angles.

The area of the square is calculated by raising the length of the side to the square, a formula generally represented by A = l². This concept of area is widely used in everyday and professional situations, from calculations of the amount of material needed to cover an area, to defining planting areas in agriculture, to even technical drawings and architectural projects.

Importance of the Theme

Measuring the area of a square is essential in various areas of real life. For example, imagine that you need to paint a square wall: to know the amount of paint needed, you need to calculate the area of the wall. Or, if you want to plant a square-shaped garden in your backyard, knowing the area of the square will allow you to determine the amount of seeds or seedlings to buy.

This interdisciplinary project, which will fit into the disciplines of Mathematics and Arts, aims to deepen your understanding of the area of the square, applying the theoretical concepts learned in a practical and creative way. Thus, it is expected that you will be able to integrate theoretical knowledge with practical experience, becoming more confident and accurate when dealing with real situations in which the calculation of the area of the square is necessary.

Practical Activity

Activity Title: "Art Squares - Creating a Mosaic"

Project Objective

The objective of this activity is to apply the theoretical knowledge of calculating the area of the square, through the creation of an artistic mosaic, where the concepts of area of the square will be applied.

Project Description

Students, in groups of 3 to 5, will use squares of paper of different sizes to create a mosaic on a large sheet of kraft paper. Students will calculate the area of each square of paper used, as well as the total area of the mosaic created. Part of the activity is planning and executing the artwork, another part is documenting the calculations and measurements used in the process.

Students will design the mosaic so that they use at least 4 (four) different sizes of squares, calculating the area of each one to determine the amount needed to cover the panel. They should use tiling techniques to fill the entire space of the panel, creating an attractive and creative mosaic.

Students should document the creative process, the calculations made, and the mathematical concepts used, as well as reflect on the socio-emotional skills developed during the project.

The activity will take approximately 12 to 15 hours to complete, considering the time for planning the mosaic, execution, calculations and writing the report.

Necessary Materials

• Kraft Paper for the board (1m x 1m)
• Colored paper or magazines for cutting squares
• Ruler, scissors and glue
• Pencil and calculator
• Camera or cell phone to document

Step by Step

1. Organize the group and distribute the tasks. Discuss ideas for the mosaic you will create.
2. Decide together the sizes of the squares that will be used. Remember: there must be at least 4 different sizes.
3. Calculate the area of each square that will be used.
4. Determine how many squares of each size will be needed to fill the entire area of the panel. Do the calculations and see if you need to adjust anything.
5. With all the calculations done and the material prepared, start assembling the mosaic.
6. Document the whole process with photos and notes.
7. When finishing the mosaic, review all the calculations and check if the area of the panel has been completely filled.
8. Reflect on the whole process: from planning to execution. What did you learn from this experience?

Project Deliverables

At the end of the project, each group must deliver:

1. The Finished Mosaic: The panel should be presented along with an oral explanation of the creative process and the calculations made.
2. Written Report: The report should be written according to the previously given guidelines (Introduction, Development, Conclusions and Bibliography). This report should detail the entire process, from planning, through calculations and execution, to the completion of the project. The photos documenting the process should be included in the report.
3. Oral Presentation: Each group will present their work to the class, explaining the creative process, the calculations involved, and the conclusions reached.

In the "Development" category of the report, students should describe in detail all stages of the project, from the planning phase to the completion and completion of the artwork. The mathematical calculations should be presented and explained in detail, as well as presenting the relationship between these calculations and the theoretical concepts studied in the classroom.

The use of photos and drawings is strongly encouraged to make the explanation clearer and visually appealing. In addition, they should discuss the mistakes and corrects, the challenges encountered and how they were overcome, and the teamwork skills developed during the project.

Remember: this is a hands-on project, but writing the report is equally important. It should be clear, precise and comprehensive, reflecting the hard work you put into all parts of the project.