Context and Introduction

The concept of area is one of the most fundamental in mathematics, and its complete understanding is vital for advancement in many branches of the discipline, such as geometry, calculus, and even physics. Area can be understood as the amount of space a certain plane occupies. This may seem quite simple at first, but its study becomes more complex and fascinating as we work with more complex figures.

To imagine how area is calculated, we can think of a unit square, which is a square whose sides measure one unit of length. The area of the unit square is, therefore, the amount of space it occupies, and it is equal to one. But what if we want to calculate the area of a more complex figure? This is where unit squares come in!

Think of a puzzle piece. Each piece is a unit square, and our task is to find out how many of these squares make up a larger figure. If the figure is a rectangle, for example, you just need to count the number of unit squares that compose it to find its area. But what if the figure is more complex? Well, that's where the fun begins!

Learning to calculate area through the concept of unit squares is essential not only for further study of mathematics but also for many practical applications. Architects, engineers, and designers, for example, use these concepts daily when designing and building structures. By understanding area, we can also better understand the space around us and how to use it efficiently.

Furthermore, the study of area also allows us to develop a series of valuable skills, such as logical reasoning, problem-solving skills, and mathematical thinking. Through this activity, we hope that the student has fun learning, unravels mathematics, and develops valuable skills that will help them throughout their academic and professional life.

Practical Activity

Activity Title: Building Figures and Calculating Areas with Unit Squares

Project Objective:

To understand and apply the concept of area through unit squares, develop spatial and logical-mathematical reasoning skills, and provide the experience of teamwork.

Detailed Project Description:

Students, in groups of 3 to 5, will create geometric figures using unit squares and later calculate their respective areas. To make the activity more complex and challenging, students will be encouraged to create shapes that include partial areas of unit squares.

Required Materials:

1. Cardboard or cardboard for the base.
2. Colored paper squares measuring 1x1cm (can be replaced by flat building blocks or felt cut into small squares).
3. Ruler.
4. Pen.
5. Glue.

Step-by-Step Guide for Carrying Out the Activity:

1. In groups, students must decide on the shape of the geometric figure they want to create. They can be regular shapes, such as triangles and rectangles, or more complex and irregular shapes. Let creativity flow!

2. Once the shape is decided, the group will draw the shape on the cardboard or cardboard base using the pen.

3. After drawing the shape, the group will start filling the shape with the colored paper unit squares, gluing them to the base.

4. If the shape includes partial areas of unit squares, the group needs to decide how to deal with them. They can choose to cut the paper squares into smaller pieces, for example.

5. When the shape is completely filled with unit squares, the group will count how many unit squares were used. This will give the area of the shape.

6. The group will record all steps of the process, including decisions made, problems faced, and how they were solved. This information will be important for writing the final report.

Project Deliverables:

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

1. The figure filled with unit squares.
2. A written report that explains the project and presents its results.

The report should include the following parts:

• Introduction: In this section, the group must contextualize the theme and explain the relevance of area in mathematics and the real world. Additionally, the project's objective should be explained.

• Development: Here, the group must explain the theory of areas and unit squares, describe in detail the project's steps, indicate the methodology used, and present the results obtained.

• Conclusion: In this section, the group must review the main points of the work, highlighting what they learned and what the main findings were.

• Bibliography: Here, the group must list all sources used for the project, such as books, web pages, videos, etc.

Remember: the report should be a representation of the group's work, showing the learning process and progress made. This is a moment for students to reflect on what they have learned, how they interacted as a group, and how mathematics can be applied practically and creatively.