Calculating Area with Unit Squares

Chapter Title

Systematization

In this chapter, you will learn how to calculate the area of plane figures drawn on a grid. Through practical activities, you will develop the skill to count whole squares and pieces of squares to determine the area. Additionally, we will see how this knowledge is applied in professions such as architecture, engineering, and interior design.

Objectives

The objectives of this chapter are: To calculate the area of plane figures drawn on a grid. To count squares or pieces of squares to determine the area. To apply the concepts of area calculation in practical everyday situations and the job market.

Introduction

Calculating the area of plane figures is a fundamental skill in mathematics, especially when dealing with grids. Area is the measure of the surface of a figure and is expressed in square units. In our case, we will use unit squares as a basis for counting and calculating the area. This concept is widely used in various everyday situations and professions, such as in construction, urban planning, and interior design. For example, when designing a house, an architect needs to calculate the area of the different rooms to plan the placement of furniture and ensure that the space is used efficiently.

Understanding how to calculate the area of plane figures is also essential for practical activities, such as determining the amount of material needed to cover a surface. Imagine that you need to know how much paint will be required to paint a wall. Calculating the area allows you to estimate these quantities accurately, avoiding waste and optimizing resources. Additionally, this knowledge helps solve space division problems, such as organizing a garden or planning the arrangement of furniture in a room.

In the job market, the ability to calculate areas is crucial for professionals such as engineers, designers, and urban planners. These professionals use area calculations daily to design and construct safe and functional structures. For instance, a civil engineer needs to calculate the area of different sections of a building to ensure that the construction will be stable and safe. Similarly, a landscape designer needs to calculate the area of different sections of a garden to plan the distribution of plants and other decorative elements. Therefore, learning to calculate the area of plane figures not only strengthens your mathematical skills but also prepares you to face practical challenges in various professions.

Exploring the Theme

In this chapter, we will explore how to calculate the area of plane figures using unit squares. This concept is fundamental in mathematics and has practical applications in various professions and everyday activities. Through examples and exercises, you will learn to count whole squares and pieces of squares to determine the area of different figures drawn on a grid.

Calculating areas is an essential skill not only for students but also for professionals such as architects, engineers, and designers. They use these calculations to plan and execute construction, decoration, and landscaping projects, ensuring the optimization of spaces and resources. Throughout this chapter, you will see how these mathematical concepts are applied in practice and understand their importance in the job market.

Theoretical Foundations

The area of a plane figure is the measure of the surface it occupies. To calculate the area of figures drawn on a grid, we use unit squares. A unit square is a square with a side length equal to one unit of measurement, such as a centimeter or a meter.

Calculating the area can be done in various ways, depending on the shape of the figure. In the case of figures drawn on a grid, the simplest and most direct method is to count the whole squares that make up the figure. When the figure does not perfectly fit into the squares of the grid, we also count the pieces of squares.

Definitions and Concepts

Area: The measure of the surface of a plane figure, expressed in square units.

Unit Square: A square with sides of equal length of one unit of measurement.

Grid: A network of unit squares used to draw and measure plane figures.

Counting Squares: A method of calculating the area of a figure by counting the whole squares and the pieces of squares that make it up.

Practical Applications

Now let’s apply what we have learned through practical examples. Imagine that you are designing a garden and need to calculate the area of different sections to decide how many plants of each type to place. You draw the garden on a sheet of graph paper and use unit squares to count the area of each section.

Another example is the construction of a house. An architect draws the floor plan of the house on a grid and calculates the area of each room to plan the arrangement of furniture and ensure that each space is used efficiently.

Useful tools for these calculations include graph paper, ruler, colored pencils, and design software like AutoCAD for more complex projects.

Assessment Exercises

Draw a rectangle of 5 squares wide by 3 squares high on a sheet of graph paper. Calculate the area of the rectangle.

On a sheet of graph paper, draw a figure composed of 8 whole squares and 4 half squares. Calculate the total area of the figure.

Imagine that you have a piece of fabric drawn on a grid with 6 whole squares and 3 pieces of squares that together form one more whole square. Calculate the total area of the piece of fabric.

Conclusion

In this chapter, you learned the importance and practical application of area calculation using unit squares. Through practical activities and real examples, you developed fundamental skills that will be useful in both everyday situations and various professions. Understanding how to calculate area is essential for planning and optimizing spaces, whether in architecture, engineering, or interior design.

As the next steps, prepare for the lecture by reviewing the studied concepts and practicing the proposed exercises. During the lecture, you will have the opportunity to deepen your understanding further and discuss your doubts with the teacher and classmates. In addition, continue exploring how area calculations can be applied in different contexts and practical challenges you may encounter.

To prepare adequately, review the practical examples and the fixed exercises from this chapter. Try to solve the proposed discussion questions and reflect on how the concepts of area calculation can be applied in everyday situations and in the job market. This will help consolidate your knowledge and feel more confident in applying these concepts in different contexts.

Going Beyond- Explain the importance of area calculation in architecture and engineering projects.

• Describe how you can apply your knowledge of area calculations in everyday situations.

• How can the practice of calculating areas help optimize resources in a project?

• Discuss the relevance of area calculation for interior design and landscaping professionals.

• How does counting whole squares and pieces of squares facilitate area calculations in grids?

Summary- The area of a plane figure is the measure of the surface it occupies.

• Unit squares are used to calculate the area of figures drawn on grids.

• Area calculation can be done by counting whole squares and pieces of squares.

• Knowing how to calculate area is essential for various professions, such as architecture, engineering, and interior design.

• Practical activities, such as building a miniature city, help consolidate the understanding of the concepts learned.