Exploring Areas: Building Knowledge with Unit Squares

Objectives

1. Calculate the area of flat shapes drawn on a grid.

2. Count squares or pieces of squares to determine the area.

Contextualization

Imagine you are in a park and want to know the total area of the space where people can have picnics. To do this, we need to learn how to calculate the area of flat shapes. This calculation is very useful in various everyday situations, such as determining how much grass is needed to cover a field or how much paint is needed to paint a wall. Architects and engineers, for example, use area calculations every day in their projects, whether to plan the construction of houses, buildings, or stadiums. Additionally, interior design and landscaping professionals also need this knowledge to organize spaces efficiently.

Relevance of the Theme

Area calculation is a fundamental skill not only for school mathematics but also for various professions and everyday situations. Understanding how to determine the area of flat shapes is essential for the planning and execution of projects in architecture, engineering, interior design, landscaping, and even gardening. Mastering this knowledge prepares students for future challenges in the job market and for solving practical problems in their daily lives.

Area Concept Using Unit Squares

The concept of area using unit squares is a way to measure the extent of a flat shape by counting the number of small squares that fit inside it. Each small square represents one unit of area. This technique is especially useful for figures drawn on grid patterns, where each square represents a uniform unit of measurement.

• Area is measured in square units.

• Each small square in the grid represents one unit of area.

• Counting the small squares allows you to determine the total area of a figure.

Counting Whole Squares and Pieces of Squares

To find the area of figures that are not composed solely of whole squares, it is necessary to also count pieces of squares. This technique involves identifying full squares and summing the fractions of squares to obtain the total area.

• Identify whole squares and count them.

• Add the fractions of smaller squares to complete whole units.

• Accuracy in counting the pieces of squares is crucial for obtaining the correct area.

Practical Application of Area Calculation

The calculation of area has numerous practical applications, from construction planning to space organization. Professionals in various fields, such as architecture, engineering, interior design, and landscaping, use this knowledge to plan and execute projects efficiently.

• Architects use area calculations to design building plans.

• Engineers apply these concepts in the construction of infrastructures.

• Interior designers and landscapers use area calculation to organize spaces and decorate environments.

Practical Applications

• Architecture: Planning and designing house and building plans.
• Civil Engineering: Area calculations for infrastructure projects, such as roads and bridges.
• Interior Design: Organizing interior spaces, determining the area available for furniture and decoration.

Key Terms

• Area: Measure of the extent of a flat surface.

• Unit Squares: Standard-sized small squares used to measure area.

• Grid Pattern: A network of lines forming uniform squares, used to draw and measure flat figures.

Questions

• How do you think knowledge of area calculation can be useful in your daily life?

• In what way can you apply the concept of area in practical activities, such as organizing your room or planning a garden?

• Which professions do you believe depend most on the knowledge of area calculation and why?

Conclusion

To Reflect

Throughout this lesson, we explored the concept of area calculation using unit squares. We understood the importance of this skill both in theory and practice, and how it applies in various professions and everyday situations. Knowing how to calculate areas allows us to better plan spaces, whether to build a house, organize a garden, or decorate a room. This understanding not only improves our academic performance, but also prepares us for real-world challenges we will encounter in the future.

Mini Challenge - Drawing and Measuring Your Own Space

In this mini-challenge, you will apply what you learned about area calculation to draw and measure a space of your choice on a piece of grid paper.

• Choose a specific space that you would like to measure, such as your room, a living room, or a garden.
• Draw the outline of that space on a piece of grid paper, ensuring that the scale is correct (for example, each square of the paper can represent 1 square meter).
• Divide the drawn space into simpler flat shapes, such as rectangles and squares.
• Calculate the area of each figure separately by counting the whole small squares and adding the fractions of small squares.
• Add the areas of all the figures to find the total area of the drawn space.
• If possible, compare the total calculated area with the actual area of the space and discuss any possible differences.