Contextualization

Studying mathematics can be much more fascinating when we can see its practical applications and its daily presence. The theme "Floor Plan and Aerial Views" is a perfect example of this, as it is directly linked to architecture and space planning, a valuable skill for life.

Introduction

The floor plan is a graphic representation that uses a scale to illustrate the organization of a location seen from above, as if we had made a horizontal cut about 1.5m from the ground - about half the average height of an adult. With this view, we can see walls, windows, doors, furniture, among other items, all at the same time. The floor plan is an indispensable tool for architects, engineers, decorators, and anyone who needs to visualize the layout of elements in a space.

We can understand floor plans as maps of indoor environments, and like any map, scale is a fundamental concept. The scale is the relationship between the measurements of the drawing and the actual measurements of the space represented. For example, on a 1:100 scale, 1cm on paper represents 100cm (or 1m) in reality.

Aerial views, on the other hand, are images captured from an elevated point of view, as if we were looking from top to bottom, providing a broad view of the location. They can be obtained through photographs taken by drones, helicopters, airplanes, or even satellites.

Relevance

The ability to interpret and create floor plans and aerial views is extremely useful in everyday life. They allow us to visualize a space even before it is built, facilitating planning and decision-making. They are essential in construction, interior decoration, urban planning, among other fields of work. In addition, this skill aids in understanding maps and spatial orientation.

Resources that can be used to deepen knowledge on the subject include:

• Practical Study: Understanding the Floor Plan
• Mathematics and Architecture: The Scale in the Floor Plan
• Aerial View and its importance

Practical Activity

Activity Title: "Designating Spaces: Building and Interpreting Floor Plans and Aerial Views"

Project Objective:

This project aims at the application and understanding of the concept of floor plan and aerial view, as well as the importance of scales in map interpretation. Students will create their own floor plans and aerial views of a space chosen by them, and furthermore, they will calculate the area of this space from the floor plan.

Detailed Project Description:

The activity will be carried out in groups of 3 to 5 students. Each group will choose a room in the school or their homes and will first draw a floor plan of the chosen space, respecting the proper proportions and representing the furniture and items in the space. After drawing the floor plan, they should calculate the area of the represented space. Next, they will create an aerial view representation of the same space. The activities should be carried out outside of school hours, with an estimated time of two to four hours per student for execution and the final submission to be made by the end of the following week.

Required Materials:

1. White A4 or graph paper
2. Ruler
3. Pencils and erasers
4. Colored pens
5. Tape measure

Methodology and Step by Step:

1. The students, in their groups, should choose a space of their choice. It can be a room in the school or their homes.
2. Using the tape measure, students should measure all dimensions of the chosen space: width, length, and the position of each object/furniture within the space.
3. After the measurements, students should draw the floor plan of the space on paper, using the ruler to maintain precision. Choose an appropriate scale to represent the real measurements on paper.
4. In the floor plan, in addition to the walls and doors, students should also represent the furniture and objects present in the space, all according to the collected measurements.
5. Students should then calculate the total area represented in their floor plan using the defined scale.
6. Next, the group should create an aerial view representation of the same space, also respecting the defined scale.
7. After completing the drawings and calculations, each student should produce an individual report containing: introduction (contextualization of the theme, relevance, real-world application, project objective), development (explanation of concepts, activity details, methodology used, and results obtained), and conclusion (summarizing the main points, learnings, and conclusions about the project). Finally, each student should include the bibliography used.

Deliverables:

At the end of the project, the following deliverables are expected:

1. Hand-drawn Floor Plans and Aerial Views with their respective measurements and scale.
2. Calculation of the total area represented in the floor plan.
3. Individual written report on the activity, containing all the mentioned topics.

By creating and interpreting floor plans and aerial views, students will gain important technical skills. Working in groups to execute the project will help develop socio-emotional skills such as time management, communication, problem-solving, and creative thinking.