Contextualization

Theoretical Introduction

The concept of volume is a measure of space brought by three-dimensional geometry. It refers to the capacity that an object has to store something, whether it be a liquid, a gas, or even another object. Volume is commonly measured in cubic units, such as cubic meters, cubic centimeters, liters, among others.

In the context of mathematics, especially in geometry, the volume of a body is the number of unit cubes that can fit inside it. When we talk about volumes of rectangular blocks, we are referring to the capacity of a rectangular prism - a three-dimensional object with rectangular faces. The calculation of the volume of a rectangular block is done by multiplying its three dimensions: length, width, and height.

Understanding volume is essential not only for mathematics but also for various other disciplines and real-world applications, from engineering to biology. Therefore, understanding theoretical concepts is crucial for developing a precise spatial vision and the ability to solve complex problems involving three-dimensionality.

Contextualization of the theme: The importance of Volume

Understanding volume is not only useful for solving mathematical problems. It is a valuable skill in various practical situations in daily life and in various professions. For example, to know the amount of paint needed to paint a wall or to calculate the space required to store a specific amount of material.

In engineering and architecture, this understanding is essential to calculate the amount of material needed in a construction or to determine the available space in a building project. In medicine, volume is important for calculating medication doses. In all these situations, the ability to correctly calculate volume can mean not only resource savings but also ensuring the safety and effectiveness of a project or treatment.

Practical Activity: Building and Calculating Volumes

Project Objective

The objective of this project is for students to apply their knowledge of volume to the construction of building models, considering the specifications of each group. In addition to applying Mathematics, students will also be involved with concepts of Arts and Architecture, seeking to bring harmony and creativity to their buildings.

Detailed project description

Students will be divided into groups of 3 to 5 members. Each group will be assigned to create a model of a building with different specifications: an apartment building, a school, a hospital, among others. Then, students must calculate the volume of each part of their model and the total volume of the building.

Required materials

• Cardboard
• Ruler
• Scissors
• Glue
• Pencil and eraser
• Graph paper
• Calculator

Detailed step-by-step for carrying out the activity

1. Plan and draw the shape of each part of the building on paper.
2. Measure and cut out the parts of the building on cardboard.
3. Glue the parts together to form the building.
4. Measure the dimensions (length, width, and height) of each part of the building.
5. Calculate the volume of each part of the building and the total volume.
6. Record all measurements and calculations.
7. Reflect on the construction and calculation process, identify the challenges faced, and how they were overcome.

Project Deliverables and Connection with Suggested Activities

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

• The model of their building.
• A report with the following elements:
  1. Introduction: Students must introduce the concept of volume and explain its importance in the context of the project. Additionally, they must present their building and explain what they took into consideration to plan it.
  2. Development: Students must describe how they built the building, step by step. It is important that they present the measurements of each part of the building and the calculations made to arrive at the volume of each part and the total volume.
  3. Conclusion: Students must reflect on the construction and calculation process, identifying the challenges faced and how they were overcome. Additionally, they should point out what they learned from the experience and how they can apply this learning in other situations.
  4. Bibliography: Students must list all the research sources used during the project.

The report must be written clearly and organized, with all calculations and measurements duly presented. This writing is a crucial part of the project and will serve as a way for students to review the content and reflect on their learning experiences.