Contextualization

Mathematics, especially geometry, is an essential tool in everyday life and technology. Through its concepts, we can make precise measurements and solve complex problems. Within geometry, the topic of volume has intrinsic importance, being applied in various everyday situations, such as calculating the amount of water in a pool, the amount of concrete needed for a construction, among others.

A fundamental understanding for the study of volumes is that of fractions. Fractions are numbers that represent one or more parts of a whole. When we talk about volume, we often deal with cubes and prisms that have at least one of their sides represented by a fraction of another side. This relationship may seem complex, but with practice and application, it becomes simpler.

Theoretical Introduction

Volume is a measure that determines the space occupied by a three-dimensional body, that is, it has three dimensions: length, width, and height. In the case of simple geometric figures such as cubes and prisms, calculating the volume is relatively easy, being the product of these three dimensions.

When dealing with cubes, the situation is even simpler, as all faces are squares and equal, that is, the volume is the edge (side of the cube) raised to the power of three. In the case of prisms, we have a base that can have any shape and the height. The volume will be the area of this base multiplied by the height.

Learning to deal with fractions in this context is important because measurements are often not whole numbers. Fractions are also important for showing relationships between different dimensions and can be used to solve more complex problems.

Practical Activity

Activity Title: "Exploring Volume with Fractions: A Practical Approach"

Objective:

1. Understand and apply practically the concept of volume of prisms and cubes with at least one dimension given as a fraction.
2. Work in a team, exercising time management, communication, creativity, and problem-solving skills.

Project Description:

Students, divided into groups of 3 to 5, should build 3D models of cubes and prisms using easily accessible materials, with at least one of the dimensions represented by a fraction. They will then determine the volumes of these figures using fractions, demonstrating understanding of the theoretical concepts learned. This project will integrate mathematical concepts with artistic and manual skills, making learning more interactive and applicable.

This project should be carried out over a period of three weeks, with an estimated average dedication time of 12 hours per student.

Required Materials:

1. Cardboard for building the models
2. Ruler and compass
3. Colored pens for decoration
4. Calculator
5. Scissors and glue

Step by Step:

1. Students should conduct theoretical research on the concept of volume, focusing on prisms and cubes and how to work with volumes whose dimensions are given in fractions.

2. Next, they will decide which models of cubes and prisms they will build. At least one dimension of each figure should be a fraction of another. For example, a cube where the height is 1/2 of the length, or a prism whose height is 3/2 of the base width.

3. Students will then build their models using cardboard, ruler, compass, and scissors. They can use colored pens to decorate the models.

4. After building the models, students should calculate the volume of each one, proving in practice the theory studied.

5. Finally, each group should present their models and calculations to the class, as if they were teachers, teaching their peers about what they have learned.

Deliverables:

1. 3D models of cubes and prisms

2. Volume calculations, with detailed steps

3. Presentation to the class

4. Written report, containing:

   a. Introduction: Remember to contextualize the theme, explain its relevance, and the objective of this project.

   b. Development: Here, detail the theory studied, the choices of models built, the methodology used, and the results obtained.

   c. Conclusions: Summarize the main points, the learnings acquired, and the conclusions drawn from the project.

   d. Bibliography: Indicate all sources used for research and project development. You can use books, websites, videos, etc.

Students should strive to make the report as didactic as possible, as it will serve as a means to share their learnings with the rest of the class.