Context

Math is a language that uses symbols and formulas that help us understand and interpret the world around us. In this context, the concept of common denomination in fractions, although seemingly simple, is of great importance and applicability. By understanding this topic, we are able to make comparisons, sums, and subtractions of fractions, becoming an essential skill for solving mathematical problems.

Fractions are ways of expressing a division or proportion between two numbers. The denominator, the number at the bottom of the fraction, indicates how many equal parts the whole is divided into. When you have fractions with different denominators, to perform operations between them, such as addition and subtraction, you need to find a common denominator. That is, a number that is a multiple of the original denominators.

Introduction

In our daily lives, we constantly use fractions, often without realizing it. For example, when we divide a pizza among friends or when we compare the prices of products that have different quantities. For these and other reasons, it is essential to understand how fractions work and, more specifically, how to find and apply common denominators.

The idea of a fraction is directly linked to the idea of division. When we say that something is "half" or "one third" of something, we are, in fact, dividing that something into equal parts and considering only one or some of those parts. And this is exactly where the common denominator comes in. Without it, it would be impossible to add or subtract fractions that have different denominators.

The contents worked on in this project, although within the scope of the Mathematics discipline, have great interdisciplinarity. This is because the ability to work with fractions and find common denominators is vital for disciplines involving calculations and proportions, such as Chemistry and Physics, and even for understanding statistics in Social Sciences.

For a deeper understanding of the topic, you can refer to the book "Mathematics: Single Volume", by Gelson Iezzi, and the website Só Matemática (www.somatematica.com.br), which has several exercises and explanations on the topic. Video lessons from the Matemática Rio channel, available on YouTube, are also a good source of study, as they explain the content in a didactic and fun way.

Practical Activity

Activity Title:

"The Race of the Common Denominators"

Project Objective:

The objective of this project is to deepen students' understanding of the concept of common denominators, encourage teamwork, time management, and creativity. In addition, the activity will promote the connection between mathematics and the students' reality.

Detailed Project Description:

Groups of 3 to 5 students will participate in "The Race of the Common Denominators". In this game, each group member will be responsible for one "stage" of the race. Each stage consists of a mathematical problem involving finding common denominators in a set of fractions.

The project requires students to delve into the concept of common denominators, gather real-life problems (such as comparing prices, dividing tasks, etc.), and apply the solution using the common denominator. In addition, the activity also requires students to draw the "race track", which should show the problems of the stages and the solutions found.

Required materials:

• Pencils and paper for the elaboration of the work.
• Computer with internet access for research.
• Textbooks for consultation.

Detailed Step-by-Step for the Activity:

1. Formation of groups and assignment of stages to each group member.
2. Research and study on common denominators using the suggested sources and others that the group finds necessary.
3. Each group member should look for real problems where the use of common denominators is applicable.
4. Each group member should solve the problem they proposed and explain the solution to the other members.
5. The group should draw the "race track" with the stages (problems) and solutions.
6. Final revision of the work and verification if all requirements have been met.

Project Deliverables:

The groups must deliver the "race track" design, which must contain all the problems and their respective solutions, as well as a brief explanation of the process of finding the common denominators in each case. In addition, the groups must produce a written report following the outline: Introduction, Development, Conclusions, and Bibliography used.

1. Introduction:

• In this part, the group should talk about the topic, contextualize the use of common denominators in daily life, and explain the objective of the work.

2. Development:

• Here, the group should describe in detail each stage of the "race", with the problems encountered and the solutions proposed. It should be explained how the common denominator was found in each case. A brief explanation of the concept of a common denominator should be given, and its importance for solving the problems should be explained.

3. Conclusions:

• In this section, the group should go back to the main points discussed in the development, conclude about the importance of understanding the concept of common denominators in solving problems, and highlight the skills developed during the project.

4. Bibliography used:

• In this part, the group should indicate all the sources they used to develop the project.

Each group member should actively participate in the development of the project, promoting an environment of cooperation and teamwork. The project should be executed in a total of 12 hours per student participant and should be delivered on a pre-arranged date.