Context

When we study Mathematics, many concepts may seem disconnected from our reality. However, as we will learn in this project, mathematics is much closer to our daily lives than we imagine. One very interesting and applicable concept is the LCM (Least Common Multiple). The LCM is the smallest positive integer, different from zero, that is a multiple of two or more numbers at the same time.

In our project, we will delve into the concept of LCM and understand how it manifests in our daily lives, even without us realizing it. We will explore its applications and relate it to other areas of study, such as Physics, in questions of periodicity and movement of celestial bodies, and Chemistry, in stoichiometric calculations, which involve proportions between the quantities of reactants and products in a chemical reaction.

Now, you must be wondering: why do we need to learn about LCM? The answer is simple: this concept is a powerful tool that helps us solve numerous mathematical problems, especially those involving ratios, proportions, and even fractions. Furthermore, it is a magnificent example of how mathematics connects and interacts with other disciplines, showing that knowledge is a great interdisciplinary puzzle.

I will recommend some reliable sources for you to start your studies on LCM and its application in everyday life. The first one is the book "Elementary Mathematics - Volume 1: Sets, Functions, and Numbers", by professors Osvaldo Doce and Luiz Márcio Pereira (Scipione Publisher, 2019). In this book, you will find an excellent introduction to the concept of LCM and its applications. Another suggestion is the website "Just Mathematics" (https://www.somatematica.com.br/fundam/mmc.php), where you can find detailed explanations and several exercises to practice the concept of LCM and its applications.

This project will be challenging, but I am sure you will have fun and learn a lot. So, let's get started!

Practical Activity: "Discovering the Secrets of LCM - An Interdisciplinary Journey"

Project Objective

This project aims to deepen students' knowledge of LCM (Least Common Multiple) in solving mathematical problems, as well as to highlight the importance of this concept in interdisciplinarity, through the application and integration between Mathematics, Physics, and Chemistry.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. The project will consist of a series of interrelated mathematical tasks and challenges, involving the calculation of LCM, the use of this concept to solve problems involving fractions, and the exploration of its applications in other areas of knowledge, such as Physics and Chemistry.

The estimated duration is 12 hours of work per student, which should be divided over a week, allowing collaboration and exchange of ideas among group members.

Required Materials

• Notebook or sheets of paper for notes and problem resolutions
• Materials for making the poster (cardboard paper, colored pens, glue, scissors, magazines for cutouts, etc.)
• Computer or smartphone with internet access
• Textbooks of Mathematics, Physics, and Chemistry for the 1st year of High School

Detailed Step-by-Step

1. Research and Study of LCM and its Applications: Initially, each group should conduct in-depth research on the concept of LCM, study its applications in daily life, in Mathematics, as well as in other disciplines (Physics and Chemistry).

2. Solving Mathematical Problems: After the study, the groups will receive a list of mathematical problems involving LCM to solve, including fraction problems.

3. Interdisciplinary Applications: Each group should apply the concept of LCM in solving Physics problems (involving periodicity and movement of celestial bodies) and Chemistry problems (related to stoichiometric calculations).

4. Creation of a Poster: Next, each group should create a creative and informative poster illustrating the concept of LCM and its applications in daily life and in the studied disciplines.

5. Writing a Report: Finally, students should write a report containing: Introduction (contextualizing the concept of LCM and its application), Development (detailing the theory, the execution of activities, and the results obtained), Conclusion, and Bibliography.

Project Deliverables

The deliverables of this project are:

1. Illustrative Poster: Each group must present their poster to the class, explaining how they used the concept of LCM and its applications.

2. Solved Exercise List: The solved exercise list should be submitted along with the poster.

3. Final Report: The written document should follow the structure of a scientific report and complement the practical activities carried out. It should contextualize the concept of LCM, present the theory, detail the execution of activities, discuss the results obtained, and list the bibliography used.

I remind you that, in addition to the final result, teamwork, effort, creativity, and organization of each group during the project execution will be evaluated.