Contextualization

Mathematics is a universal language, capable of describing patterns, proposing solutions, and helping us better understand the world around us. Within this vast science, we have numbers, fundamental entities that support many calculations and operations. An interesting aspect of numbers is the existence of the Least Common Multiple (LCM), a useful tool for many calculations and everyday problems. It is this concept that our project will focus on, exploring its applications, implications, and methods of obtaining it.

The LCM is, in simple terms, the smallest number that can be evenly divided by two or more other numbers. This may seem a bit abstract at first, but it is a concept widely used in various practical situations. For example, suppose you have two packages of different sizes of the same product and want to know after how many units the total quantity will be the same. The answer to this question is the LCM of the sizes of the packages!

The world is full of daily situations where the LCM is applied, often without us realizing it. Whether dividing a pizza among friends, organizing schedules, or even in more complex situations like calculating fractions. And that's the challenge: to understand the LCM, know how to calculate it, and apply it in real situations, demonstrating the relevance and applicability of Mathematics in our daily lives.

In this project, you will work in teams, both to understand the concept and to propose and develop fun activities that illustrate the application of the LCM. The work will be divided into two phases: the first will be for study and the second for the elaboration and execution of the activities.

To delve deeper into the topic, we suggest the following sources:

• The video from the channel 'Matemática Rio with Prof. Rafael Procopio' on YouTube, which explains in a fun and simple way what the LCM is and how to calculate it (link).
• The InfoEscola page, which brings the concept of LCM and examples of how to calculate it (link).

Enjoy the journey and remember: the focus is on learning collaboratively and having fun!

Practical Activity

Activity Title: 'Building the World of LCM'

Project Objective

The objective of this project is, based on the theoretical understanding of the LCM concept, to create an educational board game that involves calculation, strategy, and cooperation, to demonstrate the use of LCM in practical situations and stimulate collaboration among students.

Detailed Project Description

Groups must develop a board game that explores everyday situations where the LCM is applied. In addition, the game must include elements of strategy and luck to provide a complete and engaging experience. The game development should be carried out in a series of face-to-face or virtual meetings, totaling at least 12 hours of work.

Required Materials

• Cardboard or other material for building the board.
• Chips, pieces, or tokens to represent the players.
• Challenge cards (can be made of paper).
• Dice or numerical cards to determine player movement.
• Drawing and writing materials: pencils, colored pens, ruler, etc.

Detailed Step-by-Step

Part 1: Definition of the Concept and Game Rules

The first task for the groups is to understand the LCM concept well and define how it will be applied in the game. In this part, the group must:

1.1. Study the LCM concept and discuss in the group how it can be applied in practical situations.

1.2. Define the basic rules of the game, such as the objective, the game dynamics, and the challenges that players will face involving the LCM.

Part 2: Game Construction

In the second part, the groups must put into practice what they discussed in the first stage and create the game. For this, they must:

2.1. Draw the game board on cardboard, considering the defined game dynamics.

2.2. Create the pieces that will be used by the players.

2.3. Design challenge cards that will incorporate LCM problems.

2.4. Finalize the game by adding any other materials or resources they deem necessary.

Part 3: Game Testing and Presentation

Groups must test the game to ensure it functions as expected. Subsequently, they must present it to the rest of the class. For this part, they must:

3.1. Play a few rounds of the game to ensure it is balanced and interesting.

3.2. Make adjustments to the game based on feedback from test rounds.

3.3. Prepare a presentation explaining the game rules, how the LCM is applied, and what they learned during the process.

Project Deliverables

The final delivery of this project will consist of two main parts: the board game and a written report.

The board game must be presented physically or in digital format (if the group chooses to do it in a virtual environment) and must be playable according to the rules defined by the group.

The written report should contain the following sections:

Introduction

In this section, the group must explain the LCM concept and its applicability in everyday life. Additionally, the project's objective and the relevance of teamwork for its development should also be presented.

Development

Here, the group must explain in detail how the game was developed, indicating the methodology used, the decision-making process, and the challenges encountered. An explanation of how the LCM concept was integrated into the game and how it contributed to its overall dynamics should be included.

Conclusions

The group must summarize the main points of the project, state the learnings obtained, and draw conclusions about the project. Here, the group should also reflect on teamwork and the socio-emotional skills developed during the project execution.

Bibliography

The group must indicate all sources of information used for the project development, including books, web pages, and videos.