Context

The Least Common Multiple (LCM) is an important topic in the study of mathematics, especially in arithmetic. It is used to identify the smallest number, excluding zero, that is a multiple of two or more numbers. The ability to calculate the LCM is fundamental for solving various mathematical problems, especially those involving fractions.

The LCM is a concept that we encounter in various situations in our daily lives. From determining the number of installments in a loan or financing, organizing events on non-conflicting dates, to calculating how many packages of ingredients we need to buy to make a recipe that serves exactly a specific number of people. Understanding the LCM and knowing how to calculate it is undoubtedly a valuable skill for our daily lives.

The study of LCM also paves the way for understanding other mathematical concepts. It is linked to the study of prime numbers, factorization, and the study of other multiples and divisors. Therefore, mastering the LCM means taking a big step in mathematical knowledge.

For this project, the resources we recommend for reading are:

1. Your Research - LCM: Explanatory article about LCM, with practical examples.
2. Brazil School - LCM: Explanation of the LCM concept and its formula.
3. Khan Academy - GCD and LCM: Detailed explanatory video about GCD and LCM.

Please note that these are just some initially recommended resources; feel free to search for other materials that help in understanding the topic.

Practical Activity

Activity Title: "The Magic of Common Multiples: LCM in Action"

Project Objective

The project aims to lead students to deeply and practically understand the concept of LCM by developing an activity involving probability, planning, and collaboration.

Detailed Project Description

In this practical activity, students will be divided into groups of 3 to 5 members. Each group will be tasked with creating a "Multiples Game" based on the calculation of LCM. In the game, players must advance on a board as they solve LCM problems.

Each group will have to plan the game, create the rules, develop the mathematical challenges, and define the strategy for progressing on the board. In addition, the groups must present the solution to each challenge proposed in the game, proving the accuracy of the answers.

Required Materials

1. Cardboard for creating the game board.
2. Colored pens, colored pencils, or other materials for decorating the board.
3. Paper blocks for creating challenge cards.
4. A die to determine the moves.
5. Pieces or markers to represent each player.

Detailed Step-by-Step

1. After forming the groups, students should start planning the game. It should have a board where players advance as they solve problems involving the calculation of LCM.

2. The group defines the game rules, including how a player advances on the board, what happens when a player answers a challenge incorrectly, and how the winner of the game is determined.

3. Students will create challenge cards, which will be randomly selected by players during the game. Each card should present a problem involving the calculation of LCM.

4. The group must prepare an answer sheet containing the solutions to each challenge in the game. This sheet will be used by the teacher to verify the accuracy of the answers in each match.

5. The game is tested and adjusted as needed by the group before the final presentation.

6. All groups will present their games and play another group's game, providing feedback.

Project Deliverables

At the end of the project, in addition to the created game, each group must prepare a report on the work done. The report should contain the following topics:

1. Introduction: Presentation of the LCM theme, its relevance, and real-world application. The group must explain their understanding of LCM and how it applies to the game they created.

2. Development: Detailed description of the game rules, the challenges developed, and the creation process. The group must explain how the LCM concept was incorporated into the game. The group must also present the answers to the challenges proposed in the game and explain how they arrived at those answers.

3. Conclusions: Reflection on the experience of creating the game and what the students learned from it. The group should make observations about the usefulness and application of LCM based on their experience.

4. Bibliography: References to the materials consulted during the project preparation.

The evaluation will be based on the originality and applicability of the game, the quality and accuracy of the challenge answers, the organization and clarity of the report, and the ability to work in a team.