Contextualization

Theoretical Background

To understand the world around us, it is essential that we learn the principles of mathematics, and among them, the concepts of multiples and divisors are basic and important. A multiple is the result of one number multiplied by another. If we have the number 5 and multiply it by 3, we get 15, which is a multiple of 5. The same concept applies to any number: the multiples are the results of their multiplications.

The divisor, on the other hand, is the number by which we divide another. If we have the number 15 and divide it by 5, the result will be 3. Therefore, we can say that 5 is a divisor of 15. Again, this is applicable to all numbers: the divisors are the numbers by which we can divide a number without leaving a remainder.

There are rules and tricks to identify multiples and divisors, and learning this can help us greatly simplify mathematical operations. For example, if a number ends in 0, 2, 4, 6, or 8, it is a multiple of 2. If a number ends in 0 or 5, it is a multiple of 5. These are just a few examples of the many rules that exist to identify multiples and divisors.

The Importance of Multiples and Divisors in the Real World

Multiples and divisors are more than just abstract concepts; they have practical applications in the real world. For example, if you are planning a party and want to make sure there is enough food for everyone, you need to calculate how many sandwiches, slices of pizza, or pieces of cake each person can eat. In this case, you are using multiples. Similarly, if you want to divide something equally among a group of people, you are using divisors.

In addition, multiples and divisors are used in music to create different tones and rhythms, in engineering to calculate the strength of materials, and even in our time system, with 60 seconds in a minute, 60 minutes in an hour, and so on.

Practical Activity

Title of Activity: The Number Race

Project Objective:

The main objective of this project is to reinforce the understanding of the concepts of multiples and divisors and relate them to everyday situations. Through the creation of a game based on these concepts, we will seek to develop mathematical skills, while also improving socio-emotional skills such as teamwork, problem solving, creative thinking, and time management.

Detailed Project Description

In this activity, students will have to create a race based on multiples and divisors. The racetrack will be a sequence of numbers, and the players advance based on the challenges related to multiples and divisors presented on cards that they draw from a pile. The first player to reach or pass the final number is the winner. Students must design the game board, the rules, and the challenges present on the game cards.

Materials Needed

• Cardstock or cardboard to create the game board.
• Paper and colored pens to create the game cards.
• Game pieces that can be obtained from existing games or created from materials such as clay, paper, etc.
• Ruler and markers for the board design.

Step by Step

1. The group should start by discussing and planning the design of their game. They should decide how many numbers will be on their track and what types of challenges, based on multiples and divisors, will be on the game cards.

2. Once the plan is ready, students can start building the game, starting with the game board. The numbers should be clearly visible and evenly spaced.

3. Next, they should create the game cards. Each card should contain a challenge or a question about multiples and divisors. For example, a card could say "Advance to the next multiple of 5." or "Move back to the last divisor of 24."

4. Once the game is ready, the group should write the rules. They should make sure that the rules are clear and easy to understand.

5. Finally, they should play the game several times to check if everything works as expected. They should make any necessary adjustments to the rules or the game design.

6. Throughout the project, students should document the development of their activities, the decisions made, the challenges faced, and how they were overcome.

Project Deliverables

The groups will have to deliver the game created, along with a detailed written report on the project.

The report should contain:

1. Introduction: A brief contextualization of the concepts of multiples and divisors, their relevance and application in the real world, as well as the objective of this project.

2. Development: Explanation of the theory behind the central themes of the project, detailed explanation of the activity in detail, methodology used, and representation of the results obtained. Here, students should describe how they developed the game, explaining the step-by-step process, the rules of the game, and the challenges present on the cards.

3. Conclusion: A conclusion of the work restating its main points, explaining the lessons learned, and the conclusions drawn about the project. They should discuss the impact of this project on their understanding of multiples and divisors.

4. Bibliography: Students should indicate the sources on which they based their work on the project, such as course books, web pages, videos, etc.