Context

Introduction

Mathematics is a universe of concepts, rules, formulas, and numbers that allow us to interpret and solve real-world problems. Within this vast universe, there are mixed numbers, a combination of integers and proper fractions that help us represent quantities that are not whole numbers, such as 1 1/2 (one and a half) or 3 3/4 (three and three quarters).

Mixed numbers are extremely useful in everyday situations. For example, if it is necessary to divide a pizza among three friends, the result of this division would be a mixed number (one whole pizza and one third of another). Similarly, if you want to know how long it takes to travel a distance of 3 1/2 hours, you will also be dealing with a mixed number.

In the field of mixed numbers, basic operations (addition, subtraction, multiplication, and division) have specific rules. When performing these operations, it is important to convert the mixed numbers into improper fractions and only then carry out the operation. Likewise, when finishing the operation, it is necessary to convert the answer back to the mixed number format so that it can be easily understood.

The Importance of Mixed Numbers

Mixed numbers are a tool that allows us to represent and understand in a more intuitive way quantities that are not whole numbers. This is a fundamental principle that applies not only to mathematics but to all physical sciences, such as physics and engineering. In many professions, such as architecture, interior design, gastronomy, sewing, among others, mixed numbers are indispensable.

Furthermore, mixed numbers are frequently used in everyday situations. When we cook and the recipe calls for 1 1/2 cups of sugar, or when we want to measure a distance that is not a whole number of meters or kilometers, we are using mixed numbers.

Practical Activity: 'Operating in Mixed Numbers'

Project Objective

This project aims to strengthen students' understanding of mixed numbers, as well as practice basic mathematical operations (addition, subtraction, multiplication, and division) with these numbers. Additionally, the project also seeks to improve socio-emotional skills, such as teamwork, time management, and problem-solving.

Project Description

Each group of students will be challenged to create an educational board game centered on mixed numbers. The game should be designed to incorporate questions and challenges involving operations with mixed numbers, making learning fun and interactive.

The game can have the theme of your choice (e.g., superheroes, animals, cars, etc.) and must contain rules that encourage the practice of mathematical operations with mixed numbers. The group will be responsible for creating all the questions and challenges to be presented in the game.

The group should also prepare a presentation about the game, where each member must have an active role.

Required Materials

• Cardboard or paper for the board
• Cardstock, colored paper, or other materials for decoration
• Dice
• Game pieces (can be made of clay, paper, pieces from other games, etc.)
• Computer with internet access (for research)
• Mathematics textbooks

Step by Step

1. Group Formation: Divide the class into groups of 3 to 5 students. Each group should appoint a coordinator to manage task allocation.

2. Theme Selection and Rule Development: The group should choose a theme for their game and develop the rules. The rules should be clear and include the use of operations with mixed numbers.

3. Creation of Challenges: Students should create questions and challenges using mixed numbers. These challenges should be incorporated into the game.

4. Board and Pieces Construction: Students should build the board and game pieces. The design of the board and pieces should align with the chosen theme.

5. Game Testing and Adjustments: Students should play the game several times to verify that it is working correctly and, if necessary, make adjustments.

6. Presentation Development: Each group should prepare a presentation to explain the theme, the game rules, the strategies used to create the challenges, and demonstrate a round of the game being played.

7. Project Report Submission: Each group should submit a written report, developed together, containing the main topics: Introduction (the relevance of mixed numbers, the project idea, and the game's objective), Development (with an explanation of the theory of mixed numbers and the applied operations, the game creation process, teamwork, and the results obtained), Conclusions (learnings, benefits of teamwork, improvements that could be implemented in the game), and the Bibliography used.

Project Deliverables

Presentation: Each group will deliver a presentation of the game to the class, explaining the chosen theme, the game rules, the questions and challenges created, and demonstrating a round of the game.

Board Game: The group will deliver the game board along with the pieces.

Written Report: Each group must submit a written report detailing the Introduction (the relevance of mixed numbers, the project idea, and the game's objective), Development (with an explanation of the theory of mixed numbers and the applied operations, the game creation process, teamwork, and the results obtained), Conclusions (learnings, benefits of teamwork, improvements that could be implemented in the game), and the Bibliography used.