Contextualization

Rational numbers are a fundamental concept in mathematics. They include all numbers that can be expressed as a fraction or a ratio of two integers. Rational numbers include positive and negative integers, as well as fractions and mixed numbers. These numbers can be operated on using addition and subtraction, which is the focus of this project.

Addition and subtraction of rational numbers are not simply arithmetic operations but also a demonstration of real-world concepts. They are used in several areas, including finance, science, and even in our daily activities. For example, when we add or subtract money in a bank account, we are using addition and subtraction of rational numbers. Similarly, in science, these operations are used to calculate temperature changes, distances, and time.

Understanding how to add and subtract rational numbers is vital because it forms the basis for more advanced mathematical concepts, such as algebra and calculus. Without a solid understanding of these operations, it will be difficult to progress in mathematics. Moreover, these operations also develop important skills such as critical thinking, problem-solving, and logical reasoning, which are not only essential for mathematical success but also for success in other areas of life.

To get started, you can refer to the following resources:

1. Adding and Subtracting Rational Numbers - A detailed explanation of the concept with examples from Purplemath, a trusted source for mathematics.
2. Adding and Subtracting Fractions - A video tutorial from Khan Academy, a renowned online learning platform.
3. Adding and Subtracting Integers - An interactive lesson from MathsIsFun, a website known for its friendly and accessible math explanations.
4. National Council of Teachers of Mathematics (NCTM) - A wealth of resources and articles on rational numbers and their operations.

These resources will provide you with a strong foundation in the topic and prepare you for the exciting and challenging project ahead!

Practical Activity

Activity Title: "Rational Number Race"

Objective of the Project:

The primary objective of this project is to develop the students' understanding and skills in adding and subtracting rational numbers. Students will be working in groups to design and create a board game that will allow players to practice these mathematical operations in a fun and engaging way. The game should be challenging, yet intuitive, providing a balance of both learning and enjoyment.

Detailed Description of the Project:

In this project, students will work in groups of 3 to 5 to design and create a board game called "Rational Number Race". The game will involve the addition and subtraction of rational numbers, and players will need to solve these operations correctly to advance in the game. The game will be designed in such a way that it will be educational, engaging, and enjoyable.

Necessary Materials:

1. Large poster board or cardboard for the game board.
2. Markers, colored pencils, and other art supplies for game board design.
3. Index cards or small pieces of paper for question cards.
4. A container to hold the question cards.
5. Game pieces (can be small objects like buttons or coins).
6. A timer (can use a smartphone or an actual timer).

Detailed Step-by-Step for Carrying Out the Activity:

1. Planning Phase (Approximately 1-2 hours): Students will brainstorm ideas for their board game. They need to consider the following: a. The objective of the game (e.g., to reach the finish line first). b. The rules of the game (e.g., how many steps can a player move, what to do if a player lands on a certain space). c. The design and layout of the game board (e.g., how to represent positive and negative numbers, how to show the operations to be solved). d. The type of questions to be used (e.g., addition of fractions, subtraction of integers). e. The difficulty level of the questions (should increase as the game progresses).

2. Building Phase (Approximately 2-3 hours): Once the planning is complete, students will start building their game. They will: a. Draw and design the game board. b. Write down the rules. c. Create the question cards, with each card containing a different addition or subtraction problem involving rational numbers.

3. Testing and Revising Phase (Approximately 1-2 hours): After the game is built, the students will test it with their peers or other groups. They will: a. Play the game, ensuring that the rules are clear and the game is engaging. b. Make any necessary revisions (e.g., changing the difficulty of some questions, adjusting the rules based on feedback).

4. Finalizing Phase (Approximately 1 hour): Once the game is tested, the students will: a. Finalize the game board, rules, and questions. b. Prepare a short presentation about their game, including the objective, rules, and how it helps in understanding and applying the concept of adding and subtracting rational numbers.

5. Report Writing (Approximately 3-4 hours): After the completion of the practical part, students will work on a written report. The report will be structured as follows:

   • Introduction: Contextualize the theme, its relevance, and the objective of the project.
   • Development: Detail the theory behind adding and subtracting rational numbers, explain the game in detail (including its rules, objective, and how it relates to the theory), indicate the methodology used, and finally present and discuss the obtained results.
   • Conclusion: Revisit the main points of the project, explicitly state the learnings obtained, and draw conclusions about the project.
   • Bibliography: Indicate the sources used to work on the project such as books, web pages, videos, etc.

The project will take approximately 10 to 15 hours per student to complete, and the delivery time for the written report is one week after the completion of the practical part.

Project Deliverables:

1. A completed board game called "Rational Number Race".
2. A short presentation about the game.
3. A written report detailing the project's development, including the theory behind adding and subtracting rational numbers, the methodology used, the designed game and its results, and the conclusions drawn about the project.

Through this project, students will not only gain a deeper understanding of adding and subtracting rational numbers but will also develop important skills like teamwork, problem-solving, and time management.