Context

Mathematics accompanies us throughout our lives, in our daily tasks and actions. Therefore, the study of 'Ratios and Proportions' becomes extremely relevant, as it is present in various real-life situations. This study allows the understanding of the relationships between quantities, the interpretation and solution of problems involving direct proportions, and the practical application of these concepts in real situations.

A ratio is a concept that refers to the relationship between two quantities. For example, if there is a room with 10 girls and 5 boys, the ratio of girls to boys is 2 to 1, meaning that for every boy there are 2 girls. Proportion, on the other hand, is the equality of two ratios. If we have two rooms and in both, for every 2 girls there is 1 boy, we can say that the ratio of girls to boys is the same in both rooms.

Importance of the Theme

In the real world, we use ratios and proportions to solve problems in different areas. For example, in cooking, recipes are based on proportions to ensure that the final product is perfect. In economics, proportions are used to calculate rates, such as inflation. In everyday life, we can use ratios and proportions to calculate the quantities of materials needed to perform a task, such as painting a wall or planting a garden.

Furthermore, the ability to understand and manipulate ratios and proportions is essential for the comprehension of more advanced mathematical concepts, such as percentage, compound interest, probability, among others.

Practical Activity

Activity Title: Card Games of Ratios and Proportions

Project Objective

In this activity, students will apply the concept of ratios and proportions in a practical and playful activity, creating cards and a game from them. This will help consolidate their understanding in a fun and practical way, as well as stimulate group collaboration, teamwork, and problem-solving skills.

Detailed Project Description

The activity consists of creating a card game, in which each card will have a problem associated with ratios and proportions. The group of students must separate the cards into two piles, one with the questions and the other with the answers. When playing, a student picks a card from the question pile and tries to find the correct solution in the answer pile. If they get it right, they keep the card; if they get it wrong, they return it to the pile and lose their turn. The player with the most cards at the end wins.

Required Materials

1. Cardboard paper for making the cards.
2. Colored pens.
3. Ruler.
4. Scissors.

Detailed Step-by-Step

1. Divide the class into groups of 3 to 5 students.
2. Each group should create at least 10 pairs of cards. Each pair will have a ratio and proportion problem on one card, and its solution on the other.
3. The cards should be colorful and well-drawn to make the game more enjoyable.
4. After creating the cards, the groups should shuffle them and separate them into two piles.
5. The students will take turns, picking a card from the question pile and trying to find the corresponding card in the answer pile.
6. The game ends when all the cards from the question pile have been drawn. The winner is the one with the most cards.

Students should document the game creation process, including the decision on the problems to be placed on the cards, the design of the cards, and the game rules. This documentation will be used to write the final report.

Project Delivery

The group must present the game created to the class and the teacher, explaining the rules and demonstrating how it is played. In addition, students must prepare a report on the project, which should include the following topics:

1. Introduction: Provide context for the project, explaining the importance of the chosen theme and how the game helps to understand the concepts of ratios and proportions.
2. Development: Explain in detail the process of creating the game, including the decision on the problems, the design of the cards, and the game rules. Discuss the game results, how the students managed to solve the problems, and how it helped them better understand the concepts of ratios and proportions.
3. Conclusion: Conclude the work by summarizing its main points, highlighting the learnings obtained and the conclusions drawn from the project.
4. Bibliography: Indicate the sources used to work on the project such as books, websites, videos, etc.

The report must be submitted to the teacher on the specified date and will be evaluated based on the quality of the game produced, the ability to explain and apply the concepts of ratios and proportions, and the quality of the written report.