Contextualization

Theoretical Introduction

Ratio is a mathematical relationship that compares two quantities. It is expressed as a division or relationship between two magnitudes, where the magnitude of the numerator is compared to the magnitude of the denominator. In other words, the ratio expresses how many times one quantity is greater or smaller than the other.

Ratio is explicitly applied in various everyday situations, and its understanding and correct practice are fundamental for the development of logical thinking and problem-solving skills.

Multiplication and division are basic operations in mathematics. Multiplication is repeated addition, while division is repeated subtraction. The relationship between multiplication and division is that they are inverse operations. This means that if you multiply something and then divide the result by the same number, you will get the original number.

Contextualization

Ratios are found in many places in the real world. For example, on a map, the ratio (or scale) indicates the relationship between a certain distance on the map and the actual distance on the ground. This is fundamental knowledge for engineers, architects, geographers, and many other professionals.

And the relationship between multiplication and division is essential to understand many mathematical and scientific concepts, from solving simple everyday problems to understanding more complex concepts, such as exponential and logarithmic growth rates.

Therefore, with these concepts, you will be able to better understand the mathematical relationships present in many aspects of your daily life.

Practical Activity

Activity Title: "Cookie Engineering"

Project Objective

Apply the concepts of ratios and the relationships between multiplication and division in the preparation of a cookie recipe. In addition to promoting mathematical practice, this project also aims to foster teamwork, problem-solving, and time management.

Detailed Project Description

Students will be divided into groups of 3 to 5 students. Each group will receive a cookie recipe that serves 4 people and will be challenged to adapt this recipe to serve a different number of people (which will be drawn by the teacher).

The group must use the concept of ratios to calculate the quantities of the necessary ingredients for the new recipe. In addition, they must use multiplication and division to calculate the baking and cooling time of the cookies, considering that the available oven can only accommodate a certain amount of cookies at a time.

The final result of the project will be a written report where the students explain how they arrived at the new quantities of ingredients and baking and cooling times, along with the new recipe and photos of the produced cookies.

Required Materials

1. Cookie recipe for 4 people.
2. Numbers to draw the quantity of people to be served by the new recipe.
3. Ingredients for making the cookies.
4. Access to an oven for baking the cookies.
5. Camera to take photos of the cookies.

Detailed Step-by-Step for Carrying Out the Activity

1. Divide the class into groups of 3 to 5 students.
2. Each group draws a number that will be the quantity of people the new recipe should serve.
3. With the original recipe in hand, students must use the concept of ratios to calculate the required quantity of each ingredient for the new recipe.
4. Next, students need to calculate how many batches of cookies will be needed to reach the desired quantity, using the capacity of the available oven. With this number, they should calculate the total baking and cooling time using multiplication and division.
5. After all calculations are ready, the group must bake the cookies following the new recipe. During baking, students should take photos of the process.
6. Finally, each group must write a report detailing the entire process, explaining how they used the ratio, multiplication, and division to adapt the recipe and calculate the baking and cooling times. The report should also include the new recipe and photos of the cookies.

Project Deliverables

Students must submit a final report that includes:

• Introduction: Where the theme is contextualized, its relevance and application in the real world. Students must explain the importance of using ratios and the relationship between multiplication and division.
• Development: In this section, students must explain the theory behind the concepts of ratio and the relationship between multiplication and division. It should explain how these concepts were applied to adapt the recipe and calculate the baking and cooling times.
• Conclusion: Students must summarize the main points discussed during the development, explain the learnings obtained, and draw conclusions about the project.
• Bibliography: In the bibliography, students must cite all sources used to support the work. In addition to the school's educational material, students can cite books, articles, websites, and videos that helped understand the concepts.