Contextualization

Mathematics is a science that permeates our daily lives and, therefore, is considered a universal language. Within this science, the theme of ratios and proportions is one of the most applicable in everyday life. And that is why we are pleased to bring a project that addresses in a playful, didactic, and exciting way the application of these concepts to our students.

In the study of Mathematics, ratios and proportions are fundamental concepts that need to be well understood. A ratio is a comparison between two quantities or measures, while a proportion is an equality relationship between two ratios. These concepts are present in many situations in our daily lives, such as in cooking, economics, architecture, among others.

For example, when following a cake recipe, we need to observe the proportion between the ingredients so that the result is as expected. If we double the amount of one ingredient, we need to double the amount of the others. Or, when buying fruits at the market, we can compare the amount of fruits that can be bought with a certain value, and that is a ratio.

Importance of the Theme

The study of ratios and proportions is vital for the understanding of many mathematical concepts and for solving daily problems. These concepts not only help to better understand Mathematics but also develop reasoning and problemsolving skills that are useful in many other areas of life.

In the real world, ratios and proportions are the basis of many professions and careers, from engineering to economics, through arts and design. For example, an architect needs to understand proportions to design buildings and spaces that are aesthetically pleasing and functional. An economist uses ratios to understand the relationship between different economic variables.

In this sense, learning about ratios and proportions is not just about absorbing school content but about a valuable tool to be used in the real world.

Practical Activity

Activity Title: Mathematics in the Kitchen - Cake of Incredible Proportions!

Project Objective:

The objective of this project is to apply the knowledge of ratio and proportion in practice, through the elaboration of a cake recipe. Students should understand and manipulate the proportions of the ingredients in a recipe, modifying the quantities to obtain a larger or smaller cake. This project aims to combine mathematical concepts with practical and everyday skills, such as cooking, as well as to develop time management, teamwork, planning, and execution skills.

Detailed Project Description:

Divided into groups of up to five people, students will receive a cake recipe that should be doubled, tripled, or halved, according to the class's needs and ingredient availability. Each group will have to calculate the new quantities of ingredients, prepare the recipe, and bake the cake. The activity will be accompanied by a detailed report, which will be elaborated collectively by the group.

Necessary Materials:

• Cake recipe
• Ingredients for the recipe
• Kitchen utensils (bowls, spoons, mixer, oven, etc.)
• Notepad and pens for recipe tracking and notes
• Access to the Internet or books for research on the concepts of ratio and proportion
• Camera to document the project's steps

Detailed Step-by-Step for the Activity:

1. The class will be divided into groups of up to five students.
2. Each group will receive a copy of the cake recipe.
3. The groups must discuss and decide together how much they want to increase or decrease the recipe, and calculate the new quantities of the ingredients based on that decision.
4. Students will gather the necessary ingredients and prepare the cake according to the calculated proportions.
5. During preparation, students must document all steps of the process, either through photos, videos, or notes. These records will be used later in the report.
6. After baking and tasting the cake, students will reflect on the result: was the cake good? Were the calculated proportions correct? What could be done differently to improve the result?
7. Finally, each group must produce a detailed report on the project, including: introduction, development, conclusions, and bibliography used.

Project Deliverables:

The project will consist of two main deliverables: the cake and the report.

The cake will be evaluated on its physical characteristics and taste, and the report will address four main topics.

1. Introduction: The group must introduce the theme (ratio and proportion) and discuss its relevance and application in the real world. They should present the project's objective and the justification for its choice.

2. Development: Students must explain the theory behind the theme and detail all project steps. The methodology and calculations used to recalculate the recipe's proportions must be explained.

• Photos or videos of the project in progress should be included.

3. Conclusions: In this section, students must discuss the results obtained and what they learned from the project. What were the difficulties encountered? What would they do differently next time? How did the concepts of ratio and proportion prove useful in practice?

4. Bibliography: Students must indicate the sources used to theoretically support their work, such as mathematics books and websites, videos on ratio and proportion, among others.

Thus, the project dedicated to the theme 'Ratios and Proportions' will provide stimulating and practical learning, where students can associate the mathematical concepts learned with a daily and tasty activity!