Contextualization

Hello, young mathematicians! Let's embark on an adventure in a fascinating world full of ratios and proportions, which are powerful tools we use every day without even realizing it. Have you ever wondered how mathematics is present in such common things, like a cake recipe, a map, or even in our allowance? That's what we are going to discover together!

Ratios and proportions are ways of comparing quantities and magnitudes. When we compare two quantities, the ratio is the way to express the relationship between them. For example, if you have 3 apples and your friend has 2, the ratio between the number of apples you have is 3:2. Proportion, on the other hand, is an equality between two ratios, like 3:2 = 6:4.

Introduction

Now, let's talk about how we use ratios and proportions in our daily lives. Imagine you are making a cake recipe, but you need to make half the amount. How would you do that? You can use a proportion! Dividing all the ingredients by 2 maintains the same relationship between them, and you will have a delicious half of a cake.

And what about a map? When we look at a map, distances are usually reduced. If the actual distance between two cities is 100 km, but on the map it looks like 10 cm, we can say that the ratio between the distance on the map and the actual distance is 10:100, or 1:10. Proportions are used to create these representations.

Our allowance can also be an example of a ratio. If you receive R$ 10 and your friend receives R$ 5, the ratio between your money and theirs is 10:5, or 2:1. This means you receive twice as much as your friend.

Now that you understand the importance of ratios and proportions, imagine how they can be useful in many different situations. In this project, we will further explore this concept and apply it to real challenges. Ready? Let's go!

Practical Activity: "The Mathematics of Everyday Life"

Project Objective

The objective of the project is to explore the concepts of ratios and proportions in a practical and fun way, creating everyday situations where these concepts apply. Students will be tasked with creating scenarios, problems, and solutions, and presenting them creatively to the class.

Project Description

Students, divided into groups of 3 to 5, will be responsible for creating a series of everyday situations where ratios and proportions are present. They will develop a story, a recipe, a map, and an allowance scenario, all based on ratios and proportions. The final result will be a presentation in the form of an exhibition, where groups will share their creations and explain how ratios and proportions apply in each context.

Necessary Materials

• Paper, pencil, and eraser for planning
• Materials for creating models (optional)
• Ruler, crayons, and cardboard paper to create the map (optional)
• Ingredients and kitchen utensils for the recipe (with parents' permission)

Step by Step

1. Group Formation: Students will be divided into groups of 3 to 5 members. Each group will receive a detailed copy of this project.

2. Planning: Groups will discuss and plan the four situations they will create: a story, a recipe, a map, and an allowance scenario. They should think of situations from their daily lives where ratios and proportions are applicable, and how they will represent these situations.

3. Creating the Situations: Each group will develop the planned situations, creating a story about ratios and proportions, a recipe that uses ratios and proportions, a map with reduced proportions, and an allowance scenario with ratios and proportions.

4. Presentation: After completing the creations, groups will prepare a presentation for the class. They should explain how ratios and proportions apply in each situation. The presentation can be done creatively, such as a theatrical play, a cooking show, a travel guide, etc.

5. Exhibition: Groups will present their creations to the class, sharing their learnings about ratios and proportions. Everyone will have the opportunity to see how these concepts are present in our daily lives and learn from their classmates' work.

Delivery Format

The project will be delivered in the form of an exhibition, where each group will present their creations and explain the ratios and proportions involved in each situation. Additionally, students must also deliver a written description of each situation, describing how ratios and proportions were used. This description can be done on a piece of paper and must be well-organized and legible. Remember, the most important thing is to learn and have fun!