Contextualization

Introduction

Mathematics is present in many moments of our lives, even if we don't always realize it. One of the most important areas of mathematics is the study of 'Ratios and Proportions'. Have you ever stopped to think that a large part of our actions involves making choices? And that many of these choices are made after considering the advantages and disadvantages of each option?

Ratios and proportions help us make these choices. They are mathematical tools that allow us to compare quantities and decide which is the best option. For example, if you are in the school cafeteria and want to buy a juice, you can use ratios and proportions to decide which is the best option: a 200ml juice for R$2.00 or a 300ml juice for R$3.00.

Real-World Applications

Ratios and proportions are not only useful in the school cafeteria. They are present in many situations in our daily lives. For example, if you are planning a car trip, you need to think about the distance you will travel and the amount of fuel you will need. Ratios and proportions can help you make these calculations.

Another example is when you go to the supermarket and need to choose between two products, one weighing 500g and the other 1kg. How can you decide which is the best option in terms of price? By using ratios and proportions, you can make this comparison quickly and easily.

Practical Activity

Activity Title: 'Deciding the Best Option'

Project Objective:

The objective of this project is to apply the concept of ratios and proportions in real-life situations, developing problem-solving skills, teamwork, communication, and critical thinking.

Detailed Project Description:

Students, in groups of 3 to 5, will be challenged to create a choice situation involving two different options and use ratios and proportions to decide which is the best choice. They must then present their decisions and the process they used to reach them.

Required Materials:

• Paper and pen for notes and calculations
• Materials for creating the choice situation (for example, food figures to represent two snack options, or photos of travel destinations to represent two tour options)

Step-by-Step for Activity Execution:

1. Group Formation: Students will be divided into groups of 3 to 5 people.

2. Choice of Situation: Each group must choose a choice situation involving two different options. For example, they can choose between two snacks, two toys, two travel destinations, etc.

3. Creation of the Situation: Using the provided materials, students must create the choice situation. They can draw, cut out from magazines, use photos, etc.

4. Analysis of Options: Students must analyze the two options and come up with some characteristics that can be compared. For example, in the case of snacks, they can think about the size, price, taste, etc.

5. Calculation of Ratios and Proportions: With the characteristics of the two options in hand, students must calculate the ratios and proportions for each of them. They should discuss as a group the best way to make these calculations.

6. Final Decision: Based on the ratios and proportions they calculated, students must make a decision on which is the best option.

7. Presentation of Work: Each group must present the result of their work to the class. They should explain the choice situation they created, the characteristics they analyzed, the ratios and proportions they calculated, and the final decision they made.

8. Class Discussion: After all presentations, the class should discuss the different choice situations, the ratios and proportions that were calculated, and the final decisions that were made. The teacher should guide the discussion, highlighting the main points of the concept of ratios and proportions.

By the end of the project, students will have learned in a practical and fun way how to use ratios and proportions to make decisions in everyday situations. Additionally, they will have developed important skills such as problem-solving, teamwork, communication, and critical thinking.