Contextualization

Introduction

Linear functions are one of the fundamental concepts in mathematics, and their applications go far beyond the classroom. They are the first example of functions you learn in mathematics and establish the basis for understanding more complex functions.

In linear functions, the relationship between variables is direct and proportional, meaning an increase or decrease in one variable causes a proportional increase or decrease in the other. The general formula f(x) = mx + b (where m is the coefficient of the independent variable x and b is the linear coefficient) represents this relationship.

Recognizing and dealing with linear functions is essential to advance in the study of mathematics and understand how numbers relate to each other. Therefore, with this project, we hope you can develop a deep understanding of this concept.

Contextualization

Linear functions are present in our daily lives in ways that we often do not realize. They are used to calculate speeds, simple interests, temperature variations, population growth, among others.

For example, if you are saving money to buy a new video game and add a fixed amount of money to your savings every week, the total amount of money you have is a linear function of time. Similarly, if you drive at a constant speed, the distance you travel is a linear function of time.

Mathematics is a powerful tool that helps us understand and interpret the world around us. Understanding linear functions will allow us to solve more complex problems in the future.

Practical Activity

Activity Title: Surviving in the Linear Jungle!

Project Objective

The objective of this activity is to learn to identify, write, and solve problems involving linear functions.

Project Description

Students will be divided into groups of 3 to 5 people. Each group will receive a fictional scenario involving a character who needs to survive in a jungle and achieve a goal (for example, find food, water, shelter, etc.). The jungle will be represented by a game board, and the goal will be achieved by moving through the board in a determined number of turns, representing the passage of time.

Each group will receive a set of cards describing events that occur in the jungle (for example, finding a water source, a predator appearing, etc.). Each event affects the character's movement on the board (increase or decrease), and each event occurs linearly over time.

Students should use linear functions to calculate the best path for the character to reach their goal, taking into account the events that may occur.

Required Materials

• Game board representing the 'Jungle'
• Event cards
• Game pieces to represent the character
• Paper sheets and pens for calculations
• Calculators (optional)

Step by Step

1. Divide students into groups of 3 to 5 people.
2. Explain the story and objective of the game.
3. Distribute the materials to each group.
4. Explain the game rules and scoring.
5. Start the activity.
6. Monitor and assist the groups as needed.
7. At the end of the activity, ask each group to prepare a report with an explanation of the strategy used, the calculations made, the difficulties encountered, and the solutions found for these difficulties.

Project Deliverables

At the end of the project, groups must submit a written report containing:

• Introduction: A description of the project, its relevance, and how linear functions are applied in it.
• Development: A detailed description of the activity. Presentation and explanation of the strategy used by the group, explanations of the calculations made (using linear functions), a list and discussion of the difficulties encountered, and proposed solutions.
• Conclusion: A description of the learnings obtained from the project, including technical skills (related to linear functions) and socio-emotional skills (teamwork, planning, etc.) developed.
• Bibliography: A list of sources consulted by the group during the project.

The report should be collaboratively prepared by the group, and each student should contribute to all sections of the report. This activity not only provides a deep understanding of the concept of linear functions but also promotes collaboration, planning, and problem-solving.