Context

Mathematics is a central subject in our basic education, and one of its most important topics is functions and their graphs. In general, a mathematical function describes the relationship between two or more variables. Its graph is a visual representation of this relationship, which facilitates understanding and interpretation.

Function graphs are a powerful tool in analyzing a multitude of real-world phenomena. They allow us to visualize the change of one quantity in relation to another, which is extremely useful in many areas such as physics, economics, biology, engineering, among others. An example of this is the graph of a function that shows the evolution of the growth rate of a population of organisms over time.

For this reason, the ability to understand and construct function graphs is a vital skill for all of us. Besides being fundamental knowledge for those intending to pursue a career in exact sciences or engineering, it is also extremely useful in many other fields, as functional reasoning and graph interpretation are increasingly demanded skills in the current job market.

Introduction

In this project, we will explore the theme of function graphs in a practical and playful way. We will start with a theoretical review of functions and their graphs, using online educational resources such as videos, games, and interactive exercises. Then, we will propose a practical challenge that will require students to apply the acquired knowledge and work as a team to solve a problem.

The challenge will be to create a game that involves the construction of function graphs. For this, students will be introduced to a simple and intuitive programming language that they can use to implement their ideas. They will need to understand the properties of function graphs well to create an interesting and challenging game that can be played by their peers.

By the end of the project, we hope that students will have acquired a solid knowledge of function graphs, that they will know how to interpret and construct basic function graphs, that they will have developed teamwork and problemsolving skills, and that they will have had fun in the process!

The main resources we recommend for theoretical preparation are:

1. Matemática Rio with Prof. Rafael Procopio - YouTube channel with several educational videos about functions and function graphs.
2. Geogebra - free mathematics software that allows dynamic and interactive exploration of the behavior of functions and their graphs.
3. Descomplica - online education website that offers various classes and exercises on functions and function graphs.

Practical Activity

Activity Title: Function Game: The Graphical Challenge

Project Objective

In this project, the objective is to develop a simple computer game whose gameplay is based on the understanding and manipulation of functions and their graphs. Working in groups of 3 to 5 students, you will apply mathematical skills in understanding and constructing function graphs and their properties. At the same time, you will learn basic programming and game development concepts, and enhance teamwork and problemsolving skills.

Detailed Project Description

Each group will be responsible for creating a simple game based on mathematical functions. The game should involve the construction and/or interpretation of function graphs, challenging players to use their mathematical knowledge to progress or win in the game.

The game can take any format the group desires, from puzzles that require the correct placement of points on a graph, to platform games whose obstacles and rewards are determined by functions. Be creative!

Required Materials

1. A computer with internet access for each group of students
2. Free account on the Scratch website, a visual online programming platform that is easy to learn and allows the creation of interactive games.

Step-by-Step Guide for Activity Execution

1. After forming the groups, each group should spend some time brainstorming about the type of game they would like to create. It is important that all group members are on board with the idea.

2. Once the game idea has been established, the group should outline a plan of how the game will work, what type of functions will be involved, and how the understanding of these functions will be necessary for success in the game.

3. With the plan in hand, students should then learn how to use the Scratch platform to implement their idea. There are many tutorials and useful resources available directly on the Scratch platform and on the internet in general.

4. The next step is to implement the game on Scratch. This will likely require a lot of experimentation, testing, and adjustments, so do not be discouraged if things do not work perfectly on the first try.

5. Once the game is finished, students should extensively test it to ensure that everything is working correctly. This includes not only the programming aspect of the game but also ensuring that the function-based gameplay makes sense and is challenging yet achievable.

6. After the game is complete, each group will present their game to the class, explaining how the game works, what type of functions are involved, and how they implemented the game on Scratch.

7. Finally, the group should prepare a written report detailing the entire process. This document should contain the following sections:

   • Introduction: Provide context for the project, its relevance and real-world application, the problem to be solved by the game, and the objective of this project.
   • Development: Explain the theory behind the functions used in the game, the strategies that were used to develop the game, and the methodology to test it. Present and discuss the game test results.
   • Conclusion: Summarize your main points, explain the learnings and skills acquired, and draw conclusions about the project.
   • Bibliography: Indicate the sources used to develop the project, such as tutorials, videos, etc.