Contextualization

Introduction

Systems of equations are a set of two or more equations with two or more unknowns. Solving a system of equations means finding the values of the unknowns that satisfy all the equations at the same time. There are different methods to solve systems of equations, including substitution, elimination, and graph.

The main goal of this project is to understand how systems of equations can be applied in solving real-world problems. Furthermore, through group work, you will develop socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.

Real Contextualization

Why do we learn systems of equations? The answer is simple: they are extremely useful in everyday life. Some of the most common applications include financial planning, resource optimization, data analysis, sales forecasting, route planning, and much more.

Does it sound complex? Don't worry! In this project, you will see that it is quite intuitive. You will have the opportunity to create a system of equations from an applied problem, solve it, and then interpret the result in the context of the problem.

Practical Activity

Activity Title: "System of Equations: The Path to the End of the Game"

Project Objective

Develop a board game where movements are determined by solving systems of equations.

Detailed Project Description

Can you win the game by solving equations? In this project, the goal is to create an exciting narrative and a game board. Progress in the game will be determined by solving systems of equations that will be related to the game's story. This project will be carried out by groups of 3 to 5 students and will have an estimated duration of over twelve hours of work for each participant.

Another objective is interdisciplinarity. Thus, in addition to Mathematics, the Portuguese Language discipline will be addressed in the project, as the game's narrative must be well-written and captivating.

Necessary Materials

• Cardboard or similar material for the base of the board
• Colored papers
• Markers, colored pencils, etc.
• Scissors
• Glue
• Dice
• Pawns (can be made of cardboard or using small objects)
• Computer with internet access for research and report elaboration

Detailed Step by Step

1. Brainstorming: Start by thinking about the game's narrative. It can be a magical journey, a car race, a space mission, a police investigation, etc. Use your creativity!

2. Game Development: Once you have decided on the narrative, it's time to develop the game rules. Write down the systems of equations that will be solved during the game and decide how they will influence the players' progress. For example, the solution may indicate the number of spaces the player should move forward.

3. Board Creation: With the narrative and rules defined, create the game board. You can draw maps, characters, items, etc. Let your imagination flow!

4. Game Testing: Play the game a few times to check if the rules are clear and if the game is fun.

5. Adjustments and Improvements: Make necessary adjustments and improve the game based on the tests.

6. Project Report: Each group must then elaborate a project report. The report should contain an introduction, development, conclusion, and bibliography used as described in the introduction of this project.

Project Deliverables

Board Game

The first outcome of this project is the board game that you will create. It must be elaborated with care and creativity and, above all, must serve to solve systems of equations.

Written Report

In the written report, you should address the following topics:

• Introduction: In this topic, contextualize the problem solved through the game. What was the inspiration for the game's narrative? How can systems of equations be applied in this context?

• Development: Explicit the theory of systems of equations used to solve the game situations. Describe your game in detail and explain the methodology used to create the game and the rules. Present and discuss the results obtained in the game tests.

• Conclusion: Summarize the main points, explaining the learnings obtained and the conclusions drawn from the project. Could you perceive the applicability of systems of equations in practical life?

• Bibliography: Indicate the sources on which you based your work on the project, such as books, web pages, videos, etc.

Remember that it is not enough to just solve the equations, it is important to interpret the result and make the connection with the presented problem. This way, you will be practicing the application of theoretical concepts and also the communication skill, by clearly explaining how the system of equations applies to the game context.