Contextualization

Introduction

Mathematics, as a broad and diversified field of knowledge, presents fundamental concepts that are at the core of routine calculations and even the most complex equations. One of these key concepts is mathematical expressions. Knowing them, understanding them, and being able to manipulate them correctly is an essential step for a good mathematical education.

Mathematical expressions, by definition, are sequences of numbers, variables, and operations that, when put together coherently, result in a single numerical value. The operations that we can find in an expression include addition, subtraction, multiplication, division, exponentiation, and rooting. Each one has its particularity, but all follow a specific hierarchy when present in the same expression, the well-known MDAS rule (Multiplication and Division before Addition and Subtraction).

Studying expressions encompasses not only knowing how to calculate correctly but also knowing how to interpret them. Different expressions can have the same numerical resolution but represent mathematically distinct situations. Therefore, it is necessary to acquire a precise reading and a careful interpretation of these mathematical symbols.

Contextualization

Mathematical expressions are an integral part of our daily lives, even if we do not always realize it. They are present when we calculate distances, perform financial operations, solve logic puzzles, and even in video games. In many cases, we are able to solve everyday problems through them.

In the professional world, this skill becomes even more essential. Engineers use expressions to calculate the strength of materials, economists use them to model market behaviors, and so on. Developing mastery over mathematical expressions now is therefore ensuring a valuable tool for the future.

Practical Activity

Project Title: "Expressions in Action!"

Project Objective:

The objective of this project is to develop students' skills in manipulating and solving mathematical expressions collaboratively and creatively.

Project Description:

In this project, students will create a board game that involves the use of mathematical expressions. The game will be designed to be played by 2 to 4 players and should include rules that involve solving mathematical expressions to advance in the game.

Necessary Materials:

• Cardboard or cardstock for the board
• Colored pencils, pens, and markers
• Small pieces, coins, or buttons to be used as game pieces
• Dice
• Blank cards to write the mathematical expressions
• Calculators (Optional)

Step by Step:

Step 1: Game Planning

Each group should plan the structure of their board game, defining the basic rules, the path to be followed by the pieces, and how mathematical expressions will be integrated into the game mechanics.

Step 2: Creation of Mathematical Expressions

Groups should create a series of mathematical expressions to be used in the game. These expressions should include addition, subtraction, multiplication, division, exponentiation, and rooting operations. Each mathematical expression should be written on a blank card.

Step 3: Board Creation

Groups should draw and color the game board on cardboard or cardstock, considering the path to be taken by the pieces and the spaces available for the mathematical expressions.

Step 4: Game Testing

Each group should test the game by playing it repeatedly and making adjustments to the rules or the board as necessary. At this stage, students should ensure that the game functions correctly and that all mathematical expressions are solved properly.

Step 5: Writing the Written Document

After the testing phase, groups should write a report containing the following topics:

• Introduction: Contextualization of the project, the relevance of studying mathematical expressions, and explaining the objective of the created game.
• Development: Describe the theory behind mathematical expressions, explain in detail the creation and execution of the game, report the methodology used, and discuss the results obtained.
• Conclusion: Summarize the main points of the project, the lessons learned, and the conclusions drawn about the game and the role of mathematical expressions in it.
• Bibliography: Cite the sources consulted during the project.

Step 6: Presentation

Finally, each group will present the game to the class, explaining the rules and demonstrating a round of the game. The presentation should be accompanied by the delivery of the written report.

At the end of this project, the groups will have created, tested, and presented an original board game based on mathematical expressions, and developed technical and socio-emotional skills throughout the process.