Contextualization

Math is a discipline full of concepts and procedures that can sometimes seem abstract. But, in fact, everything we learn in it has practical and everyday applications in our lives. Within this vast world of mathematics, the topics that we will explore now are the properties of operations - addition, subtraction, multiplication, and division.

Mathematical operations are the basis for performing calculations, solving problems, and abstracting information. It is through them that we can, for example, count money, divide tasks, estimate travel times, and many other things in our daily lives. But have you ever stopped to think that these operations have specific properties that allow us to manipulate them in an intelligent and practical way?

Addition and multiplication, for example, have commutative and associative properties. This means that, in the case of the commutative property, the order of the elements does not affect the final result. The associative property allows us to rearrange the numbers inside parentheses without changing the result. Subtraction and division, on the other hand, do not have these properties, which forces us to be more careful when manipulating them.

Because they are so present in our lives, it is important that we understand how these operations work and what their properties are. Thus, we will be able to use them efficiently to solve the most varied everyday problems, from calculating the amount of ingredients for a recipe to dividing the expenses of a trip among friends.

The resources that we suggest for further study on the properties of mathematical operations are:

• Book: "Fundamentals of Elementary Mathematics" - Vol. 1: Sets and Functions, by Gelson Iezzi and Carlos Murakami. This book provides a complete and detailed approach to operations and their properties, in addition to offering solved and proposed exercises.

• Website: Khan Academy (https://www.khanacademy.org). This teaching platform has a section dedicated to mathematical operations and their properties, with video lessons and practical exercises.

• YouTube: Channel "Matemática Rio com Prof. Rafael Procopio" (https://www.youtube.com/user/matematicario). This channel offers a series of videos explaining in detail about operations and their properties, in a relaxed and didactic way.

Practical Activity

Activity Title: "Operations in Teams"

Project Objective

Learning and applying the properties of mathematical operations (addition, subtraction, multiplication, and division) in real problems through collaborative work, developing technical and socio-emotional skills.

Detailed Project Description

Each group of students will be transformed into a construction team. They will be responsible for calculating and planning the resources needed to build a house. Each team member will be responsible for a section of the house: material, labor, time, and cost. They should use the properties of operations to optimize resources and ensure project efficiency.

Materials Required

1. Paper
2. Pen
3. Calculator
4. Textbooks or online math resources for reference
5. Data sheet containing specifications for construction (provided by the teacher).

Detailed Step by Step

1. Form groups of 3 to 5 students. Assign each group their "construction team" and provide them with the data sheet containing the specifications of the house they are responsible for building.

2. After receiving the data sheet, the team members should meet and divide the sections among themselves (material, labor, time, and cost).

3. Each team member should then calculate the amount of resources that his section requires. They should use the properties of the operations to optimize these calculations.

4. Once the calculations are complete, the team then meets to compile all the data. They should check if the total calculated resources correspond to the total budget provided in the data sheet.

5. The team should then prepare a detailed report of their project, explaining each calculation and how the properties of the operations were used.

Project Submission

The final product is a written report of their project, divided into four main parts:

1. Introduction: Here, students should contextualize the theme of the properties of operations, explaining their relevance and application in the real world in the construction of a house. They should also include their team's project objective.

2. Development: Students should explain the theory behind the properties of operations, describe the activity carried out in detail, indicate the methodology used and, finally, present and discuss the results obtained.

3. Conclusion: Students should conclude the work by summarizing their main points, explaining what they learned about the properties of operations and what conclusions were drawn on the topic.

4. Bibliography: Students should indicate the sources of information used to work on the project, including books, web pages, videos, etc.

Students have one week to complete and deliver the project, from the moment the groups are formed and the activity is delivered.