Contextualization
Theoretical Introduction
Mathematics, which may often seem distant from our reality, is more present in our lives than we can imagine. One of the essential concepts of this discipline is the basic operations: addition, subtraction, multiplication and division. These four operations are the basis for understanding mathematics and are present in everyday situations, such as shopping at the market, calculating distances and times, among others.
In addition to executing these operations, there are properties that are fundamental for solving more complex mathematical problems, they are: commutative property, associative property and distributive property. Each of these properties has a specific function and is applicable to one or more types of operations.
The commutative property, for example, states that the order of the terms does not change the result of the operation, applicable in addition and multiplication. The associative property says that the result does not change when we change the grouping of the terms, also applicable in addition and multiplication. And finally, the distributive property, which relates multiplication to addition or subtraction, stating that multiplying a number by a sum (or subtraction) is equal to the sum (or subtraction) of the products.
Contextualization
The use of mathematical operations and their properties is essential for countless daily activities. Imagine that you go to a supermarket to buy several identical items, such as juice boxes. Is it necessary to count one by one or is it possible to use multiplication? What if you want to divide the juice boxes equally among your friends, how can division help you? Also, in a situation where you need to calculate the total value of your purchase, can you change the order of the items without changing the total value? The answers to these questions can be found when we understand the basic options and their properties.
Mathematics, through the operations and their properties, allows us to solve problems more quickly and efficiently, contributing to the development of logical thinking and problem-solving skills. In addition, this knowledge is fundamental for various professions, such as engineering, accounting, physics, among others, making the study of these operations and properties fundamental for the education of students.
Practical Activity: Building the Market of Mathematics
Project Objective
To understand and apply the properties of basic mathematical operations (addition, subtraction, multiplication and division) by creating a "Mathematics Market", where each student will have to perform calculations to buy and sell products.
Detailed Description of the Project
Students, grouped into teams of 3 to 5, will have to create a "Mathematics Market". Each group will select about 10 to 15 items (which can be real or cardboard signs), assign a price to each item and create a shopping list for each one.
Students will have to make purchases and sales, using the four basic operations and their properties. For example, use the commutative property of addition to find the total cost of the items regardless of the order, or use the distributive property to calculate the total of several identical items.
Required Materials
- Items for the "Mathematics Market" (real objects or drawn on cardboard).
- Paper and pen to create price lists and shopping lists.
- Calculator (optional).
Detailed Step by Step
- Divide students into groups of 3 to 5.
- Each group should gather between 10 to 15 items for their market and assign a price to each one.
- Each group should create a shopping list for each customer of the market.
- The groups should practice buying and selling items, applying the properties of the mathematical operations.
- Each group should record their transactions, noting the calculations performed and the properties used.
- Students will have to write a report detailing their experiences, the challenges faced and how they applied the properties of the mathematical operations.
Project Documentation
After carrying out the practical activities, the students, by group, must produce a report containing the following sections:
- Introduction: Contextualize the project, describe the relevance of the properties of mathematical operations and the objective of the Mathematics Market project.
- Development: Here, the group should discuss the activities carried out, explaining the decisions made and the challenges encountered. It is important to report which properties of the mathematical operations were used and how they helped to solve the proposed problems.
- Results: The students will have to present and discuss the results obtained, such as the calculations performed and the transactions completed.
- Conclusion: The students should express the learnings obtained from the project, reiterate the importance of the properties of the mathematical operations and their practical uses in everyday life.
- Bibliography: Indicate the sources used to study the properties of operations, whether books, websites or videos.
