Contextualization

Multiplication is one of the fundamental operations of arithmetic, present in various everyday situations. From calculating how many apples we have when buying two bags with five apples each, to more complex problems such as the spread of a pandemic, multiplication is an indispensable tool. But what about when we encounter multiplications with unknown or missing values? How do we proceed to solve such questions?

For this, we must understand well the fundamentals of what multiplication is, how it works, and how we can use already known mathematical tools to discover these missing values. Multiplication can be seen as a repeated addition. For example, if we have 5 times 2, this is the same as adding the number 2, five times. With practice, we memorize the results of these operations to facilitate our calculations in everyday life. But the essence of multiplication is still this: a repeated sum.

Now, let's imagine that we have a multiplication where we know the result and one of the multipliers, but we do not know the other. For example, we know that some quantity of apples, times 2, gives a total of 10 apples. How many apples did we initially have? To solve this type of problem, we will use the concept of division, the inverse operation of multiplication.

Studying multiplication with missing values is fundamental not only for mathematics, but to form the basis of logical reasoning, something we constantly use in our lives. Knowing how to solve problems is an important skill that goes beyond the classroom or exact sciences disciplines. Learning to deal with unknown elements and discovering how to find them is a practice that translates much of our daily lives, both in simple everyday situations and in professional challenges.

A great source of study for students is the book 'Elementary Mathematics: Fundamental Operations' available in all municipal libraries. In addition, the website Just Mathematics has an entire section dedicated to the topic, with explanations and solved exercises. The YouTube channel Mathematics Rio with Prof. Rafael Procopio also has several explanatory and dynamic videos on the subject.

Practical Activity

Activity Title:

'Discovering the Unknown: An adventure through the world of multiplication with missing values'

Project Objective

Enhance students' understanding of multiplication and its practical applications, especially when dealing with the situation of having an unknown value in the problem. This project also aims to develop teamwork skills, effective communication, and time management.

Project Description

Students will be divided into groups of 3 to 5 people, and each group will receive a mystery kit. This kit will contain problems that must be solved through the use of the concept of multiplication with missing values. Solving each problem in the kit will lead to a next clue or stage, forming a didactic and playful sequence to be followed.

Teams will have to work collaboratively to solve the problems, discover and apply theoretical concepts learned in the classroom. During the process, they will acquire a deeper understanding of the importance and applicability of multiplication in the real world.

Students will have one month to complete the project, and it is estimated that each student will need to dedicate five to ten hours to the project.

Required Materials

1. Mystery Kit (containing mathematical problems that will trigger a series of enigmas)
2. Pencils, erasers, and paper
3. Calculator
4. Textbooks (for reference)
5. Internet access for research

Detailed Step-by-Step

1. Students will be divided into groups of 3 to 5 people.
2. Each group will receive the Mystery Kit with problems and enigmas related to multiplication with unknown values.
3. Students must solve each problem together, recording how they arrived at the solution. This record will include the problem description, the theory applied, the methodology used, and the result obtained.
4. By solving each problem, students will discover a clue that will lead them to the next enigma. They will follow this procedure until they solve all the enigmas contained in the kit.
5. Throughout the process, students must manage their time to ensure that all activities are completed within the one-month deadline.

Project Deliverables

At the end of the project, each group must submit a detailed report of the work done. The report should follow the following format:

1. Introduction: Students must contextualize multiplication with unknown terms and its importance, as well as the project's objective and its relevance to their learning.

2. Development: Students must describe each problem and its resolution process, including the theory used, the methodology applied, and the discussion of the results obtained. Each solved problem corresponds to a subchapter of this item.

3. Conclusions: Students must provide a retrospective of the work, point out what they learned throughout the project, which skills were developed, and how the activity contributed to the understanding of multiplication with unknown terms.

4. Bibliography: Students must list all research sources used during the project, whether to understand the theory, to assist in solving the problems, or to prepare the report.

This report will be a crucial part of the final project evaluation, as it will demonstrate not only the knowledge acquired by the students but also the development of socio-emotional skills, such as teamwork, effective communication, and time management.