Contextualization
Theoretical Introduction
Addition and Subtraction with Missing Values is a fundamental step in the development of mathematical thinking in basic education. The concepts of addition and subtraction are some of the first ones children encounter in school and are essential for building more complex knowledge in mathematics.
This skill is developed in stages. First, children learn to perform basic addition and subtraction operations with known values. Then, they start working on problems where a part of the operation is unknown, meaning a value is missing. This requires a higher level of mathematical reasoning, as the student needs to understand the operation's structure and apply inversion (or the 'opposite operation') to find the unknown value.
Moreover, it is important to emphasize that, in the context of mathematical operations, terms have specific names: in addition, the numbers being added are called addends and the result is the sum; in subtraction, the initial number is the minuend, the number being subtracted is the subtrahend, and the result is the difference.
Contextualization and Practical Application
The ability to understand and perform operations with missing values is extremely practical and useful in many real-life contexts. It can be applied in everyday activities, such as managing a household budget or checking change in purchases, to more complex situations like solving problems in various professional careers such as engineering, physics, chemistry, and computer science, where solving equations (which is nothing more than finding unknown values through mathematical manipulation) is a common skill.
Furthermore, the use of contextualized problems helps develop problem-solving skills, as in addition to applying mathematics, students learn to interpret the problem, understand what is being asked, and how the situation can be mathematically represented.
To delve deeper into the topic and better understand the theoretical concepts and practical applications, I suggest the following resources:
- Brazil School - Addition and Subtraction
- Only Mathematics - Operations with natural numbers
- YouTube - Rio Mathematics with Prof. Rafael Procopio
Practical Activity
Activity Title: Operation Detective
Project Objective
The objective of this project is to provide students with the opportunity to apply and deepen their knowledge of addition and subtraction with missing values, also working on logical reasoning, problem-solving skills, and teamwork. They will be challenged to unravel mysteries and solve mathematical puzzles. Additionally, students will develop research and writing skills while preparing a detailed report on the project.
Project Description
Students will solve a series of challenges of addition and subtraction with missing values, which together form a mystery story. The project will be carried out in groups of 3 to 5 students and should last approximately 15 hours, divided into different stages of learning, discussion, problem-solving, and preparation of the final report.
Required Materials
- Pencil, eraser, and graph paper for calculations and notes.
- Computer with internet access for research and report writing.
- Printed mathematical puzzles and riddles provided by the teacher.
Activity Step-by-Step
- The teacher will divide the class into groups and present the mystery story involving addition and subtraction with missing values.
- Each group will receive a series of puzzles to be solved to advance in the story. These puzzles will be problems of addition and subtraction with missing values.
- Students should, together, discuss and find solutions to the proposed challenges, recording all their reasoning steps.
- After solving each puzzle, students must record the solution and the strategy used, as well as the mathematical concepts involved.
- As they progress, students will unravel the story and finally solve the mystery.
- In the end, each group must produce a detailed report of the project.
Project Deliverables
The final product of this project will be a written report that must contain the following elements:
1. Introduction
Students must contextualize the project, explain the relevance of learning about addition and subtraction with missing values, and describe the application of these concepts in the real world.
2. Development
In this section, students must present the theory studied to conclude the project, explain the activity carried out in detail, and indicate the methodology used. They must also present and discuss the results of the challenges they solved, explaining the strategy used and the mathematical concepts involved.
3. Conclusion
In the conclusion, students must summarize the most important points of the work, summarizing what they learned from the activity and the conclusions they drew about the project.
4. Bibliography
Students must indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.
Each group must deliver a revised, formatted, and typed report, presenting the results of the problems solved, the strategies used, and reflecting on what they learned and achieved with the project.
