Contextualization
Order of operations is one of the fundamental topics in Mathematics. It tells us which operation to perform first in a mathematical expression that involves more than one operation, such as addition, subtraction, multiplication, division, and exponentiation. Without this rule, expressions like 2 + 3 * 4 could be interpreted in different ways, leading to different results. This is why we have parentheses, brackets, and braces to indicate the order in which expressions should be solved.
The concepts of order of operations are essential to understanding mathematics, and it is frequently applied in many disciplines, such as Physics, Engineering, Economics, among others. To organize this order, we use the order of operations precedence rule, known by the acronym PEMDAS or BODMAS, which helps us to remember the correct sequence of solving operations in Mathematics: Parentheses (or Brackets), Exponents (or Orders), Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
However, the order of operations goes beyond Mathematics. It is also a valuable tool for the development of logical and critical thinking, essential skills in the modern world. Understanding the correct order of performing operations can help develop the ability to solve complex problems, make informed decisions, and reason more structuredly.
To deepen their knowledge on the subject, students can resort to several reliable sources, such as:
- Khan Academy - This website provides interactive lessons and explanatory videos on a variety of Mathematics topics, including the order of operations. Khan Academy - Order of Operations
- Only Math - This Brazilian website dedicated to Mathematics has a section that explains in detail the concept of order of operations. Only Math - Numerical Expressions
- YouTube – Several channels address the topic in a didactic and interactive way. One example is the channel "Matemática Rio com Prof. Rafael Procopio", which presents the subject in a light and relaxed manner. Math Rio - Order of Operations
Practical Activity: The Order of Operations Challenge
Project Objective
The objective of this activity is to challenge students to create and solve mathematical puzzles that involve the order of operations. They will have to use their creativity and logical reasoning to create and solve numerical expressions, in addition to developing teamwork and communication skills to interact with colleagues. In addition, students will apply the concept of order of operations in a real game scenario.
Detailed Project Description
Each group of students will have to create a board game with the objective of reaching the end of the board by correctly solving numerical expressions involving the order of operations. The board's squares must contain different mathematical operations, and the players must solve the operation correctly to advance in the game. Players can also create additional challenges, such as squares that make the player go back or advance on the board.
Students will have to rely on their knowledge of Geometry, for the layout of the board, as well as Portuguese, for the rules of the game, connecting skills from different disciplines.
Required Materials
- Cardboard or card stock to make the board.
- Colored pens, crayons, or markers.
- 1 die.
- Pieces to indicate the position of each player (buttons, bottle caps, or whatever creativity allows can be used).
- Calculators (optional).
Detailed Step-by-Step to Carry Out the Activity
- Each group should define the dimensions of the board and divide it into squares.
- In each square, the group must create a numerical expression that involves at least three different operations and fits into the order of operations. The expressions can vary in difficulty, to make the game more dynamic.
- The rules of the game should be written clearly and objectively so that all players understand. It is important to define what happens when a player correctly solves an expression and when they make a mistake.
- After creating the game, the groups should exchange their games and play the game created by the other group. They should verify the correctness of the numerical expressions and the correct application of the rules of the game.
- Finally, each group should write a detailed report describing the game creation process, explaining the rules, and reflecting on the experience of creating and playing the game. The report should contain an introduction, development, conclusions, and the bibliography used.
Project Deliverables and Connections with the Suggested Activities
The student groups will make two main deliverables:
-
The created board game - This board should be complete and functional, with all the rules clearly defined and all the correct numerical expressions. It is the practical application of the order of operations concepts.
-
The written report - The report should detail the entire game creation process, including the challenges encountered and the solutions adopted. This document serves as a reflection on student learning and the application of order of operations concepts.
From the proposed activities, students will have to prepare a structured report on the following topics:
- Introduction: Students should contextualize the project, elaborate its objective, and describe the relevance of the order of operations in the real world and in the Mathematics discipline.
- Development: Here, the students will describe in detail all the stages of the game creation, explain each rule, and the mathematical expressions used in each square of the board. They should also discuss the application of the order of operations concept during the game creation.
- Conclusions: At this stage, the students should reflect on the activity, discuss the lessons learned, and the difficulties encountered. They should also relate the theoretical concepts studied with the practice carried out.
- Bibliography: The students should indicate all the sources of information that were used to carry out the project, such as websites, videos, books, etc.
