Context

Theoretical Introduction

Mathematics is a science that is present in our daily lives in various ways, whether in measurements, prices, schedules, distances, etc. And among all the mathematical concepts we learn, one of the most fundamental is the Order of Operations.

The Order of Operations is a convention that was established so that we all have a uniform way of interpreting certain expressions. Imagine if each person solved a mathematical expression in their own way. That would cause a lot of confusion, right? That's why we follow a predefined order when performing mathematical operations.

This order is easily remembered by the acronym PEMDAS, which stands for Parentheses, Exponents (or Powers), Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This set of rules is essential for us to correctly solve equations and numerical expressions.

Context

The Order of Operations is a very important concept in real life and has applications in areas such as engineering, computing, finance, statistics, physics, etc. For example, in engineering and physics, it is essential in solving equations that model the behavior of physical systems.

Imagine an engineer who is designing a bridge. They need to calculate the force that the bridge can withstand to ensure its safety. This calculation involves several mathematical operations that need to be done in a specific order. If the engineer does not use the correct order of operations, the calculation will be wrong and the bridge may not be safe.

Practical Activity

Activity Title: "PEMDAS Dominos - Learning the Order of Operations"

Project Objective

The objective of this project is to develop students' understanding of the Order of Operations (PEMDAS) in a practical and fun way, through a custom domino game. In addition, students will also enhance socio-emotional skills such as teamwork, critical thinking, time management, problem-solving, among others.

Detailed Project Description

In this activity, groups of students (3 to 5 members) will be invited to create a domino game that involves the Order of Operations. Each piece of the game will have, on one side, an expression to be solved respecting the Order of Operations and, on the other side, the result of this operation. For example: [2*(3+5)] | 16. Students must use the four mathematical operations (addition, subtraction, multiplication, and division), as well as exponentiation, in their expressions.

Students should create 28 domino pieces, which is the number of pieces in a traditional domino game. They can use cardboard to make the pieces or create digitally if they prefer. The results of the operations should range from 0 to 20. It is important that all pieces are different from each other.

After created, the domino game should be tested by the group and adjusted if necessary. Once completed, students should play the dominoes, placing the pieces on the table, relating the result of the numerical expression on one piece to the result contained on the other side of the next piece.

Required Materials

• Cardboard (or similar) for making the domino pieces;
• Markers, pencils, or pens for writing on the pieces;
• Ruler to help with drawing the pieces;
• Scissors for cutting the pieces.

Step-by-Step Guide for the Activity

1. The teacher divides the class into groups of 3 to 5 students;

2. After understanding what the Order of Operations is, students begin to think about the numerical expressions and their respective results for the domino pieces;

3. Using cardboard, students draw and cut 28 rectangles of the same size (or create digitally);

4. On one half of each piece, students write a numerical expression that must be solved respecting the Order of Operations. On the other half, they write the result of this operation;

5. Students play the domino game to test if all pieces are correct and make necessary adjustments;

6. Students write a report on the activity, detailing the entire process, their learnings, and conclusions.

Project Deliverables

At the end of the project, students should deliver:

1. The completed and corrected domino game;

2. A project report. In the report, students should write an introduction about the project, explaining what the Order of Operations is and its importance; then, they should describe in detail how the project was executed, the strategies used, the problems encountered, and how they were solved; finally, they should discuss the results obtained and conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project. The bibliography used should be clearly referenced in the report.