Lesson Plan | Traditional Methodology | Operations: Order of Operations

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to introduce students to the concept of order of operations, highlighting its importance and usefulness in solving mathematical expressions. By establishing clear objectives, students will be able to understand what is expected of them and prepare to apply the concepts learned in practical situations.

Main Objectives

1. Understand the importance of the order of operations in solving mathematical expressions.

2. Identify and correctly apply the sequence of operations in numerical expressions.

3. Solve problems involving the four basic operations and exponentiation, following the correct order of operations.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to introduce students to the concept of order of operations, highlighting its importance and usefulness in solving mathematical expressions. By establishing clear objectives, students will be able to understand what is expected of them and prepare to apply the concepts learned in practical situations.

Context

Explain to students that, just like in a cooking recipe where specific steps must be followed to get the desired dish, in Mathematics there is also a specific order to perform operations in a numerical expression. This order is essential to ensure that everyone arrives at the same correct result. Tell them that today they will learn about the 'Order of Operations', a set of rules that helps us solve mathematical expressions correctly and efficiently.

Curiosities

Did you know that the order of operations is used in various areas of our daily lives, such as in computer programming, engineering, and even in video games? Without these rules, it would be very difficult to ensure that everyone arrived at the same result when solving complex problems.

Development

Duration: (50 - 60 minutes)

The purpose of this stage is to deepen students' understanding of the order of operations through detailed explanations and practical examples. By addressing each step of the operations sequence and solving guided problems, students will be able to apply these concepts in their own resolutions, ensuring a solid and practical understanding of the content.

Covered Topics

1. 1. Introduction to the Order of Operations: Explain that the order of operations is a set of rules used to determine the sequence in which operations should be performed in a mathematical expression. Emphasize the importance of following this order to obtain correct results. 2. 2. Parentheses ( ): Address the first rule which indicates that operations inside parentheses should be performed first. Provide clear examples and solve some expressions that contain parentheses. 3. 3. Exponents and Radicals: Explain that the next step is to solve the exponents (powers) and radicals. Provide examples of expressions with exponents and solve them step by step. 4. 4. Multiplication and Division: Detail that after solving parentheses and exponents, multiplication and division should be carried out from left to right. Provide examples that show this rule in action. 5. 5. Addition and Subtraction: Explain that the last step is to perform additions and subtractions, also from left to right. Provide practical examples and solve them with the class. 6. 6. Practical Examples: Combine all previous topics and solve complex expressions that involve all the mentioned operations. Encourage students to write down the steps for future reference.

Classroom Questions

1. 1. Solve the expression: 3 + 5 × (2 + 3)² ÷ 5 2. 2. Solve the expression: 6 + 4 × (3² - 1) ÷ 2 3. 3. Create a numerical expression that involves all operations (addition, subtraction, multiplication, division, and exponentiation) and solve it.

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to review and consolidate students' understanding of the order of operations through a detailed discussion of the resolved questions. By engaging students in reflections and questions, the teacher ensures that concepts have been understood deeply and practically, stimulating active participation and idea exchange among students.

Discussion

• Discussion of the Questions:

• 1. Question 1 - Solve the expression: 3 + 5 × (2 + 3)² ÷ 5:

• First, solve the expression inside the parentheses: (2 + 3) = 5.

• Next, square it: 5² = 25.

• Now, perform the multiplication: 5 × 25 = 125.

• Then divide the result: 125 ÷ 5 = 25.

• Finally, add the result to 3: 3 + 25 = 28.

• • Final Answer: 28
• 2. Question 2 - Solve the expression: 6 + 4 × (3² - 1) ÷ 2:

• First, solve the power: 3² = 9.

• Next, subtract the value: 9 - 1 = 8.

• Perform the multiplication: 4 × 8 = 32.

• Then divide the result: 32 ÷ 2 = 16.

• Finally, add the result to 6: 6 + 16 = 22.

• • Final Answer: 22
• 3. Question 3 - Create a numerical expression that involves all operations (addition, subtraction, multiplication, division, and exponentiation) and solve it:

• This open-ended question encourages students' creativity. For example, the expression: (2 + 3)² - 4 ÷ 2 × 3 + 1.

• First, solve the expression inside the parentheses: (2 + 3) = 5.

• Next, square it: 5² = 25.

• Then perform the division: 4 ÷ 2 = 2.

• Perform the multiplication: 2 × 3 = 6.

• Subtract the result from the power: 25 - 6 = 19.

• Finally, add the result to 1: 19 + 1 = 20.

• • Final Answer: 20

Student Engagement

1. Questions and Reflections: 2. 1. Why is it important to follow the order of operations when solving mathematical expressions? 3. 2. How would you feel if each person solved an expression differently and arrived at a different result? 4. 3. Can you think of daily situations where the order of operations is important? 5. 4. What was the most challenging part of solving the expressions? Why? 6. 5. Would anyone like to share the expression they created and how they solved it?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to recap and consolidate the main points addressed in the lesson, ensuring that students have a clear and summarized view of what was taught. By connecting theory with practice and highlighting the relevance of the topic, students can understand the importance of the content and how to apply it in different contexts.

Summary

• Order of Operations: Introduction to the set of rules used to determine the sequence of operations in mathematical expressions.
• Parentheses ( ): All operations inside parentheses should be solved first.
• Exponents and Radicals: Solve the exponents and radicals after parentheses.
• Multiplication and Division: Perform these operations from left to right after solving parentheses and exponents.
• Addition and Subtraction: Perform these operations from left to right after solving multiplications and divisions.
• Practical Examples: Combination of all previous steps in complex expressions for practice and understanding.

The lesson connected theory with practice by explaining each order of operations rule in detail and then applying these rules in practical examples. Students could see directly how theory is applied in solving numerical expressions, reinforcing the importance of each step in obtaining correct results.

The order of operations is fundamental not only to solve mathematical problems accurately, but also to understand processes in various areas of daily life, such as programming, engineering, and even video games. Understanding these rules helps ensure consistency and accuracy in various activities and professions.