Lesson Plan | Traditional Methodology | Equality: Same Operation on Both Sides

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to provide students with a clear understanding of the concept of equality in mathematical equations. By performing operations on both sides of an equality, students will be able to verify that the original equation remains true. This understanding is fundamental for building more advanced mathematical skills and solving problems accurately and logically.

Main Objectives

1. Understand the importance of maintaining equality when performing operations on both sides of an equation.

2. Learn to apply the same operation on both sides of an equality to verify the preservation of the equation.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to provide students with a clear understanding of the concept of equality in mathematical equations. By performing operations on both sides of an equality, students will be able to verify that the original equation remains true. This understanding is fundamental for building more advanced mathematical skills and solving problems accurately and logically.

Context

Start the lesson by explaining to students that in mathematics, just like in life, equality is a central concept. For example, if two people have the same amount of money and one of them earns an extra coin, to maintain equality, the other person must also earn a coin. This helps us understand how to maintain balance in various everyday situations.

Curiosities

Did you know that this concept of equality is used in various areas beyond mathematics? For instance, when we make a cake, if we add more sugar, we also need to adjust the other ingredients to maintain balance and ensure that the cake tastes good. Similarly, in sports, if a team makes a substitution, it may be necessary to adjust the strategy to maintain performance.

Development

Duration: 40 to 50 minutes

The purpose of this stage is to ensure that students understand how to apply mathematical operations on both sides of an equality to keep it true. By addressing these topics and solving practical questions, students will develop a solid understanding of the concept of equality and be better prepared to handle more complex equations in the future.

Covered Topics

1. Definition of Equality: Explain that an equality is a relation between two mathematical expressions that have the same value. Illustrate with simple equalities, like 2 + 3 = 5. 2. Operations in Equality: Detail that operations such as addition, subtraction, multiplication, and division can be performed on both sides of an equality without altering the truth of the equation. Use examples like adding 2 on both sides of 3 = 3, resulting in 5 = 5. 3. Verification of Equality: Show how to check if an equality holds after performing operations on both sides. For example, if 4 + 1 = 5, adding 2 to both sides results in 6 = 7, which is still true. 4. Practical Examples: Present practical and everyday examples where equality is maintained, such as equally dividing a number of candies among friends. Example: if two people have 4 candies each and receive 2 more candies each, equality is maintained: 4 + 2 = 4 + 2.

Classroom Questions

1. If you have the equality 6 = 6 and add 3 to both sides, what will be the new equality? 2. Given the equality 8 - 2 = 6, does subtracting 4 from both sides maintain the equality? If so, what will be the new equality? 3. If 10 = 10 and you multiply both sides by 2, what will be the new equality? Is the equality still true?

Questions Discussion

Duration: 20 to 25 minutes

The purpose of this stage is to consolidate students' understanding of applying operations on both sides of an equality to maintain the truth of the equation. By discussing the answers and engaging students with reflective questions, the teacher reinforces the concept of equality and fosters a deeper understanding, preparing them to apply this knowledge in more complex situations in the future.

Discussion

•  Explanation of Question 1: If you have the equality 6 = 6 and add 3 to both sides, the new equality will be 9 = 9. This is because we added the same value (3) to both sides of the equation, thus maintaining equality.

•  Explanation of Question 2: Given the equality 8 - 2 = 6, does subtracting 4 from both sides maintain the equality? Yes, it does. Subtracting 4 from both sides, the new equality will be 4 - 2 = 2. The equality is still true since subtracting the same value from both sides does not alter the truth of the equation.

•  Explanation of Question 3: If 10 = 10 and you multiply both sides by 2, the new equality will be 20 = 20. Multiplying both sides of the equation by the same number keeps the equality true.

Student Engagement

1. 樂 Reflection Question: Why is it important to perform the same operation on both sides of an equality? 2. 樂 Reflection Question: How can we use the concept of equality to solve everyday problems? 3. 樂 Reflection Question: Can you think of another operation that, when applied to both sides of an equality, still maintains the truth of the equation? What would that operation be?

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to review and consolidate the main concepts covered during the lesson, ensuring that students have a clear and solid understanding of the topic. Additionally, it reinforces the importance and applicability of the concept of equality in practical situations, preparing students to use this knowledge in their future studies and in daily life.

Summary

• Equality is a relation between two mathematical expressions that have the same value.
• Operations such as addition, subtraction, multiplication, and division can be performed on both sides of an equality without altering the truth of the equation.
• Verify if an equality holds after performing operations on both sides.
• Practical examples where equality is maintained, such as equally dividing a quantity of candies among friends.

The lesson connected the theory of equality with practice by using everyday and mathematical examples to demonstrate how performing the same operation on both sides of an equation maintains the truth of the equality. This helped students understand the concept in a more concrete and applicable way in different contexts.

The concept of equality is fundamental not only in mathematics but also in various everyday situations. For example, in games, culinary recipes, and fair resource distribution. Understanding how to maintain equality when performing operations is essential for solving problems accurately and logically.