Lesson Plan | Traditional Methodology | Comparisons between fractions

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to establish a clear and specific foundation of the objectives to be achieved during the lesson. This helps students understand the importance of the content that will be addressed and prepares them for the subsequent activities and explanations, promoting a more focused and efficient learning.

Main Objectives

1. Understand how to compare fractions of different whole quantities.

2. Identify which fraction is larger between two given fractions.

3. Put fractions in ascending or descending order.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to spark students' interest in the topic of fractions, contextualizing it in real-life situations. This facilitates the understanding of the importance of learning to compare fractions and prepares students for the more detailed explanation that will follow.

Context

To start our lesson on comparing fractions, let's imagine two everyday situations: at a picnic, you have a large pizza and divide it among your friends. In another scenario, you have a birthday cake that will also be divided among the guests. How can we know if the amount of pizza each person receives is greater or less than the amount of cake? This is the essence of comparing fractions: understanding which part of a whole is larger and how these parts relate to different quantities.

Curiosities

Did you know that mathematicians from ancient Greece, like Euclid, studied fractions over 2000 years ago? They used fractions to solve practical problems related to dividing land and food, concepts that we still use in our daily lives, such as splitting a restaurant bill or measuring ingredients in the kitchen.

Development

Duration: 40 to 50 minutes

The purpose of this stage is to provide a detailed and practical explanation of how to compare fractions with the same denominator and with different denominators, as well as to teach how to order fractions. This will help students develop fundamental skills for comparing and ordering fractions, applying this knowledge in practical examples and everyday questions.

Covered Topics

1. Concept of fraction: Explain that a fraction represents a part of a whole. Detail that a fraction consists of a numerator (upper part) and a denominator (lower part), where the denominator indicates how many parts the whole has been divided into and the numerator indicates how many of those parts we are considering. 2. Comparison of fractions with the same denominator: Show that when comparing fractions with the same denominator, it is enough to compare the numerators. For example, 3/8 is less than 5/8 because 3 is less than 5. 3. Comparison of fractions with different denominators: Explain that to compare fractions with different denominators, it is necessary to find a common denominator or convert the fractions to decimal numbers. Use practical examples, such as 1/2 and 2/3, and demonstrate the process of finding the common denominator (6) and converting each fraction (1/2 = 3/6 and 2/3 = 4/6), showing that 3/6 is less than 4/6. 4. Resolution of practical examples: Present problems involving the comparison of fractions in real situations, such as comparing half of 50 with a third of 60. Show the calculation: half of 50 is 25 and a third of 60 is 20. Therefore, 25 is greater than 20. 5. Ordering fractions: Teach how to put fractions in ascending or descending order. Use practical examples, such as ordering 1/4, 1/3, and 1/2. Convert all to a common denominator (12), resulting in 3/12, 4/12, and 6/12, and then order them: 1/4 < 1/3 < 1/2.

Classroom Questions

1. Compare the fractions 3/5 and 7/10. Which is larger? 2. Put the fractions in ascending order: 2/7, 4/7, 1/7. 3. Which is larger: half of 80 or a quarter of 100? Justify your answer.

Questions Discussion

Duration: 20 to 25 minutes

The purpose of this stage is to consolidate the knowledge acquired by students during the lesson, providing a moment for reflection and discussion of the answers. This allows students to review and reinforce the concepts learned, clarify doubts, and practice mathematical communication. In addition, it engages students in a collaborative learning process, promoting a deeper and more lasting understanding of the content.

Discussion

• 1. Comparison of fractions 3/5 and 7/10: To compare these fractions, a common denominator is found. The least common multiple between 5 and 10 is 10. Converting 3/5 to a fraction with a denominator of 10 gives us 6/10. Thus, we compare 6/10 and 7/10, where 7/10 is greater than 6/10.
• 2. Ordering in ascending order: 2/7, 4/7, 1/7: As all fractions have the same denominator, it is enough to compare the numerators. Ordering the numerators 1, 2, and 4, we have: 1/7 < 2/7 < 4/7.
• 3. Comparison between half of 80 and a quarter of 100: Half of 80 is 40 and a quarter of 100 is 25. Therefore, 40 is greater than 25. Explaining that this is done by converting the fractions to absolute values makes it easier for students to understand.

Student Engagement

1. 1. Why do we need to find a common denominator to compare fractions with different denominators? 2. 2. How can you use the comparison of fractions in your daily life? Give an example. 3. 3. If we have the fractions 3/8, 5/8, and 7/8, how would we order them in descending order? Explain your reasoning. 4. 4. What is a practical example of when it would be useful to know how to compare fractions? 5. 5. If you had to explain to a classmate how to compare fractions with different denominators, how would you do it?

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to review and consolidate the main points covered during the lesson, ensuring that students fully understand the concepts taught. By summarizing the content, connecting theory with practice, and demonstrating the relevance of the topic, this section reinforces learning and highlights the importance of the knowledge acquired.

Summary

• Understanding the concept of fraction as part of a whole.
• Comparison of fractions with the same denominator through the numerators.
• Comparison of fractions with different denominators by finding a common denominator or converting them to decimals.
• Resolution of practical examples, such as the comparison of half of 50 with a third of 60.
• Techniques for ordering fractions in ascending or descending order.

The lesson connected theory with practice by using real-life situations, such as dividing food at a picnic, to explain the concept of fractions and demonstrate the comparison between them. Practical examples helped illustrate how to apply these concepts to everyday problems, making the learning more relevant and understandable for students.

The importance of the subject presented reflects in various everyday situations, such as splitting a restaurant bill or measuring ingredients for a recipe. Understanding fractions and knowing how to compare them allows students to make informed and accurate decisions in their daily activities. Furthermore, the ability to compare fractions is fundamental in various areas of knowledge, such as science and economics.