Lesson Plan | Traditional Methodology | Fractions: Equivalent Fractions

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to introduce students to the concept of equivalent fractions, establishing a solid foundation for understanding how different fractions can represent the same amount. It is essential for students to understand that, despite having different denominators, some fractions can be equivalent and that there is a simplified or irreducible fraction for each group of equivalent fractions.

Main Objectives

1. Identify equivalent fractions with natural numbers, even when they have different denominators.

2. Recognize that among all equivalent fractions, there is only one that is irreducible.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to introduce students to the concept of equivalent fractions, establishing a solid foundation for understanding how different fractions can represent the same amount. It is essential for students to understand that, despite having different denominators, some fractions can be equivalent and that there is a simplified or irreducible fraction for each group of equivalent fractions.

Context

To start the lesson on equivalent fractions, it's important to connect the topic to the students' daily lives. Ask the students if they have ever divided a pizza or a cake with friends. Explain that when cutting the pizza into different amounts of slices, each slice represents a fraction of the whole. For example, if a pizza is divided into 4 equal parts, each part represents 1/4 of the pizza. If the same pizza is divided into 8 equal parts, each part represents 1/8 of the pizza. Even with different denominators, both fractions represent the same amount of pizza when compared correctly.

Curiosities

Did you know that equivalent fractions are frequently used in cooking recipes? For example, half a cup of sugar (1/2) is the same as two quarters of a cup (2/4) or four eighths of a cup (4/8). This allows chefs to easily adjust ingredient amounts without altering the final result of the recipe. Additionally, equivalent fractions are essential in civil construction, engineering, and even in finance, where precise calculations are necessary.

Development

Duration: 40 - 45 minutes

The purpose of this stage is to deepen students' understanding of equivalent fractions through detailed explanations and practical examples. It is important for students to know how to identify, simplify, and visualize equivalent fractions, understanding their application in everyday situations. This stage also aims to provide a moment of guided practice where students can apply the knowledge acquired through specific exercises.

Covered Topics

1. Concept of Equivalent Fractions: Explain what equivalent fractions are. Use visual examples, such as dividing a pizza into different numbers of slices, to show that 1/2, 2/4, and 4/8 represent the same amount. 2. Method of Simplifying Fractions: Detail the process of simplifying fractions. Show how to find the greatest common divisor (GCD) to simplify fractions to their irreducible form. For example, 4/8 simplified to 1/2. 3. Identification of Equivalent Fractions: Teach how to identify equivalent fractions by multiplying or dividing the numerator and denominator by the same number, using practical examples. 4. Visualization of Equivalent Fractions: Use charts and diagrams, such as fraction bars or pie charts, to help students visualize equivalent fractions. 5. Practical Applications: Present practical examples where equivalent fractions are used, such as in cooking recipes and construction measurements, reinforcing the importance of the concept in daily life.

Classroom Questions

1. What is the equivalent fraction to 2/3 by multiplying the numerator and denominator by 2? 2. Simplify the fraction 6/9 to its irreducible form. 3. List two fractions equivalent to 3/4.

Questions Discussion

Duration: 20 - 25 minutes

The purpose of this stage is to consolidate students' learning through a detailed discussion of the answers to the questions presented in the Development stage. This stage aims to ensure that students fully understand the concept of equivalent fractions, promoting reflection and active engagement in the learning process. Additionally, it provides a moment to clarify doubts and reinforce the knowledge acquired.

Discussion

• 📌 What is the equivalent fraction to 2/3 by multiplying the numerator and denominator by 2?

• Explain that to find an equivalent fraction, you can multiply the numerator and denominator by the same number. In this case, multiplying both by 2 gives us: (2 x 2)/(3 x 2) = 4/6. Therefore, the equivalent fraction to 2/3 is 4/6.

• 📌 Simplify the fraction 6/9 to its irreducible form.

• To simplify a fraction, it is necessary to find the greatest common divisor (GCD) between the numerator and denominator. The GCD of 6 and 9 is 3. Dividing both by the GCD, we have: 6 ÷ 3 / 9 ÷ 3 = 2/3. Therefore, the simplified fraction of 6/9 is 2/3.

• 📌 List two fractions equivalent to 3/4.

• To find equivalent fractions, simply multiply or divide the numerator and denominator by the same number. Multiplying by 2: (3 x 2)/(4 x 2) = 6/8. Multiplying by 3: (3 x 3)/(4 x 3) = 9/12. Therefore, two fractions equivalent to 3/4 are 6/8 and 9/12.

Student Engagement

1. 📚 Questions and Reflections to Engage Students: 2. 1. Why is it important to identify equivalent fractions? How can this be useful in your daily life? 3. 2. If you had to explain to a friend what equivalent fractions are, how would you do it? 4. 3. Think of a situation in the kitchen or in construction where you would use equivalent fractions. Can you share an example? 5. 4. Do you think all fractions can be simplified? Why?

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to recap the main points presented in the lesson, ensuring that students have a solid understanding of the concepts covered. Additionally, this stage reinforces the connection between theory and practice, highlighting the relevance of the topic to students' daily lives and consolidating their learning.

Summary

• Concept of Equivalent Fractions: Equivalent fractions are different fractions that represent the same amount.
• Method of Simplifying Fractions: Find the greatest common divisor (GCD) to simplify fractions to their irreducible form.
• Identification of Equivalent Fractions: Multiply or divide the numerator and denominator by the same number.
• Visualization of Equivalent Fractions: Use charts and diagrams to help visualize equivalent fractions.
• Practical Applications: Equivalent fractions are used in cooking recipes, construction measurements, among others.

The lesson connected theory with practice by using everyday examples, such as dividing pizzas and measurements in cooking recipes, to demonstrate equivalent fractions. Students visualized how different fractions can represent the same amount through charts and diagrams, making learning more concrete and applicable to daily life.

Understanding equivalent fractions is essential for various practical situations, from following cooking recipes to making precise measurements in construction. Knowing how to identify and simplify fractions facilitates problem-solving in mathematics and understanding proportions in the real world, making learning relevant and useful.