Objectives

1. Teach students to identify and understand the concept of equivalent fractions, explaining that equivalent fractions are fractions that represent the same amount of a total amount.
2. Develop students' ability to recognize equivalent fractions, through practical examples and visual illustrations.
3. Provide students with the opportunity to manipulate and explore equivalent fractions in a playful way, through games and group activities.

During this stage, the teacher should clearly explain the objectives of the lesson, ensuring that all students understand what will be learned. It should also be checked if there is any prior knowledge necessary for understanding the topic and, if necessary, review it briefly.

Introduction

1. Reviewing concepts: The teacher begins the class by reminding students about the concept of a fraction, explaining that it represents a part of a whole. Examples from everyday life, such as dividing a pizza among friends, can be used to illustrate the concept.

2. Problem situations: The teacher proposes two problem situations for the students:

   • Situation 1: "If we have a whole chocolate bar and we divide it into four equal parts, each part is a fraction of the bar. Now, if we divide the same bar into eight equal parts, each part will still be a fraction of the bar. Do you think these fractions represent the same amount of chocolate? Why?"
   • Situation 2: "If we have a rectangle divided into four parts, and each part is painted red, and we have another rectangle divided into eight parts, and the same amount of parts is painted red, do these two rectangles represent the same amount of red? Why?"

3. Contextualization: The teacher explains that the idea of equivalent fractions is very important in mathematics and in everyday life. For example, in a cake recipe, we can use one cup of flour or two half-cups of flour, which are equivalent fractions, to represent the same amount. Or, when dividing a plot of land between two people, we can use equivalent fractions to represent the parts that belong to each one.

4. Getting the students' attention: The teacher presents two curiosities about fractions:

   • Curiosity 1: "Did you know that the ancient Egyptians were one of the first peoples to use fractions? They used fractions to measure land and build pyramids!"
   • Curiosity 2: "Did you know that fractions can also be used to represent whole numbers? For example, 1 is the same as 1/1, 2 is the same as 2/1, and so on."

During this stage, the teacher should ensure that all students are engaged and understanding the content presented. Encourage active student participation and answer any questions or concerns that may arise. This is an important time to capture students' interest and prepare them for the rest of the class.

Development

1. Equivalent Fractions Theory: The teacher begins this stage by explaining that equivalent fractions are fractions that represent the same amount, even if the numbers that compose them are different. A visual illustration of two pizzas, one divided into 4 pieces and the other into 8, can be used to show that even if the representation is different, the amount of pizza is the same.

2. Finding Equivalent Fractions: The teacher should then explain how to find equivalent fractions. First, students should be reminded that for a fraction to be equivalent to another, the numerator (top number) and the denominator (bottom number) must be multiplied (or divided) by the same number.

3. Multiplying to find Equivalent Fractions: The teacher can then show several examples of how to multiply a fraction to find an equivalent fraction. For example:

   • Multiply 1/2 by 2: 1/2 x 2 = 2/4
   • Multiply 2/3 by 3: 2/3 x 3 = 6/9
   • Multiply 3/4 by 4: 3/4 x 4 = 12/16

4. Dividing to find Equivalent Fractions: The teacher should then show several examples of how to divide a fraction to find an equivalent fraction. For example:

   • Divide 2/4 by 2: 2/4 ÷ 2 = 1/2
   • Divide 6/9 by 3: 6/9 ÷ 3 = 2/3
   • Divide 12/16 by 4: 12/16 ÷ 4 = 3/4

5. Guided Practice: The teacher should then propose some exercises for the students to solve on the board. Start with simpler exercises and gradually increase the complexity. For example:

   • 1/2 = __/4 (Answer: 2)
   • 3/4 = __/8 (Answer: 6)
   • 1/3 = __/9 (Answer: 3)

6. Practical Applications: The teacher should then propose some practical applications of equivalent fractions. For example:

   • "If I have 1/2 of a cake and I want to share it with two more friends, how many parts should I divide the cake into so that each one receives the same amount as me?" (Answer: 6 parts, because 1/2 is equivalent to 3/6).
   • "If I have 3/4 of a liter of juice and I want to divide it equally into 8 cups, how much juice will each cup have?" (Answer: 3/4 ÷ 8 = 3/32, so each cup will have 3/32 of a liter of juice).

During this stage, the teacher should ensure that all students are understanding the concepts presented. It is important to allow sufficient time for students to solve the exercises and to be available to answer any questions or doubts. The teacher should also encourage students to think critically about the practical applications of the concepts, fostering a deeper understanding of the topic.

Backlog

1. Group Discussion (5 - 7 minutes): The teacher begins this stage by promoting a group discussion on the solutions to the proposed exercises. Students are encouraged to share their answers and how they came up with them. The teacher should ask questions to verify that students have correctly understood the concept of equivalent fractions and how to find them. Some examples of questions that can be asked are:

   • "How do you know that these two fractions are equivalent? What did you do to find out?"
   • "What is the relationship between the numerator and the denominator when we multiply or divide to find equivalent fractions?"
   • "Can you think of other equivalent fractions for the ones we found in the exercises? How can we find them?"

2. Connection with the Theory (3 - 5 minutes): The teacher then connects the students' answers with the theory presented, reinforcing the concepts learned. For example, the teacher might say:

   • "When you said that these two fractions are equivalent because the result of multiplying (or dividing) the numerator and the denominator by the same number is the same, you are using the concept of equivalent fractions that we learned."
   • "When you found other equivalent fractions for the ones we gave in the exercises, you are applying the concept of equivalent fractions in practice."
   • "Can you think of other situations in which you could use the concept of equivalent fractions?"

3. Reflection (2 - 3 minutes): The teacher ends the class with a moment of reflection, asking students to think about what they have learned. Two simple questions are proposed to guide this reflection:

   • "What did you find most interesting about what you learned today about equivalent fractions?"
   • "How can you use what you learned today in your life outside of school?"

During this stage, the teacher should ensure that all students participate in the discussion and reflection. It is important to value the answers of all students and encourage them to express their opinions and thoughts. The teacher should also reinforce the concepts learned, connecting the theory with the practice and with the students' daily life. This helps to solidify the knowledge and the importance of the topic.

In addition, the moment of reflection allows the students to internalize what they have learned, making the learning experience more meaningful. At the same time, the teacher can assess the students' level of understanding and identify any areas that may need review or reinforcement.

Conclusion

1. Lesson Summary (2 - 3 minutes): The teacher begins the lesson conclusion by making a brief summary of the main points covered. He reinforces the concept of equivalent fractions, explaining that they are fractions that represent the same amount, even if the numbers that compose them are different. The teacher also recalls the strategies for finding equivalent fractions, either by multiplying or dividing the numerator and the denominator by the same number. He can do this through a chart on which he writes and highlights these points.

2. Connection between Theory and Practice (1 - 2 minutes): The teacher emphasizes how the lesson connected theory to practice. He highlights that, through the exercises and activities carried out, the students had the opportunity to apply the theoretical concepts of equivalent fractions. In addition, the teacher points out how the topic of equivalent fractions is relevant in everyday life, mentioning examples such as dividing a cake among friends or distributing land.

3. Extra Materials (1 minute): The teacher suggests extra materials for students who wish to deepen their knowledge on the subject. An educational video on equivalent fractions, an online game involving equivalent fractions, or a math book that explores the topic in more detail may be suggested. The teacher should also remind students that they can always reach out to him with any questions or additional questions.

4. Importance of the Subject (1 - 2 minutes): Finally, the teacher highlights the importance of the topic learned. He explains that understanding equivalent fractions is fundamental for the development of more complex mathematical skills. In addition, the teacher mentions that the ability to recognize and work with equivalent fractions is a useful skill in many real-life situations, such as in cooking, sharing resources, and even reading and writing decimal numbers.

During this stage, the teacher should ensure that all students understand the concepts presented and how they apply in practice. He should encourage students to continue exploring the topic outside of the classroom and to see mathematics as a relevant and interesting subject. At the same time, the teacher reinforces their availability and their role as a resource for students, helping to promote a positive and supportive learning environment.