Objectives (5 - 7 minutes)

1. Understanding the concept of equivalent fractions: Students should be able to understand that equivalent fractions are fractions that represent the same quantity, even if their numerators and denominators are different. They should be able to recognize that, even though the fractions may look different, they can still represent the same quantity.

2. Identifying equivalent fractions: Students should be able to identify whether two fractions are equivalent or not. They should be able to compare fractions and realize that, even if they look different, if the represented quantity is the same, then the fractions are equivalent.

3. Building equivalent fractions: Students should be able to build equivalent fractions. They should be able to use the concept of equivalence to create fractions that represent the same quantity as a given fraction, but with different numerators and denominators.

Secondary objectives:

• Developing critical thinking: Students should be able to apply the concept of fraction equivalence in problem-solving situations, promoting the development of critical thinking and mathematical problem-solving.

• Encouraging cooperation: Students should be encouraged to work in groups, sharing ideas and strategies to solve problems. This will promote cooperation and teamwork.

Introduction (10 - 12 minutes)

1. Review of previous content: The teacher should start the lesson by reminding students about the concept of fractions and their use in everyday situations. They should review what numerator and denominator are and how they represent parts of a whole. Additionally, the teacher should reinforce the idea that different fractions can represent the same quantity.

2. Introductory problem-solving situations: The teacher can present two problem-solving situations to introduce the topic of equivalent fractions. The first situation could be: 'John ate 1/3 of a pizza and Mary ate 2/6 of the same pizza. Did they eat the same amount of pizza?'. The second situation could be: 'If we have two pizzas, one divided into 8 slices and another divided into 12 slices, what fraction of each pizza represents the same amount of pizza?'

3. Contextualization: The teacher should explain that equivalent fractions are used in many real-life situations. For example, when we receive a recipe and need to adjust the ingredient quantities to make more or less food, or when we need to divide an amount of money among a group of people.

4. Introduction to the topic: The teacher can introduce the topic of equivalent fractions with two curiosities. The first curiosity could be: 'Did you know that 1/2, 2/4, and 3/6 are all equivalent fractions? This means that they represent the same quantity, even though the numbers are different!'. The second curiosity could be: 'Have you heard of the 'Pizza Cutting Rule'? It's a simple way to understand equivalent fractions. If we cut a pizza into 4 slices and eat 2 slices, that's the same as cutting the pizza into 8 slices and eating 4 slices. Both situations represent half of the pizza!'.

5. Capturing students' attention: To spark students' interest, the teacher can show images of pizzas cut into different numbers of slices and ask: 'If I eat 3 slices of this pizza, how much did I eat? And if I eat 6 slices of this other pizza, how much did I eat?'. This can lead students to realize that, even with different quantities, the proportion of pizza they ate is the same, and therefore, the fractions are equivalent. Then, the teacher can propose a challenge: 'If I eat 4/6 of a pizza, what other equivalent fraction could represent the amount I ate?'.

Development (20 - 25 minutes)

1. 'Pizza Game' Activity (10 - 12 minutes):

   • Materials: Sheets of paper, colored pencils, drawings of pizzas (or empty circles to represent the pizzas) already divided into fractions (1/2, 1/3, 1/4, etc.), numbered chips from 1 to 10 (or playing cards with numbers from 1 to 10).

   • Procedure:

     • The teacher divides the class into groups of 4 or 5 students and provides each group with the necessary materials.
     • Each group receives a blank pizza drawing and a numbered chip (or a playing card) facing down.
     • In each round, a student from each group flips the numbered chip (or the playing card) and the group must color a fraction equivalent to the one drawn.
     • For example, if the drawn fraction is 1/2, the group can color 2/4, 3/6, 4/8, etc., on the pizza drawing.
     • The first group to correctly color an equivalent fraction shouts 'Pizza!' and earns a point.
     • The game continues until all pizza drawings have been colored. The group with the most points at the end of the game wins.

2. 'Cut and Paste' Activity (10 - 13 minutes):

   • Materials: Sheets of paper, colored pencils, scissors, glue, sheets printed with rectangles divided into different fractions (1/2, 1/3, 1/4, etc.) and blank rectangles.

   • Procedure:

     • The teacher divides the class into groups of 4 or 5 students and provides each group with the necessary materials.
     • Each group receives a sheet printed with rectangles divided into different fractions and a sheet with blank rectangles.
     • In each round, the teacher gives an instruction, for example: 'Cut a rectangle representing 1/3 and paste it on the blank rectangle. Now cut a rectangle representing 2/3 and paste it next to the first one. Do the two figures represent the same quantity? Why?'.
     • Students should discuss and answer the question. The teacher can walk around the room to assist and check students' understanding.
     • The teacher repeats the process with other fractions, always asking if the figures represent the same quantity and why.
     • The game continues until all rectangles have been pasted. The group that can best justify their answers wins.

3. 'Fraction Puzzle' Activity (10 - 15 minutes):

   • Materials: Sheets of paper, colored pencils, puzzle drawings with equivalent fractions, sheets with blank rectangles and fractions to be cut.

   • Procedure:

     • The teacher divides the class into groups of 4 or 5 students and provides each group with the necessary materials.
     • Each group receives a puzzle drawing with equivalent fractions and a sheet with blank rectangles.
     • In each round, the teacher gives a fraction to the group, for example, 2/4. Students must color or cut a rectangle representing that fraction and fit it into the puzzle.
     • Then, the group must find a fraction equivalent to the one given and color or cut another rectangle representing that fraction and fit it into the puzzle.
     • The group should continue finding equivalent fractions until the puzzle is complete.
     • The game continues until all puzzles have been completed. The group that completes the most puzzles wins.

The teacher can choose the activity that best fits the class dynamics. All activities are playful and allow students to interact with the concept of equivalent fractions in a practical and fun way. During the activities, the teacher should circulate around the room, observing students' work, clarifying doubts, and providing guidance as needed.

Feedback (8 - 10 minutes)

1. Group discussion (3 - 4 minutes):

   • The teacher should gather all students in a large circle and promote a group discussion. Each group should share their discoveries and solutions found during the practical activities.
   • The teacher can ask a student from each group to explain how they determined that two fractions were equivalent and how they created equivalent fractions.
   • During the discussion, the teacher should ask questions to verify students' understanding and for them to learn from each other. For example, 'Why do you think 1/2 and 2/4 are equivalent fractions?' or 'How did you create a fraction equivalent to 3/5?'.

2. Connection to theory (2 - 3 minutes):

   • After the discussion, the teacher should reinforce the connection between the practical activities and the theory. The teacher should explain that the practical activities were designed to help them understand the concept of equivalent fractions and how to create them.
   • The teacher can use the pizza drawings, rectangles, and puzzles as concrete examples to illustrate the concept. For example, the teacher can show that even if the pizza is divided into different slices, if the amount of pizza we eat is the same, then the fractions are equivalent.

3. Individual reflection (3 - 4 minutes):

   • The teacher should propose that students reflect on what they learned in the lesson. For this, the teacher can ask two simple questions and ask students to think about them for a minute before answering.
     • Question 1: 'How can you use what you learned today about equivalent fractions in real-life situations?'
     • Question 2: 'What did you find most challenging in today's lesson? What did you find most enjoyable?'

4. Sharing reflections (1 - 2 minutes):

   • After the reflection time, the teacher should ask some students to share their answers with the class. This not only allows students to express themselves but also helps the teacher assess students' learning and the effectiveness of the lesson.

Throughout the feedback session, the teacher should maintain a welcoming and encouraging environment, valuing each student's contributions and reinforcing learning strengths. Feedback is a crucial part of the lesson, as it allows the teacher to assess students' understanding, correct any misunderstandings, and consolidate learning.

Conclusion (5 - 7 minutes)

1. Content summary (2 - 3 minutes):

   • The teacher should start the conclusion by summarizing the main points covered in the lesson. This includes the concept of equivalent fractions, the idea that equivalent fractions represent the same quantity, even if the numbers are different, and how to build equivalent fractions.
   • The teacher can recall the problem-solving situations solved by students during the practical activities and highlight how the concept of equivalent fractions was applied to solve these problems.
   • Additionally, the teacher should reinforce the importance and applicability of equivalent fractions in everyday situations, such as in cooking, task division, and problem-sharing.

2. Connection between theory, practice, and applications (1 - 2 minutes):

   • The teacher should explain how the lesson connected theory, practice, and applications. The teacher can highlight how the practical activities allowed students to explore and apply the concept of equivalent fractions in a concrete and playful way.
   • Additionally, the teacher can mention how the real-life situations presented during the lesson helped make the content more meaningful and relevant to students.

3. Suggestions for additional materials (1 minute):

   • The teacher should suggest some additional materials for students who wish to deepen their understanding of equivalent fractions. These materials may include interactive online games, explanatory videos, children's books on mathematics, and educational apps.
   • The teacher can share some links or book titles with students and encourage them to explore these resources at home or in the school library.

4. Importance of the subject for everyday life (1 minute):

   • Finally, the teacher should emphasize the importance of the content learned for students' daily lives. The teacher can mention again the everyday situations where equivalent fractions are used, such as in task division, cooking, and problem-sharing.
   • Additionally, the teacher can highlight how understanding equivalent fractions can help students develop critical thinking, problem-solving, and cooperation skills, which are essential skills not only in mathematics but in many other areas of knowledge and life.

The teacher should conclude the lesson in a positive and encouraging manner, reinforcing that all students are capable of understanding and applying the concept of equivalent fractions. The teacher should remind students that practice is fundamental for learning mathematics, and that they can continue exploring the subject at home and at school.