Objectives (5 - 7 minutes)

1. Understanding the concept of fractions: Students should be able to understand that fractions represent parts of a whole, and that the denominator indicates the total number of parts the whole was divided into, while the numerator represents the number of parts we are considering.

2. Identifying and representing fractions in geometric shapes: Students should be able to identify fractions in geometric shapes, such as circles, squares, and rectangles, and represent them visually using colors or shading.

3. Composing shapes using fractions: Students should be able to compose different shapes from fractions, combining fractions of different sizes and shapes to form a new figure.

Secondary objectives:

• Develop logical reasoning skills: Through the manipulation of shapes and fractions, students will be encouraged to think logically and make decisions based on their observations.

• Promote collaboration and teamwork: Group activities will encourage students to share ideas, discuss solutions, and work together to achieve a common goal.

Introduction (10 - 12 minutes)

1. Recalling previous content: The teacher starts the lesson by reminding students about the concepts of parts of a whole, which were covered in previous classes. He can use visual examples, such as a pizza being divided into slices, or a cake being cut, to illustrate the concept. Additionally, the teacher can ask simple questions to check students' understanding, such as "If we have a pizza and we divide it into 8 slices, what fraction of the whole does each slice represent?".

2. Problem-solving situations: The teacher presents two problem-solving situations to engage students. The first one could be: "Have you ever seen a die? It has six sides, right? Now, imagine that each side of the die represents a slice of a pizza. If we roll the die, and it lands with the number 4 facing up, what fraction of the pizza does it represent?". The second problem-solving situation could be: "If we have a rectangle and we divide it into two equal parts, what fraction of the rectangle does each part represent?".

3. Contextualization: The teacher explains that understanding fractions is very important in our daily lives. He can give examples of everyday situations where we use fractions, such as dividing a cake at a birthday party, sharing toys with friends, or even in cooking activities, where we need to measure ingredients. He can also mention that fractions are widely used in many areas, such as science, art, and even music.

4. Introducing the topic: The teacher introduces the lesson topic, "Fractions: Composing Shapes", explaining that they will learn to represent and manipulate fractions using geometric shapes. For example, he can say: "Did you know that fractions can be represented not only by numbers, but also by shapes? Today, we will learn to represent and work with fractions using shapes like circles, squares, and rectangles. And, by the end of the lesson, you will be able to create your own shapes using fractions!".

5. Capturing students' attention: The teacher can share an interesting fact to capture students' attention. He can say: "Did you know that the ancient Egyptians were some of the first to use fractions? They used fractions to measure lands, divide wealth, and even to build their pyramids! So, when you are learning about fractions, remember that you are using a tool that has been used for thousands of years!".

With these strategies, students should be prepared and motivated to start exploring the wonderful world of fractions!

Development (20 - 25 minutes)

1. Activity: "Dividing the Pizza" (10 - 12 minutes)

   • The teacher organizes the class into groups of 3 to 4 students and gives each group a large sheet of paper and colored pencils.
   • Each group is instructed to draw a whole pizza on their sheet of paper, and then they must divide the pizza into equal fractions (for example, 1/2, 1/3, 1/4, 1/6, etc.), as if they were cutting the pizza for several people.
   • After the division, the teacher asks each group to choose a fraction and color the corresponding amount on the pizza. For example, if the group chooses 1/4, they should color a quarter of the pizza.
   • Next, the teacher asks questions to each group, such as "What fraction of the pizza is colored?" or "If we divide the pizza equally between two friends, what fraction would each receive?".
   • This activity allows students to visualize and manipulate fractions in a concrete and fun way. Additionally, it helps reinforce the concept of fractions as parts of a whole.

2. Activity: "Colored Rectangles" (10 - 12 minutes)

   • The teacher continues with the same group organization and gives each group a sheet of paper with several rectangles drawn on it.
   • The group's task is to color a specific fraction of each rectangle. For example, "Color 1/4 of a rectangle", "Now color 1/3 of another rectangle", and so on.
   • After completing the task, the teacher asks questions to each group, such as "What fraction of the rectangle is colored?" or "If we have two colored rectangles, what fraction of the whole do they represent together?".
   • This activity helps reinforce the idea that fractions can represent different quantities depending on the size of the whole, and also the practice of coloring fractions of rectangles, which is a fundamental skill in mathematics.

3. Activity: "Fraction Puzzle" (10 - 12 minutes)

   • The teacher proposes the fraction puzzle activity, where each group receives a set of puzzle pieces with different fractions drawn on them.
   • The students' task is to assemble the puzzle in a way that the fractions represented by the assembled pieces add up to 1 (or a whole).
   • The teacher circulates around the room, assisting the groups in solving the puzzle and asking questions to stimulate discussion and mathematical reasoning.
   • This activity is a fun way to engage students in problem-solving related to fractions, while developing their problem-solving and logical reasoning skills.

The proposed activities are interactive and encourage active student participation. They allow students to manipulate and experiment with fractions in a concrete way, which can help in understanding and retaining the concept of fractions. Additionally, group activities promote collaboration and teamwork, important skills for social and emotional development of students.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher gathers all students and asks each group to share their discoveries and solutions for the activities carried out. Each group should explain how they divided the pizza, colored the rectangles, and solved the fraction puzzle.
   • While the groups are presenting, the teacher can ask additional questions to stimulate reflection and deepen understanding, such as "Why did you choose to divide the pizza into 8 slices?", "How do you know that 1/4 of a rectangle is equal to 2/8?", or "What did you learn about how fractions behave when you were solving the puzzle?".
   • Group discussion allows students to learn from each other, share different approaches to problem-solving, and reinforce their understanding of the concept of fractions.

2. Connection with Theory (3 - 5 minutes)

   • After the groups' presentations, the teacher makes the connection between the practical activities and the theory. He can reinforce important concepts, such as the numerator and denominator of a fraction, and how fractions represent parts of a whole.
   • For example, he can point to the pizzas drawn by the students and say: "Look, when we divide the pizza into slices, each slice represents a part of the whole, and the number of slices we choose to color represents the numerator of the fraction. The total number of slices in the pizza represents the denominator of the fraction.".
   • The teacher can also use the shapes colored by the students to reinforce the idea that the fraction of a shape depends on the size of the whole. For example, he can say: "See, when we divide the rectangle into parts, the fraction we color depends on the total number of parts in the rectangle. If we have more parts, the fraction we color will be smaller, and if we have fewer parts, the fraction we color will be larger.".
   • This connection between theory and practice is essential for students to be able to transfer their knowledge and skills to other situations and contexts.

3. Final Reflection (2 - 3 minutes)

   • Finally, the teacher proposes that students reflect for a minute on what they learned in the lesson. He asks two simple questions to guide the reflection:
     1. "What was the most interesting part of today's lesson and why?"
     2. "How can you use what you learned today in your lives?"
   • The teacher can ask some students to share their answers with the class. This not only helps consolidate learning, but also values the different perspectives and experiences of students.

The return is a crucial part of the lesson plan, as it allows the teacher to assess students' understanding, reinforce important concepts, and promote reflection and connection with practice. Additionally, it helps create an active and engaging learning environment, where students are encouraged to think critically, share ideas, and learn from each other.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher starts the conclusion by summarizing the main points covered during the lesson. He reinforces that fractions represent parts of a whole, where the numerator indicates the number of parts we are considering and the denominator indicates the total number of parts the whole was divided into.
   • He also emphasizes the importance of understanding fractions in visual form, using geometric shapes like circles, squares, and rectangles, and encourages students to continue exploring and practicing the manipulation of fractions in a concrete way.

2. Connection between Theory and Practice (1 - 2 minutes)

   • The teacher explains that the lesson was structured to connect the theory of fractions with practice, through the activities of dividing pizza, coloring rectangles, and solving puzzles. He reinforces that fractions are not just an abstract concept, but something we can see and touch, and that we can use geometric shapes to help us understand and represent fractions more clearly.

3. Extra Materials (1 - 2 minutes)

   • The teacher suggests some additional materials for students to explore at home. These may include interactive online games involving the manipulation of fractions, children's books that address the concept of fractions in a playful way, and educational videos that demonstrate the application of fractions in real life.
   • He may also suggest that students practice manipulating fractions in their daily activities, such as dividing snacks into equal parts, or sharing toys with siblings or friends.

4. Importance of the Subject (1 minute)

   • Finally, the teacher highlights the importance of the subject. He emphasizes that fractions are a fundamental part of mathematics, and that the ability to understand and work with fractions is essential for many daily tasks, from dividing a pizza to measuring ingredients in a recipe.
   • He also mentions that the ability to think in terms of fractions can help students develop a more analytical and logical thinking, and solve problems more effectively.

With this conclusion, students should have a clear understanding of what was learned in the lesson, and should be encouraged to continue exploring and practicing the concept of fractions. Additionally, they should be aware of the relevance of the subject to their lives and to their academic and personal development.