Objectives (5 minutes)

1. Understand the concept of fractions as parts of a whole, focusing on geometric shapes. Students should be able to identify and draw fractions of simple geometric shapes, such as circles, rectangles, and squares.

2. Develop the ability to compose and decompose shapes using fractions. Students should be able to understand that different fractions can be used to compose a shape and that a shape can be decomposed into different fractions.

3. Practice reading and writing fractions. Students should be able to read and write fractions using the correct notation, with the numerator indicating the parts considered and the denominator indicating the total number of parts.

Introduction (10 - 15 minutes)

1. Reviewing concepts: The teacher starts the lesson by reviewing the students on the basic concepts of geometric shapes. He can use real geometric figures or images projected on the board to engage the students. The teacher can ask questions like: 'What is a circle?' or 'How many sides does a square have?' to assess the students' prior knowledge.

2. Problem-solving situations: The teacher then presents two problem-solving situations to introduce the concept of fractions as parts of a whole. First, he can show a cake and ask: 'If we divide this cake into 8 equal parts, and I eat 3 of these parts, what fraction of the cake did I eat?'. Second, he can show a rectangle and ask: 'If we paint 2 out of the 4 parts of this rectangle blue, what fraction of the rectangle will be blue?'.

3. Contextualization: The teacher then explains that fractions are used in many everyday situations, such as dividing a pizza among friends or sharing a toy with siblings. He can use practical examples, like dividing an apple into equal parts, to illustrate the concept.

4. Gaining attention: To make the lesson more interesting, the teacher can share some curiosities. For example, he can say that the word 'fraction' comes from the Latin 'fractus', which means 'broken'. Or, he can show that fractions are used in many places, such as in cooking recipes, in time measurements (1/2 hour), and even in money (1/4 of a real).

5. Introduction of the topic: Finally, the teacher introduces the topic of the lesson, 'Fractions: Composing Shapes', explaining that the students will learn to use fractions to draw and compose geometric shapes. He can say that they will become 'masters of shapes' by the end of the lesson. The teacher should maintain a tone of enthusiasm and encouragement to engage the students in the topic.

Development (20 - 25 minutes)

1. Applying the concept of fractions in drawing shapes (10 - 12 minutes)

   • The teacher should prepare some geometric shapes (rectangles, squares, circles) cut out of cardboard and colored with bright colors.

   • Each group of students (composed of 3 or 4 students) receives a set of geometric shapes and some strips of paper.

   • The teacher then gives an instruction to each group, something like: 'You need to use the shapes and the strips of paper to represent the fraction of shapes that I mention. For example, if I say '1/4 of circles', you need to use the shapes and the strips of paper to draw 1/4 of a circle. If I say '3/4 of a square', you need to draw 3/4 of a square.'

   • The teacher should start with simple fractions, like 1/2 and 1/4, and then progress to more complex fractions, like 3/4 and 2/3.

   • The teacher circulates around the room, checking the progress of each group and offering help when needed.

2. Composing shapes with fractions (10 - 12 minutes)

   • The teacher will now do the opposite. He will show a complete shape (for example, a square) and ask how many triangles would be needed to compose the shape.

   • Then, the teacher will divide the class into groups and give each of them a different shape (square, rectangle, circle). The students' task will be to decompose the received shape into fractions of another shape (for example, a square into triangles, a circle into sectors).

   • The teacher can start with simple shapes and easy-to-calculate fractions, and gradually increase the complexity.

   • The teacher circulates around the room, checking the progress of each group and offering help when needed.

These activities allow students to visualize and manipulate fractions, facilitating the understanding of the concept. Additionally, they promote collaboration and communication among students, as they need to discuss and reach a consensus on how to draw and compose shapes with the given fractions.

Feedback (10 - 15 minutes)

1. Group discussion (5 - 7 minutes)

   • The teacher gathers all students in a large circle and asks each group to share the shapes they drew and the logic they used to compose or decompose the given shape.

   • The teacher calls one group at a time to present, encouraging all students to pay attention and ask questions if necessary. He should praise the effort and creativity of each group, reinforcing that the most important thing is the learning process.

2. Connection with theory (3 - 5 minutes)

   • After the presentations, the teacher makes the connection between the practical activities and the theory, reinforcing the concept of fractions as parts of a whole and the ability to compose and decompose shapes using fractions.

   • He can ask: 'Which fractions did you use to compose/decompose the shapes?' or 'How did you know how many parts were needed to compose the given shape?'.

3. Individual reflection (2 - 3 minutes)

   • Finally, the teacher proposes that students reflect on what they learned in the lesson. He can ask two simple questions to guide the reflection:

     1. 'What did you find most interesting about fractions and shapes?'
     2. 'How can you use what you learned today in everyday situations?'

   • The teacher gives a minute for students to think about their answers and then invites some of them to share their reflections with the class.

Feedback is an essential part of the lesson, as it allows the teacher to assess students' understanding of the topic and reinforce key concepts. Additionally, it promotes reflection and critical thinking, important skills for students to develop throughout their lives.

Conclusion (5 - 10 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher starts the conclusion by giving a brief summary of the main points covered in the lesson. He recaps that fractions are parts of a whole and can be used to represent and draw parts of geometric shapes.

   • He also reminds that fractions can be used to compose and decompose shapes, and that the numerator indicates the parts considered and the denominator indicates the total number of parts.

   • The teacher can use the board or whiteboard to write some examples of fractions and their representations in geometric shapes, reinforcing visual learning.

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

   • Next, the teacher explains how the lesson connected theory (fraction concept) with practice (drawing and composing shapes with fractions).

   • He can say: 'We learned about fractions and how they represent parts of a whole. Then, we used this idea to draw and compose shapes. This helped us better understand the concept of fractions and apply it in a practical way.'

3. Extra Materials (1 - 2 minutes)

   • The teacher then suggests some extra materials for students to deepen their studies on fractions and geometric shapes. He can recommend math books with practical activities, educational websites with interactive games, or math apps for mobile devices.

   • He can say: 'If you want to practice more with fractions and shapes, I recommend the book 'Fun Math: Fractions and Shapes' or the website 'Matific', which has many cool games on the subject.'

4. Subject Importance (1 - 2 minutes)

   • Finally, the teacher concludes the lesson by emphasizing the importance of the subject learned for everyday life. He can say: 'Fractions are used in many everyday situations, such as dividing a pizza, sharing a toy, or following a cooking recipe. Understanding fractions and how they relate to shapes can help us solve problems and make decisions more effectively.'

The conclusion is a crucial part of the lesson, as it reinforces the main learning points, connects theory with practice, and motivates students to continue learning about the subject. Additionally, it highlights the relevance of what was learned for students' lives, encouraging the application of knowledge in real-life situations.