Objectives (5 - 7 minutes)

Main Objectives:

1. Develop the ability to convert between fractions and decimal numbers, with an emphasis on understanding the division operation and the perception that the fraction is the decimal representation of a non-exact number.
2. Apply the conversion between fractions and decimal numbers in practical situations, such as solving everyday math problems.
3. Reinforce mental calculation skills, as the conversion between fractions and decimal numbers is an operation that can be efficiently performed through mental calculation.

Secondary Objectives:

1. Stimulate critical thinking and mathematical logic, since the conversion between fractions and decimal numbers involves a series of steps that need to be followed correctly.
2. Promote active student participation in the class, encouraging discussion and problem-solving in groups.
3. Develop students' self-confidence in relation to mathematics, demonstrating that the conversion between fractions and decimal numbers is a skill that can be learned and mastered through practice and dedication.

Introduction (10 - 15 minutes)

1. Review of Related Content:

• The teacher should start the lesson by briefly reviewing the concepts of fractions and decimal numbers. It is important for students to remember that fractions are a way of expressing parts of a whole and that decimal numbers are a way of expressing quantities according to the base 10.
• The teacher can use practical and visual examples to reinforce these concepts. For example, they can show a pizza divided into fractions and a ruler with decimal markings.

2. Problem Situations:

• Next, the teacher should present two problem situations involving the conversion between fractions and decimal numbers. For example, they can propose the following question: 'If we have 1/4 of a pizza, what does this represent in terms of decimal numbers?' or 'If we have 0.5 of a pizza, what does this represent in terms of fractions?'.
• These problem situations should be used to arouse students' interest in the subject and to demonstrate the relevance of the conversion between fractions and decimal numbers in real situations.

3. Contextualization:

• The teacher should then contextualize the importance of the subject, explaining that the conversion between fractions and decimal numbers is a fundamental skill in various areas of knowledge and everyday life, such as finance, science, engineering, among others.
• To illustrate this importance, the teacher can give examples of how the conversion between fractions and decimal numbers is used in practical situations. For example, they can mention that in finance, it is common to work with interest rates expressed in decimal form, and that in science, many measurements are expressed in decimal numbers.

4. Introduction to the Topic:

• To introduce the topic of conversion between fractions and decimal numbers, the teacher can share some interesting curiosities or stories related to the subject. For example, they can tell the story of how decimal notation was developed in the Arab world in the 9th century, or how the Babylonians, who used a numerical system based on 60, probably did not have the same difficulty as us in converting between fractions and decimal numbers, since 1/3 = 0.2 in the Babylonian system.
• The teacher can also mention that the conversion between fractions and decimal numbers is a skill that can be very useful in board games and in bets, since probabilities are often expressed in the form of fractions or decimal numbers.

Development (20 - 25 minutes)

1. Theory Presentation:

• The teacher should start by explaining that the conversion between fractions and decimal numbers is a fundamental skill in mathematics and that it involves understanding that a fraction can be seen as a division and that a division can be seen as a fraction.
• They should then explain that to convert a fraction into a decimal number, you just need to divide the numerator by the denominator. For example, to convert 1/4 into a decimal number, just divide 1 by 4, resulting in 0.25.
• The teacher should also explain that to convert a decimal number into a fraction, you just need to write the decimal number as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places. For example, to convert 0.5 into a fraction, just write 0.5 as 5/10 and simplify the fraction to get 1/2.
• The teacher should demonstrate these calculations on the board, using concrete examples. For instance, they can convert 3/8 into a decimal number and 0.125 into a fraction.

2. Practical Exercises:

• After the theory presentation, the teacher should propose a series of practical exercises for the students. These exercises should include the conversion of fractions into decimal numbers and decimal numbers into fractions.
• The teacher should start with simpler exercises and gradually increase the difficulty. For example, they can start with the conversion of fractions with denominators 10 and 100 into decimal numbers and the conversion of decimal numbers with one decimal place into fractions with denominators 10 and 100. Then, they can move on to the conversion of fractions with other denominators into decimal numbers and decimal numbers with two decimal places into fractions with larger denominators.
• The teacher should walk around the classroom, observing the students' progress, answering any questions, and providing immediate feedback.

3. Group Discussion:

• After the students have worked on the exercises for a while, the teacher should promote a group discussion. They should ask students to share their strategies for the conversion between fractions and decimal numbers and to explain how they arrived at their answers.
• The teacher should use this discussion to clarify any misunderstandings and to reinforce the concepts that were addressed in the lesson. For example, they can ask a student to explain how they converted 3/8 into 0.375 or how they converted 0.875 into 7/8.

4. Discussion of Practical Applications:

• Finally, the teacher should discuss some practical applications of the conversion between fractions and decimal numbers. For example, they can mention that this skill is used in various areas of everyday life, such as finance, science, engineering, among others.
• The teacher should encourage students to think about other situations where the conversion between fractions and decimal numbers can be useful and to share these situations with the class.

Return (5 - 7 minutes)

1. Review of Content:

• The teacher should start the Return phase by reviewing the main concepts covered in the lesson. They should remind students about the definition of fractions and decimal numbers, the difference between them, and the correct way to convert between them.
• To do this, the teacher can ask direct questions to the students, asking them to explain in their own words the concepts and conversion strategies between fractions and decimal numbers.

2. Connection to Practice:

• Next, the teacher should ask students to reflect on how what was learned in the lesson connects to the real world and to other disciplines. For example, they can ask: 'How can the conversion between fractions and decimal numbers be useful in everyday situations?' or 'In which other disciplines, besides mathematics, do you think the conversion between fractions and decimal numbers can be used?'.
• The teacher should encourage students to share their ideas and experiences, promoting an open and respectful discussion.

3. Individual Reflection:

• The teacher should then propose that students make an individual reflection on what they learned in the lesson. They can ask them to write down on a piece of paper or in their notebooks the answers to the following questions:
  1. What was the most important concept you learned today?
  2. What questions do you still have about the conversion between fractions and decimal numbers?
• The teacher should give a minute for students to think about these questions and then ask them to share their answers with the class. They should use these answers to assess students' understanding and to identify possible points of confusion that need to be addressed in future lessons.

4. Feedback and Closure:

• Finally, the teacher should provide feedback to students on their performance in the lesson. They should praise students' efforts and achievements, while also pointing out areas that need improvement.
• The teacher should end the lesson by reinforcing the importance of the conversion between fractions and decimal numbers and encouraging students to practice this skill at home. For example, they can suggest that students solve some conversion problems in their free time or look for real-life situations where this skill can be applied.
• Finally, the teacher should thank the students for their participation, wish them a good day, and remind them that they will be available for any questions or help they may need.

Conclusion (3 - 5 minutes)

1. Recap of Content:

• The teacher should start the Conclusion by summarizing the main points covered during the lesson. They should remind students of the concepts of fractions and decimal numbers, the importance of the conversion between them, and the strategies to perform this conversion.
• For this, the teacher can give a brief summary of the examples and exercises carried out during the lesson, highlighting the difficulties encountered by students and the solutions found.

2. Connection between Theory, Practice, and Applications:

• Next, the teacher should emphasize how the lesson connected the theory, practice, and applications of the conversion between fractions and decimal numbers. They should explain that the lesson began with a theoretical review of the concepts, followed by a series of practical exercises and a discussion on the applications of the skill.
• The teacher should reinforce that the ability to convert between fractions and decimal numbers is not just a matter of solving math problems, but also a useful tool in various areas of life, such as finance, science, and engineering.

3. Suggestion of Extra Materials:

• The teacher should then suggest some extra materials for students who wish to deepen their knowledge of the conversion between fractions and decimal numbers. These materials may include math books, educational websites, YouTube videos, math games, among others.
• The teacher should remind students that learning mathematics is a continuous process and that regular practice is the key to success. They should encourage students to study a little every day and not let their doubts accumulate.

4. Importance of the Subject for Everyday Life:

• Finally, the teacher should reinforce the importance of the conversion between fractions and decimal numbers in everyday life. They can give concrete examples of how this skill can be used in everyday situations, such as reading food labels, understanding interest rates, solving engineering problems, among others.
• The teacher should end the lesson by reinforcing that mathematics is a practical and applicable discipline that can be used to solve real problems and to better understand the world around us.