Objectives (5-7 minutes)

1. Understand the Roman numeral system: Students should be able to understand the basic structure of the Roman numeral system, including the specific rules for combining numerals and representing numbers.

2. Convert decimal numbers into Roman numerals: Students should be able to convert decimal numbers (up to 100) into Roman numerals, by applying the rules previously learned, and developing their critical thinking and mathematical logic skills.

3. Identify and apply Roman numerals to real-life contexts: Students should be able to recognize and apply Roman numerals to everyday situations such as clocks, works of art, page numbering, etc. This will help strengthen the topic’s relevance and its practical utility.

Secondary Objectives:

• Develop critical thinking skills and mathematical logic: By manipulating and converting Roman numerals, students will have the opportunity to refine their logical and mathematical reasoning abilities.

• Foster curiosity and interest in mathematics: The use of practical, everyday examples along with the associated history and culture around Roman numerals aims to trigger the curiosity and interest of the students in the topic.

Introduction (10-15 minutes)

1. Prior knowledge check: The teacher starts the lesson with a brief review of the decimal system, highlighting the role and value of each numeral in the formation of the numbers. This review is important so that the students can compare and contrast the decimal numeral system to the Roman numeral system, which is the focus of the lesson. (3-5 minutes)

2. Initial problem situations: The teacher presents two problem situations to trigger students' interest in the topic:

   • "How do you think the Romans counted before the decimal system was invented?"
   • "Have you noticed that Roman numerals are frequently used in clocks and some film titles? Why do you suppose this happens?" (2-3 minutes)

3. Introduction to the topic: The teacher emphasizes the importance and relevance of Roman numerals in everyday life, mentioning examples such as chapter numbering in books, certain document pages, the indication of centuries and millennia, in addition to their presence on historical monuments and emblems of organizations. (2-3 minutes)

4. The presentation of the topic: The teacher introduces the topic of Roman numerals, explaining that Romans used a different numbering system from ours, and that although this system is no longer widely used, it is still important to know how to read and use it.  To pique the curiosity of the students, the teacher can mention that Roman numerals are one of the few things we still use today that dates back to the Roman Empire. (2-3 minutes)

5. Trivia and stories: The teacher can share some fun facts and stories related to the use of Roman numerals. For instance: since the number zero was not part of the Roman system, they had a hard time doing more complex calculations and therefore could not advance in mathematics as civilizations that used the decimal system did. Another curiosity is that Roman numerals are often used in fantasy and science fiction film titles to convey a sense of antiquity and mystery. (3-4 minutes)

Development (20-25 minutes)

1. Theory: Roman Numerals (10-12 minutes)

   1.1. Explanation of the origin and structure:: The teacher begins by explaining that Roman numerals are a numbering system that was used in Ancient Rome and much of Europe until the 14th century. He/She highlights that the Romans used letters from their alphabet to represent numbers and that each letter had a specific numerical value. (3-4 minutes)

   1.2. Introduction of the symbols and their values: Next, the teacher presents the symbols of the Roman numerals (I, V, X, L, C, D, M) and their respective values (1, 5, 10, 50, 100, 500, 1000).  For an easier understanding, the teacher can draw a table on the board or virtual whiteboard, displaying the symbols and their corresponding values (3-4 minutes)

   1.3. Combination rules:  The teacher explains the combination rules, which are essential for the correct writing and reading of Roman numerals. He/She highlights that a lower value symbol on the right of a higher value symbol subtracts from the larger value and that a lower value symbol on the left of a higher value symbol adds to the larger value. To illustrate, the teacher can write a few examples on the board and ask students to explain the value of each numeral (3-4 minutes)

2. Practice: Converting decimal numbers to Roman numerals (10-12 minutes)

   2.1. Explanation of the conversion process: The teacher explains that the conversion of decimal numbers into Roman numerals involves identifying the Roman numerals that correspond to each digit of the decimal number and combining them according to the rules previously presented. He/She stresses that, to avoid mistakes, it is important to convert the digits one at a time, starting with the leftmost digit (3-4 minutes)

   2.2. Practical examples: The teacher then presents a few examples of decimal numbers and asks students to convert them into Roman numerals. He/She encourages the students to work in pairs or small groups to discuss their solutions. The teacher circulates around the room, offering support and clarifying any doubts as needed (4-5 minutes)

   2.3. Discussion and Clarification of doubts: The teacher leads a classroom discussion, asking different groups to share their solutions and explaining the reasoning behind each conversion. He/She also uses this time to clarify any doubts that the students may have (3-4 minutes)

3. Ludic Activity: Board game “Mathematical Rome” (optional, 5-8 minutes)

   3.1. The teacher can choose to include a fun activity to make learning more enjoyable and engaging. The board game “Mathematical Rome” is an interesting option, where students, in small groups, have to advance on the board by answering questions about Roman numerals to win the game. The teacher can create the questions in advance, focusing on different aspects of the Roman numerals like values, combination rules, and conversion of decimal numbers (5-8 minutes)

   3.2. This activity not only reinforces the students' learning, but also promotes collaboration and healthy competition among them, making the lesson more dynamic and fun.

At the end of this stage, students should have become familiar with Roman numerals, should be capable of converting decimal numbers into Roman numerals, and should be able to apply this knowledge to real-world contexts. In addition, they should have developed critical thinking and mathematical logic skills as well as demonstrated interest and curiosity in the topic.

Closure (8-10 minutes)

1. Group discussion (3-5 minutes): The teacher reunites all the students and facilitates a group discussion about the practical activity performed.  He/She can ask questions such as:

   1.1. "What were the main difficulties encountered in converting decimal numbers to Roman numerals? How did you overcome them?"

   1.2. "Were you able to identify the real-life application of Roman numerals? What examples did you find?"

   1.3. "How did the board game contribute to your learning? what did you find most enjoyable/challenging about it ?"

   The goal of this discussion is to allow the students to share their experiences, clarify remaining doubts, and reflect on what they have learned. Furthermore, it provides the teacher with an opportunity to assess the students' understanding and identify any knowledge gaps that need to be addressed.

2. Connection with the theory (2-3 minutes): The teacher then asks the students to reflect on how the practice connects with the theory presented. He/She can have the students, in pairs or small groups, discuss and write down on a piece of paper what they have learned about Roman numerals, their combination rules, and the conversion of decimal numbers into Roman numerals. The teacher circulates around the room, offering support and clarifying doubts as needed.

3. ** Final reflection (1-2 minutes)**: To conclude the lesson, the teacher has the students silently reflect for one minute on the following questions:

   3.1. "What was the most important concept you learned today?"

   3.2. "What questions still remain unanswered?"

   After the one minute of reflection, the teacher may ask some students to share their answers with the class. This not only allows the teacher to evaluate the students' learning, but also gives students an opportunity to voice their opinions and questions, fostering an open and inclusive learning environment.

4. Feedback and guidance for the next lesson (1 minute): At the end of the lesson, the teacher thanks the students for their participation, provides general feedback on the class performance, and previews briefly the topic that will be addressed in the next lesson. He/She can also provide guidance on what the students should review at home and what extra exercises or readings they should complete in advance for the next lesson.

Conclusion (5-7 minutes)

1. Summary and Recapitulation (2-3 minutes): The teacher summarizes the key points of the lesson, reinforcing the origin and structure of Roman numerals, the combining rules, and the conversion of decimal numbers into Roman numerals. He/She can recall the practical examples and re-explain the reasoning behind each one.  The teacher can also use this time to clear up any doubts that may still exist.

2. Connection between Theory, Practice, and Applications (1-2 minutes): The teacher emphasizes how the lesson connected the theory (concepts of Roman numerals, rules, and uses) with the practice (converting decimal numbers to Roman numerals), and real-world applications (uses of Roman numerals in the real world). He/She can highlight how understanding the Roman numeral system can be useful in various contexts such as reading clocks, interpreting movie titles, and appreciating art and architecture.

3. Complementary Materials (1-2 minutes): The teacher suggests additional study materials for students who wish to broaden their understanding about Roman numerals. These materials could include explanatory videos, online interactive games, extra practice exercises, and readings on the history and application of Roman numerals.

4. Importance of the Topic and Next Steps (1 minute): Finally, the teacher highlights the importance of the topic of Roman numerals not only as a mathematical concept but also as a part of human culture and history. He/She may mention that although Roman numerals are not as commonly used today, they still appear in many places and therefore it is worthwhile to know how to use and interpret them. The teacher may also preview what will be covered in the next lesson, reinforcing the need for continued practice and self-study for success in learning mathematics.