Objectives (5-10 minutes)

Main Objectives:

1. To understand the concept of numerical expressions and their importance in solving mathematical problems.
2. To develop skills to simplify and solve numerical expressions, following the order of operations.

Secondary Objectives:

1. To apply acquired knowledge in solving practical problems, developing logical and analytical thinking skills.
2. To encourage active student participation through practical activities and classroom discussions.

Learning Objectives:

1. Students should be able to identify and solve numerical expressions in different contexts.
2. Students should be able to explain the process of solving numerical expressions, including the order of operations.
3. Students should be able to apply the concept of numerical expressions to solve real-world problems, demonstrating the relevance of the topic.

Introduction (10-15 minutes)

1. Review of Previous Content:

   • The teacher will start the class by reviewing basic concepts of mathematical operations, such as addition, subtraction, multiplication and division. This review can be done either through direct questions to students or a short review game. (Estimated time: 5 minutes)

2. Problem situations:

   • The teacher will propose two problem situations to awaken student interest and introduce the topic of the class. The first could involve solving a simple numerical expression, like 2 + 3 x 5. The second could be a real-world problem that requires solving a numerical expression, like calculating the total cost of a purchase with a discount. (Estimated time: 5 minutes)

3. Contextualization:

   • The teacher will explain the importance that numerical expressions have in our everyday life, citing practical examples like the formula for calculating the area of a square or the order of operations used in cooking recipes. This contextualization will help students understand the relevance of the topic and motivate them to learn. (Estimated time: 2 minutes)

4. Introduction of the Topic:

   • The teacher will introduce the topic of numerical expressions, explaining that these are sequences of numbers and operations that need to be solved following a specific order. To make the introduction more interesting, the teacher can share curiosities about the history of numerical expressions, like the fact that ancient Egyptians already used a primitive form of numerical expressions in their constructions. (Estimated time: 3 minutes)

Development (20-25 minutes)

1. Numerical Expressions building activity:

   • The teacher will divide the class into groups of 4 to 5 students and provide each group with a set of cards with numbers and operations (addition, subtraction, multiplication and division). Each group will also receive a sheet of large paper and a marker.
   • Students will be tasked with creating their own numerical expressions on the paper, using the cards. They must make sure that their expressions contain at least three operations and that they follow the correct order of operations. For example, an expression could be: (3 + 4) x 2 - 5.
   • After building the expression, students should solve it manually and write the result on the paper.
   • The teacher should circulate throughout the room, offering help and guidance when necessary, but encouraging students to solve the problems on their own.
   • This activity helps students visualize numerical expressions and understand the importance of following the order of operations. In addition, it promotes collaboration and discussion among members of the group. (Estimated time: 10-15 minutes)

2. Activity of applying numerical expressions to real-world problems:

   • Still in their groups, students will receive a series of real-world problems that require solving a numerical expression. The problems could involve situations like calculating the total price of a purchase with a discount, determining a person's age in a specific year, or calculating an object's speed at a given time.
   • Students should read the problems, identify the necessary numerical expression and solve it. They should then write the answer in a sentence that answers the original problem. For example, if the problem is to calculate the total price of a discounted purchase, the answer could be: "The total price of the purchase with the discount is $XX."
   • The teacher should encourage students to discuss solution strategies and share their answers. He/she should also provide feedback and guidance as necessary.
   • This activity helps students apply the concept of numerical expressions to real-world contexts, which can increase their motivation and understanding of the topic. In addition, it promotes critical thinking and problem-solving. (Estimated time: 10-15 minutes)

Feedback (10-15 minutes)

1. Group Discussion (5-7 minutes):

   • After the conclusion of the group activities, the teacher should promote a class discussion. Each group should share the numerical expression they created and the solution they found.
   • During this discussion, the teacher should encourage students to explain the reasoning behind their solutions and justify why they believe they are correct. This will allow the teacher to assess students' understanding of the topic and correct any misunderstandings.
   • The teacher can also take advantage of this discussion to highlight effective solving strategies and reinforce the importance of following the order of operations.
   • To ensure that all students actively participate in the discussion, the teacher can assign a representative from each group to present their solutions. Alternatively, the teacher can solicit input from different students by asking direct questions.

2. Connection with the theory (3-5 minutes):

   • After the group discussion, the teacher should revisit the theoretical concepts presented in the Introduction of the class. He/she should explain how the practical activities connected with the theory and how they helped students better understand the topic.
   • The teacher can, for example, highlight how the numerical expression building activity allowed students to visualize the solving process and how the application activity to real-world problems demonstrated the relevance and usefulness of numerical expressions.

3. Individual reflection (2-3 minutes):

   • To conclude the class, the teacher should propose that students individually reflect on what they have learned. He/she can do this by asking students to answer questions such as:
     1. What was the most important concept you learned today?
     2. What questions have not yet been answered?
   • The teacher can ask students to write their answers on a piece of paper or share them orally. This reflection will help students consolidate their learning and allow the teacher to identify any areas that need reinforcement in future classes.

Conclusion (5-7 minutes)

1. Recapitulation of the content (2-3 minutes):

   • The teacher should begin the conclusion of the class by summarizing the main points covered during the class. This includes the definition of numerical expressions, the order of operations and the importance of solving numerical expressions correctly.
   • The teacher can do this through a short presentation, or by asking students to share what they remember from the topics discussed. This will help reinforce learning and identify any areas of confusion that may need to be addressed in future classes.

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

   • The teacher should then explain how the class connected theory, practice and applications. He/she can highlight how the numerical expression building activity allowed students to apply theory in a practical and visual way.
   • The teacher can also discuss how the application activity to real-world problems demonstrated the relevance and usefulness of numerical expressions. This will help reinforce the importance of the topic and motivate students to continue learning.

3. Extra materials and future studies (1-2 minutes):

   • The teacher should suggest extra materials for students who wish to deepen their understanding of the topic. This could include books, websites, videos or educational games that address numerical expressions.
   • The teacher can also propose related topics that students can explore in future studies. This could include topics like linear equations, inequalities and systems of equations, which are concepts that build upon the understanding of numerical expressions.

4. Importance of the Topic for Everyday Life (1 minute):

   • Finally, the teacher should reiterate the importance of the topic for everyday life. He/she can do this by recalling the examples of real-world applications discussed during the class.
   • The teacher can also encourage students to notice and share any other everyday situations in which the ability to solve numerical expressions can be useful. This will help show students that mathematics is not just an academic topic, but a valuable tool that can be used in many aspects of their lives.