Lesson plan of Numerical Expressions

Objectives (5 - 7 minutes)

1. Understand the structure of numerical expressions: Students will be able to identify and understand the structure of numerical expressions, including the presence of operators and operands. This involves identifying terms, factors and products, and understanding the rules of precedence (PEMDAS).

2. Perform calculations with numerical expressions: Students will be able to perform calculations with numerical expressions, correctly applying the rules of precedence. This includes performing operations with integers, fractions and decimals, and simplifying complex expressions.

3. Solve problems with numerical expressions: Students will be able to apply the knowledge acquired to solve problems involving numerical expressions. This includes translating problems into expressions, simplifying those expressions, and interpreting the results obtained.

   Secondary objectives:

   • Develop logical and critical reasoning skills when dealing with mathematical operations.
   • Promote collaboration and discussion among students through group activities.

The teacher should introduce these Objectives at the beginning of the class, highlighting the importance of the topic and how it relates to mathematics as a whole. In addition, it is important for the teacher to be aware of the individual difficulties of the students and to provide support and guidance as needed.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the class by recalling the basic concepts of mathematical operations (addition, subtraction, multiplication and division) and the order of precedence of these operations. This revision can be done interactively, asking students to briefly solve some simple calculations. (5 minutes)

2. Initial problem situations: To arouse students' interest, the teacher can propose two initial problem situations. The first may involve simplifying a complex numerical expression, while the second may be solving a practical problem that involves the use of numerical expressions. The teacher can ask students how they would approach these situations, without worrying about the correct answer, but rather with the exposure of logical reasoning. (5 minutes)

3. Contextualization of the importance of the topic: The teacher should then explain how numerical expressions are widely used in everyday life and in various areas, such as in physics, engineering, economics and even in logic games. It is important to emphasize that the mastery of this topic is fundamental for solving more complex mathematical problems and for the Development of logical reasoning skills. (2 minutes)

4. Introduction of the topic with curiosities: To gain the attention of the students, the teacher can share some curiosities related to the theme. For example, you can mention that Mathematics has specific rules for solving numerical expressions, precisely to avoid ambiguity and ensure that everyone arrives at the same result. In addition, you can mention that solving numerical expressions can be compared to a puzzle, where each step is important to reach the final answer. (3 minutes)

Development (25 - 30 minutes)

1. Activity "Numerical Expressions in the Real World" (10 - 15 minutes)

   • Description: In this activity, students will be divided into groups of 4 to 5 members. Each group will receive a list of everyday situations that involve numerical expressions. Situations may include interpreting electricity bills, solving discount calculation problems on purchases, among others.

   • Step by step:

     1. Each group must choose a situation to work on.
     2. Next, they must identify the numerical expressions present in the chosen situation.
     3. After identification, they should simplify the expressions, according to the rules of precedence.
     4. Finally, the groups should present their solutions to the class, explaining the reasoning used.

2. Activity "Unveiling Numerical Expressions" (10 - 15 minutes)

   • Description: In this activity, students will continue working in groups. Each group will receive a set of cards, each containing a number and a mathematical operator (+, -, ×, ÷). The goal is for students to combine the cards to form correct numerical expressions.

   • Step by step:

     1. The teacher should prepare the cards in advance, ensuring that there are enough cards of each type.
     2. Each group will receive a random set of cards.
     3. Students must combine the cards to form as many correct numerical expressions as possible.
     4. The group that manages to form the most correct numerical expressions will be the winner.

3. Activity "Challenge of Numerical Expressions" (5 - 10 minutes)

   • Description: In this activity, students will continue working in groups. Each group will receive a set of cards, each containing a number. The teacher will project a numerical expression on the board, and the students must use the numbers on their cards to solve the expression.

   • Step by step:

     1. The teacher should prepare the numerical expressions in advance, ensuring that they are challenging, but still possible to be solved with the numbers provided.
     2. Each group will receive a set of cards with numbers.
     3. The teacher will project a numerical expression on the board.
     4. Students must use the numbers on their cards to solve the expression.
     5. The group that solves the numerical expression correctly the fastest will be the winner.

The teacher should circulate around the room during the activities, providing guidance, clarifying doubts and observing the progress of the groups. At the end of each activity, the teacher should promote a classroom discussion, allowing students to share their solutions and reasoning.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • Description: After the Conclusion of the activities, the teacher should promote a group discussion so that each team shares their solutions and discoveries. This provides an opportunity for students to learn from each other and for the teacher to assess the class's understanding of the topic.

   • Step by step:

     1. The teacher should ask each group to briefly present their solutions or conclusions, encouraging them to explain the reasoning behind them.
     2. During the presentations, the teacher should ask questions to stimulate reflection and deepen students' understanding.
     3. After each presentation, the other groups should have the opportunity to ask questions or make comments.

2. Connection with Theory (2 - 3 minutes)

   • Description: After the presentations of the groups, the teacher should resume the theoretical concepts discussed at the beginning of the class and connect with the practical activities carried out. This helps students consolidate what they have learned and realize the relevance of the content.

   • Step by step:

     1. The teacher should highlight how the activities relate to the theory presented, reinforcing the importance of the rules of precedence and the correct identification of operators and operands.
     2. The teacher can also take this opportunity to clarify any doubts that may have arisen during the activities.

3. Individual Reflection (2 - 3 minutes)

   • Description: To conclude the class, the teacher should propose that the students reflect individually on what they have learned. This helps consolidate knowledge and identify possible gaps in understanding the subject.

   • Step by step:

     1. The teacher should propose some questions to guide students' reflection, such as "What was the most important concept you learned today?" and "What questions have not yet been answered?".
     2. Students should write down their answers in a notebook or sheet of paper.
     3. After a minute of reflection, the teacher may ask some students to share their answers with the class, if they feel comfortable.

The teacher should end the class by emphasizing the importance of the topic for everyday life and for the study of mathematics, and reinforce that he or she is available to clarify any doubts that students may have. In addition, it is important for the teacher to make a brief assessment of the students' performance during the activities, in order to identify possible difficulties and plan future classes accordingly.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes)

   • Description: The teacher should summarize the key points of the lesson and recap the most important concepts and techniques that were covered. This helps students consolidate what they have learned and recall the highlights of the class.

   • Step by step:

     1. The teacher should summarize the main points that were discussed and studied, including the structure of numerical expressions, the rules of precedence and the performance of calculations with expressions.
     2. In addition, the teacher should recall the key points of the practical activities, highlighting the common errors and effective strategies for solving numerical expressions.

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

   • Description: The teacher should explain how the class connected the theory, practice and applications of the topic. This helps reinforce the relevance of the subject and show students how mathematics is present in various everyday situations.

   • Step by step:

     1. The teacher should highlight how the theory presented at the beginning of the class was applied in the practical activities.
     2. In addition, the teacher should reinforce the importance of numerical expressions in everyday life, citing examples of real situations in which these expressions are used.

3. Extra Materials (1 minute)

   • Description: The teacher should suggest extra materials for students who wish to deepen their knowledge on the subject. These materials may include math books, educational websites, explanatory videos, and logic games that involve the use of numerical expressions.

   • Step by step:

     1. The teacher should list the extra materials, briefly explaining what each one of them offers.
     2. In addition, the teacher should inform students that these materials are optional, but may be useful for reinforcing learning and deepening understanding of the topic.

4. Real World Applications (1 minute)

   • Description: Finally, the teacher should emphasize the importance of the knowledge acquired in the class for everyday life. This helps motivate students and show the relevance of mathematics beyond the classroom.

   • Step by step:

     1. The teacher should cite examples of everyday situations in which knowledge about numerical expressions is useful, such as in interpreting invoices, calculating discounts and in financial planning.
     2. In addition, the teacher can mention how numerical expressions are applied in other areas of knowledge, such as in physics and engineering.

The teacher should end the class by reinforcing the importance of the topic for mathematics and for everyday life, and remind students that practice is fundamental for the mastery of this and other mathematical topics. In addition, the teacher should reinforce the availability to clarify doubts and provide additional support, if necessary.