Lesson plan of Operations: Multiplication and Division

Objectives (5 - 7 minutes)

1. Understanding of Multiplication and Division Operations: The teacher should present the students with the definition and logic behind the operations of multiplication and division. The students should understand that multiplication is the addition of a number itself multiple times, while division is the way to distribute a number into equal parts.

2. Applying Multiplication and Division in Everyday Problems: After the initial understanding of the operations, the teacher should demonstrate to the students how they are used in everyday situations. This could include buying items at a store, sharing candies among friends, dividing chores at home, etc.

3. Developing Problem-Solving Skills: The students should be able to apply the operations of multiplication and division to solve mathematical problems. The teacher should encourage the students to think critically and develop effective strategies to solve the proposed problems.

   Secondary objectives:

   • Reinforcing Practice with Diversified Exercises: Provide a variety of exercises so that students can practice multiplication and division operations in a fun and engaging way.

   • Promoting Active Student Participation: Encourage active student participation, either through questions and answers, group discussions, or hands-on activities. This helps keep students engaged and improves their understanding of the subject.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should begin the lesson by briefly reviewing the concepts of addition and subtraction, which are fundamental operations for understanding multiplication and division. This can be done through a quick quiz or a review game. (3 - 5 minutes)

2. Presentation of Problem Situations: The teacher should then present two problem situations that involve the operations of multiplication and division. For example, the teacher could ask the students how many candies each would receive if they had to divide a box of 20 candies among themselves, or how many days it would take to complete a task if each day were divided into 4 equal parts. The problem situations should be interesting and challenging in order to pique the students’ curiosity. (3 - 5 minutes)

3. Contextualisation of the Importance of the Operations: The teacher should then contextualise the importance of multiplication and division operations, explaining that they are widely used in everyday life, in various situations, such as when shopping, cooking, sharing objects, etc. The teacher could also mention that these operations are essential for the development of more advanced mathematical skills, such as solving equations and understanding proportions. (2 - 3 minutes)

4. Introduction of the Topic with Curiosities and Stories: To arouse the students’ interest, the teacher could introduce the topic with curiosities and stories related to multiplication and division operations. For example, the teacher could tell the story of how multiplication was developed by the ancient Egyptians to facilitate counting and measurement, or how division is used in agriculture to determine the amount of seeds to be planted in a given space. Another interesting curiosity is the existence of unconventional methods of multiplication and division, such as the soroban method (a Japanese abacus) and the Russian multiplication method. (2 - 3 minutes)

Development (20 - 25 minutes)

1. "Mathematical Supermarket" Activity: The teacher should divide the class into groups of 4 or 5 students. Each group will receive a grocery list from a supermarket, containing various items and their respective quantities. The challenge is to calculate the total value of the shopping list, considering the unit price of each item. To do this, students must use the operations of multiplication (to calculate the total price of each item) and addition (to add up all the prices). In addition, the teacher could introduce the concept of a discount, proposing that the students calculate the final value considering a percentage discount. This activity aims to apply the operations of multiplication and addition in a real-life context, in addition to developing problem-solving and teamwork skills. (10 - 12 minutes)

   1.1. Preparation of the Activity: The teacher should prepare the shopping lists in advance, ensuring that the items have varied prices and that it is possible to apply different discounts. In addition, the teacher should prepare the necessary materials for the activity, such as pencils, paper, and calculators (if necessary).

   1.2. Execution of the Activity: The groups should receive the shopping lists and the other materials. They should discuss together the best strategy to calculate the total value of the list and, if applicable, the final value considering the discount. The teacher should circulate around the room, assisting the groups that present difficulties and encouraging everyone’s participation.

2. "Dividing the Pizza" Activity: Still in groups, the students will receive a toy pizza and a fictitious pizza "order", indicating the number of slices that each person in the group wants. The challenge is to divide the pizza according to the order, using the division operation. In this activity, in addition to applying the division operation, students will develop fair division skills and spatial reasoning. (7 - 8 minutes)

   2.1. Preparation of the Activity: The teacher should prepare the pizzas and the pizza "orders" in advance, ensuring that it is possible to apply the division operation fairly.

   2.2. Execution of the Activity: The groups should receive the pizza and the pizza "order". They should discuss together the best way to divide the pizza according to the order. The teacher should circulate around the room, assisting the groups that present difficulties and encouraging everyone’s participation.

3. "Building a Garden" Activity: In this activity, students will have to build a rectangular garden on a plot of land, using pieces of square cardboard of the same size. The challenge is to calculate the number of pieces of cardboard needed to build the garden, using the operation of multiplication. In addition, students will also have to calculate the area of the garden, adding the areas of each piece of cardboard. This activity aims to apply the operation of multiplication and addition in a practical context and to develop problem-solving and spatial reasoning skills. (5 - 7 minutes)

   3.1. Preparation of the Activity: The teacher should prepare the pieces of cardboard and the plots of land in advance, ensuring that it is possible to apply the operation of multiplication and addition effectively.

   3.2. Execution of the Activity: The students, still in groups, should receive the materials and the challenge to build the garden. They should discuss together the best strategy to calculate the number of pieces of cardboard needed and the area of the garden. The teacher should circulate around the room, assisting the groups that present difficulties and encouraging everyone’s participation.

At the end of the activities, the teacher should promote a classroom discussion, where each group presents its solutions and strategies used. This allows students to learn from each other and allows the teacher to correct any misunderstandings.

Conclusion (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): After completing the activities, the teacher should promote a group discussion, where each team shares their solutions, strategies used, and difficulties encountered. The teacher should encourage the students to explain their thought process and justify their answers. This not only helps to consolidate learning, but also promotes communication skills and student confidence.

2. Connection with Theory (2 - 3 minutes): The teacher should then make the connection between the practical activities and the theory, highlighting how the operations of multiplication and division were applied to solve the proposed problems. For example, the teacher could recall the concept of multiplication as addition of a number to itself several times and of division as the way to distribute a number into equal parts. The teacher should clarify any misunderstandings and answer any questions that students may have.

3. Individual Reflection (2 - 3 minutes): To conclude the lesson, the teacher should propose that the students make a brief individual reflection on what they have learned. The teacher can do this through guiding questions, such as:

   3.1. What was the most challenging thing today?

   3.2. What strategies did you use to solve the problems?

   3.3. How can the operations of multiplication and division be applied in everyday situations?

   3.4. What questions are still unanswered?

   This reflection allows students to consolidate what they have learned, identify any gaps in their understanding, and think about ways to apply the new knowledge in their daily lives. The teacher should encourage the students to share their answers, if they feel comfortable, and be open to clarifying any remaining doubts.

4. Closing the Lesson (1 minute): Finally, the teacher should close the lesson by thanking the students for their participation, reinforcing the importance of multiplication and division operations, and reminding them to review the content at home to consolidate their learning. The teacher could also mention what will be covered in the next lesson to maintain the students’ interest and curiosity.

Final Considerations (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes): The teacher should begin the Conclusion by recalling the key points of the lesson. The teacher should highlight the definitions and properties of multiplication and division operations, as well as recap the strategies used to solve the proposed problems. It is important that the teacher provides a clear and concise summary, so that all students can follow and recall the content.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should then reinforce the importance of connecting theory with practice and real-life applications. The teacher can do this by reminding the students of how the operations of multiplication and division are essential in various everyday situations, such as when shopping, dividing objects, or performing area calculations. In addition, the teacher could highlight how the practical activities carried out in the classroom help to consolidate theoretical understanding and develop problem-solving skills.

3. Extra Materials (1 minute): The teacher should suggest some extra materials for students who wish to further deepen their understanding of multiplication and division operations. This could include educational websites, explanatory videos, mathematical games, and textbooks. For example, the teacher could recommend the use of interactive math apps, such as Khan Academy or Mathway, which offer detailed explanations and practice exercises.

4. Importance of the Subject (1 - 2 minutes): Finally, the teacher should emphasise the importance of the subject presented for the students’ daily lives and for their academic trajectory. The teacher could explain that multiplication and division operations are the basis for understanding more advanced mathematical concepts, such as fractions, proportions, equations, and functions. In addition, the teacher should emphasise that the ability to solve mathematical problems is a fundamental skill, not only in school, but also in various careers and in life in general.