Lesson Plan | Active Learning | Addition and Subtraction of Decimal Numbers

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is essential to direct the focus of students and the teacher to the key aspects of the expected learning. By clearly establishing what is expected to be achieved, it facilitates the preparation and execution of subsequent activities. In this context, the main goal is to ensure that students can not only understand the properties of the addition and subtraction of decimal numbers theoretically but also apply these notions practically and effectively in everyday problems.

Main Objectives:

1. Empower students to recognize and apply fundamental properties of the addition and subtraction of decimal numbers, such as commutativity, associativity, and additive identity.

2. Develop problem-solving skills involving operations with decimal numbers, using various strategies, including mental calculation and conventional algorithms.

Side Objectives:

1. Encourage the use of verification strategies to ensure the accuracy of calculations performed.
2. Foster students' confidence in their mathematical abilities through practical and collaborative exercises.

Introduction

Duration: (15 - 20 minutes)

The Introduction aims to engage students with the topic through problem situations they might encounter in their daily lives, stimulating the practical application of prior knowledge. Furthermore, by contextualizing the importance of studying the addition and subtraction of decimal numbers, students are motivated to understand the relevance of the theme in real situations, thereby increasing their interest and perception of the usefulness of mathematical content.

Problem-Based Situations

1. Imagine that you and your friends are organizing a birthday party and decide to buy ingredients to make a cake. The total cost of the ingredients is R$ 37.80, and each of the 5 friends contributes an equal share. How much should each one pay?

2. In a swimming competition, the time for 50m freestyle of each swimmer is measured in seconds and then converted to minutes and seconds, for example, 30.56 seconds would be 0 minutes and 30.56 seconds. If 4 swimmers complete the event in 0:30, 0:35, 0:28, and 0:32 respectively, what is the total time for the team?

Contextualization

The ability to add and subtract decimal numbers is crucial not only in academic contexts but also in everyday situations, such as in shopping, splitting bills, and in sports. For example, when shopping, prices often involve decimal numbers, and it is necessary to sum them up to calculate the total cost. Additionally, in sports competitions like swimming, times are often recorded in tenths or hundredths of a second, which need to be added and subtracted to determine winners and calculate team times. These examples help show the practical relevance of the topic for students.

Development

Duration: (70 - 75 minutes)

The Development stage is designed for students to practically and interactively apply the concepts studied on the addition and subtraction of decimal numbers. Through playful and contextualized activities, students will have the opportunity to solidify theoretical knowledge in situations that simulate the real world, thus promoting a more meaningful and lasting learning experience. This stage also aims to strengthen students' ability to work in teams and communicate, essential elements for collaborative learning.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Deciphering the Treasure Code

> Duration: (60 - 70 minutes)

- Objective: Practice the addition and subtraction of decimal numbers in a playful and collaborative context, stimulating mathematical reasoning and communication among group members.

- Description: Students are divided into groups of up to 5 people. Each group receives a treasure map where several coordinates representing decimal digits are marked. They must use addition and subtraction operations to decipher a code that will reveal the exact location of the treasure.

- Instructions:

• Form groups of up to 5 students.

• Distribute a treasure map to each group, marking the coordinates in decimal numbers.

• Explain that each coordinate corresponds to a digit of a three-digit code that, when added or subtracted, will lead to the treasure's location.

• Students must use addition and subtraction operations with decimal numbers to discover the code.

• The first group to correctly decipher the code and find the treasure's location wins the activity.

Activity 2 - Mathematics Olympics: Decimal Swimming

> Duration: (60 - 70 minutes)

- Objective: Develop skills in adding and subtracting decimal numbers in a sports context, promoting teamwork and the practical application of mathematical concepts.

- Description: In this activity, students will simulate a swimming competition where they must calculate the times of each swimmer, which are given in decimal numbers of minutes and seconds. They will need to add and subtract these times to determine the winners of each stage.

- Instructions:

• Organize the class into groups of up to 5 students.

• Provide each group with a spreadsheet containing the times of swimmers in minutes and seconds (e.g., 1:30, 1:35, etc.).

• Explain that they must add and subtract these times to calculate the results of the races.

• Each group must record the final times and determine the winners of each race.

• Finally, each group presents the results and discusses the strategies used.

Activity 3 - Little Merchants

> Duration: (60 - 70 minutes)

- Objective: Apply concepts of addition and subtraction of decimal numbers in buying and selling situations, promoting practical understanding of commercial transactions and mental calculation skills.

- Description: Students will simulate a buying and selling situation in small shops, where they will need to calculate the total value of a purchase, apply discounts, and provide change, all using decimal numbers.

- Instructions:

• Divide the class into groups of up to 5 students.

• Provide each group with a list of products with prices in decimal numbers and an amount for purchase.

• Students must calculate the total purchase amount, apply a discount of x%, and then determine the change.

• Each group simulates the purchase in the classroom shop, using fake money.

• At the end, discuss the different approaches and solutions found by the groups.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback section is to consolidate the knowledge acquired by students throughout the practical activities. By discussing in groups, students have the opportunity to verbalize and reflect on their learning, which helps reinforce their understanding of mathematical concepts. Furthermore, by hearing other classmates' experiences, students can learn new approaches and strategies, promoting a collaborative and enriching learning environment.

Group Discussion

Start the group discussion by inviting each team to share their discoveries and strategies used during the activities. Ask how they applied the properties of the addition and subtraction of decimal numbers to solve the proposed problems and what they learned anew. Encourage students to express what their greatest challenges were and how they managed to overcome them. Use this opportunity to reinforce key concepts and clarify any remaining doubts.

Key Questions

1. What strategies did you find most effective for adding and subtracting decimal numbers in the activities?

2. How was the property of commutativity applied in your solutions?

3. Was there any situation where using the traditional algorithm of addition and subtraction was more advantageous than mental calculation?

Conclusion

Duration: (10 - 15 minutes)

The purpose of the Conclusion is to ensure that students have a clear and consolidated understanding of the topics covered, integrating the theoretical and practical knowledge acquired during the lesson. Additionally, by highlighting the relevance of the content in everyday life, it reinforces the perception of mathematics as a practical and necessary tool. This stage also serves to evaluate the overall understanding of the students and clarify any final doubts, ensuring that learning is effective and lasting.

Summary

To conclude, the teacher should summarize and recap the contents addressed, emphasizing the properties of addition and subtraction of decimal numbers, mental calculation strategies, and the use of traditional algorithms. It is important that this summary includes practical examples from the activities carried out, such as 'Deciphering the Treasure Code' and 'Little Merchants', to reinforce the applicability of concepts in real situations.

Theory Connection

During the lesson, the connection between the theoretical concepts studied and the practical activities was consistently established. Students were able to see the direct application of mathematical properties in playful and everyday scenarios, which helped solidify theoretical understanding through practice. This approach not only facilitated comprehension but also allowed students to see mathematics as a useful and interesting tool.

Closing

Finally, the teacher should highlight the importance of adding and subtracting decimal numbers in everyday life, reinforcing how these skills are essential in daily activities, such as shopping, sports competitions, and even in event planning, such as the parties organized in the 'Deciphering the Treasure Code' activity. This recognition helps students value and apply mathematical learning in various practical situations.