Lesson Plan | Active Learning | Operations: Mixed 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 stage of defining objectives is crucial to guide both the teacher and the students about the focus of the lesson. By clearly establishing what is expected to be achieved, students can better direct their efforts and attention during practical activities. This section also serves to align expectations and ensure that everyone involved understands the importance of the topic and how it applies both academically and in everyday situations.

Main Objectives:

1. Empower students to recognize and operate with mixed numbers in various mathematical operations, including addition, subtraction, multiplication, and division.

2. Develop students' ability to solve practical problems involving mixed numbers, identifying and correctly manipulating these formats.

Side Objectives:

1. Encourage critical thinking and the application of problem-solving strategies through practical examples and varied contexts.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the lesson topic by using problem situations they might encounter in their daily lives, thus establishing a connection between theory and practice. By contextualizing the importance of mixed numbers, students can visualize the utility of these concepts in various real situations, which stimulates interest and understanding of the topic.

Problem-Based Situations

1. Imagine that a baker needs to prepare 3 bread recipes, each asking for 1 and 3/4 cups of flour. He has 7 cups of flour. How many complete recipes can he make?

2. A farm has 4 enclosures that need to be divided equally among 3 types of animals. If each type of animal needs 1 and 1/3 enclosures, how many animals of each type can be accommodated? And is there any enclosure left?

3. An athlete runs 2 and 1/2 laps on a 400-meter track. If he continues at the same pace, how many laps will he complete in a 1.6-kilometer race?

Contextualization

Mixed numbers are often used in everyday situations, such as in cooking recipes, in measurements of length, and even in sports. For example, when making a recipe that calls for 1 and 3/4 cups of flour, it's necessary to understand how to add or subtract these fractions to adjust the quantity of available ingredients. Additionally, understanding mixed numbers is crucial in tasks like measuring fabrics for sewing or dividing land among people or animals, making the concept very practical and relevant.

Development

Duration: (75 - 85 minutes)

The Development section is intended to practically and playfully apply the mixed number concepts previously studied by students. Through the proposed activities, the goal is to consolidate learning through situations that simulate real challenges, fostering creativity, teamwork, and the application of problem-solving strategies. Each activity is designed to be completed within a period of 60 to 70 minutes, ensuring that all students have the opportunity to actively participate and deeply understand the concepts discussed.

Activity Suggestions

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

Activity 1 - The Race of Mixed Numbers

> Duration: (60 - 70 minutes)

- Objective: Practice operations with mixed numbers in a fun and competitive context, reinforcing the learning of addition, subtraction, multiplication, and division.

- Description: In this activity, students will simulate a relay race where each team must complete a total distance equivalent to a marathon (42 kilometers), but the route will be represented by mixed numbers that they must add, subtract, multiply, and divide to advance. Each stage of the route will have different types of operations.

- Instructions:

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

• Give each group a route map with mixed numbers representing distances and mathematical operations that must be performed to advance.

• Each group starts at the 'starting line' and must solve the first operation to know how many meters they advance.

• After solving each operation, the group moves a marker on the map to the new location.

• The first group to correctly complete the 'marathon' wins the race.

Activity 2 - Pizza Party and Fractions

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of mixed numbers in a practical and social context, developing planning skills and mathematical reasoning.

- Description: Students will plan a party where the main activity will be assembling pizzas. They will need to calculate how many pizzas of different flavors will be necessary, considering that each guest can consume a whole pizza or a fraction of it. The ingredients are presented in mixed numbers, and the quantities must be calculated.

- Instructions:

• Organize students into groups of up to 5 people.

• Distribute a 'menu' of pizzas that contains the ingredients in mixed numbers and the portions needed for each guest.

• Each group must calculate how many pizzas of each flavor will be needed for the party and what fractions of each pizza will be consumed by each guest.

• Groups present their planning and justify their choices based on the calculations made.

• Conduct a vote to decide which group planned the party most efficiently.

Activity 3 - Mathematical Maze Challenge

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to operate with mixed numbers quickly and under pressure, in a playful scenario that stimulates cooperation and quick reasoning.

- Description: In this challenge, students will face a maze where each path corresponds to an operation with mixed numbers that must be solved to move forward or backward. The objective is to reach the center of the maze by correctly solving the operations along the way.

- Instructions:

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

• Explain that the maze consists of a series of corridors marked with mixed number operations.

• Each group must solve the operation in each corridor to decide whether to advance or go back a step.

• The first group to reach the center of the maze, correctly solving all operations, wins the challenge.

• Create some operations that, if solved incorrectly, make the group go back one corridor to increase the challenge.

Feedback

Duration: (10 - 15 minutes)

The purpose of this feedback section is to allow students to articulate and reflect on what they learned and how they applied the concepts of mixed numbers. This group discussion helps consolidate knowledge, allowing students to share different perspectives and approaches to solving the proposed problems. Furthermore, the exchange of ideas and experiences between students and with the teacher helps identify areas that may need revision or more practice, ensuring a deeper understanding of the topic.

Group Discussion

To initiate the group discussion, the teacher should gather all students and, at first, ask each group to share their experiences and learnings from the activities conducted. The teacher can start with a brief introduction, highlighting the importance of understanding and applying mixed numbers. Next, students should be encouraged to discuss how the concepts learned can be useful in real situations and how solving the proposed problems helped solidify their understanding of mixed numbers.

Key Questions

1. What were the main challenges encountered when performing operations with mixed numbers in the activities and how did you overcome them?

2. How do the concepts of mixed numbers apply to real situations you know or can imagine?

3. Was there any strategy or method you discovered that helped simplify the manipulation of mixed numbers?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion section serves to consolidate students' learning by recapping the key points addressed during the lesson and ensuring that everyone has understood the fundamental concepts of mixed numbers. Furthermore, it highlights how the connection between theory and practice was established, reinforcing the relevance of mixed numbers in real applications. This stage is crucial to ensure that students leave the lesson with a clear and practical understanding of the content.

Summary

In this lesson, students explored the concepts of mixed numbers, applying them in various mathematical operations such as addition, subtraction, multiplication, and division. Through practical and playful activities, they could visualize the utility of mixed numbers and how these concepts apply in everyday situations, such as cooking recipes and dividing lands.

Theory Connection

Today's lesson was carefully designed to connect theory with practice, allowing students to see the applicability of mixed numbers in different contexts. Activities like 'The Race of Mixed Numbers' and 'Pizza Party and Fractions' not only reinforced theoretical learning but also taught students how to solve problems effectively and work as a team.

Closing

Understanding and operating with mixed numbers is essential, not only in academic mathematics but also in practical situations in daily life. The ability to efficiently manipulate mixed numbers can facilitate tasks such as cooking, planning events, and even in professions involving measurements and everyday calculations.