Lesson Plan | Active Learning | Fractions: Parts of Natural 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 fundamental to establish a clear foundation of what is expected to be achieved with the lesson. Defining specific objectives allows both the teacher and the students to have a precise understanding of what will be addressed and the importance of each aspect in the practical application of mathematical knowledge. This clarity helps direct the activities in the classroom, ensuring that time is used efficiently for consolidating learning.

Main Objectives:

1. Empower students to solve problems involving the calculation of fractions of quantities, focusing on obtaining results expressed in natural numbers.

2. Develop the ability to compare fractions and their corresponding quantities, using practical and theoretical examples.

Side Objectives:

1. Stimulate logical reasoning and the application of basic mathematical operations in varied contexts.

Introduction

Duration: (20 - 25 minutes)

The introduction serves to engage students with the content they previously studied, using problem situations that stimulate critical thinking and the application of fraction concepts in practical contexts. Furthermore, the contextualization seeks to show the relevance of fractions in daily life and real situations, increasing interest and perception of the topic's usefulness.

Problem-Based Situations

1. Imagine you have a large pizza and need to divide it equally among 4 friends. Each friend wants exactly 3/8 of the pizza. How can you calculate how many pieces of pizza each friend will receive if the pizza is divided into 32 equal parts?

2. A farmer has a rectangular piece of land measuring 120 meters in length and 80 meters in width. He decides to sell 3/5 of the land for construction. How can he calculate the area that will be sold in square meters?

Contextualization

Fractions are used in everyday life more than one might think, from dividing a pizza into equal parts to dividing assets in an inheritance. Knowing how to manipulate fractions is not only useful for practical situations but is also fundamental for understanding more advanced mathematical concepts and even areas like science and engineering. In this lesson, we will explore how fractions are essential parts of natural numbers and how understanding them can facilitate various everyday and professional tasks.

Development

Duration: (75 - 80 minutes)

The Development stage is designed to allow students to practically and interactively apply the fraction concepts studied previously at home. The proposed activities aim to consolidate theoretical knowledge through problem situations that simulate the use of fractions in real and everyday contexts, promoting logical reasoning, teamwork, and creativity. Each activity is planned to be dynamic and engaging, ensuring active participation from all students and deepening their understanding of the topic.

Activity Suggestions

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

Activity 1 - The Fraction Race

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of fractions in dividing quantities and reinforce teamwork.

- Description: In this activity, students will be divided into groups of up to 5 people. Each group will receive a task involving calculating fractions of quantities in the context of a relay race. The scenario consists of a relay race where each team must cover a certain distance (e.g., 100 meters) divided into segments that represent different fractions of the total distance. Each segment must be covered by a specific number of runners, determined by the fraction it represents (for example, 3/4 of the distance should be covered by 3 runners). The goal is for each group to calculate the necessary fractions to complete the race and then simulate the relay in the school yard.

- Instructions:

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

• Present the race scenario and explain how the track segments correspond to different fractions of the total distance.

• Distribute cards representing the fractions of 1/4, 1/3, 1/2, etc., and ask each group to calculate how many runners are needed for each segment.

• Ask each group to simulate the race in the yard, using the cards to represent the runners.

• At the end, discuss with the class the strategies used by the groups and the results obtained.

Activity 2 - The Fraction Market

> Duration: (60 - 70 minutes)

- Objective: Practice fraction calculations in a purchasing and budgeting context, in addition to promoting culinary skills.

- Description: Students, organized in groups, will simulate a market where they must buy ingredients for a recipe that involves fractions of quantities. Each group will receive a list of ingredients and their quantities, expressed in fractions, and a limited 'budget'. Students will have to calculate the necessary quantities, buy the ingredients in a 'market' set up in the classroom using fictional money, and prepare the recipe.

- Instructions:

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

• Distribute the ingredient lists and budgets to each group.

• Set up a 'store' in the classroom with ingredients and fictional prices.

• Students must calculate and buy the ingredients, ensuring that the fractions used correspond to the recipe's fractions.

• After purchasing, each group prepares the recipe in the classroom and shares it with the class.

Activity 3 - Building with Fractions

> Duration: (60 - 70 minutes)

- Objective: Visualize and manipulate fractions in a three-dimensional context, reinforcing the understanding of the parts that make up a whole.

- Description: In this playful activity, students will build 'houses' using blocks that represent fractions of a complete house. Each group will receive a set of colorful blocks that, together, form a house. Each block represents a different fraction of the total house. Students will start from a project to build the house using the correct fractions and discuss the parts corresponding to each fraction.

- Instructions:

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

• Present the set of blocks and explain which fraction each color corresponds to in the complete house.

• Distribute the projects that indicate how the fractions should be assembled to form the house.

• Students must assemble the house, discussing the fractions represented by each block.

• Each group presents their construction and explains the fractions used.

Feedback

Duration: (10 - 15 minutes)

The purpose of this feedback stage is to allow students to reflect and articulate what they learned during the practical activities. This discussion moment helps reinforce learning, identify areas of difficulty that may require additional review, and value the importance of teamwork as well as the application of mathematical concepts in practical contexts. Additionally, it provides the teacher with a clear view of the students' understanding, allowing for future adjustments in lesson planning.

Group Discussion

After completing the activities, gather all students in a circle for a group discussion. Start the discussion with a brief introduction, highlighting the importance of sharing learnings and insights obtained during the activities. Encourage students to express their opinions and reflect on the challenges faced and the strategies used. This moment is crucial for students to verbalize and consolidate what they learned, as well as to learn from their peers' experiences.

Key Questions

1. What were the main challenges you faced when calculating and applying fractions in the activities?

2. How did teamwork help in solving problems and understanding fraction concepts?

3. Was there any situation where you had to adapt the initially planned strategy? How was this done?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage is designed to consolidate students' learning, ensuring they can synthesize and revisit the key points of the lesson. Additionally, it serves to reinforce the connection between theory and practice, showing students how mathematical concepts are applicable in their daily lives. This moment also helps emphasize the importance of studying fractions, motivating students to value and apply what they learned in various contexts.

Summary

To conclude the lesson, the teacher should summarize and recapitulate the main concepts covered about fractions, emphasizing how fractions are essential parts of natural numbers and how they are applied in everyday situations. Review the techniques for calculating fractions of quantities and how these fractions can be compared and used in different contexts, such as dividing a pizza or determining areas of land.

Theory Connection

The teacher should highlight how today's lesson connected the theory studied at home with the practice in the classroom. Explain how activities like 'The Fraction Race', 'The Fraction Market', and 'Building with Fractions' allowed students to apply theoretical concepts in practical and playful contexts, reinforcing students' understanding of manipulating fractions and their importance in daily life.

Closing

At the end, it is essential for the teacher to reinforce the importance of studying fractions, not only as a mathematical skill but as an essential tool for solving practical and everyday problems. Highlight how understanding fractions can facilitate tasks such as cooking following recipes, splitting expenses, or calculating measurements in construction projects, reinforcing the topic's relevance to students' lives.