Lesson Plan | Active Learning | Operations: Decimals and Fractions

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 - 7 minutes)

The goal-setting phase is fundamental to guide the focus of students and the teacher during the lesson. By clearly establishing what is expected to be achieved, students can mentally prepare for practical activities in the classroom, knowing what competencies they need to demonstrate. This section also serves to align learning expectations among all participants and ensure that classroom time is effectively used to consolidate and apply students' prior knowledge about operations with decimals and fractions.

Main Objectives:

1. Empower students to perform the four basic operations (addition, subtraction, multiplication, and division) with decimal numbers and fractions, reinforcing theoretical understanding with practical exercises.

2. Develop skills to apply exponentiation and exact root extraction in contexts involving decimal numbers and fractions, enabling students to solve practical problems involving these operations.

Side Objectives:

1. Encourage critical thinking and the application of problem-solving strategies in practical situations, such as cost calculations and measurements involving decimals and fractions.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and review essential concepts that have been studied previously. The proposed problem situations stimulate critical thinking and practical application of knowledge, while the contextualization highlights the relevance of operations with decimals and fractions in real-life situations, increasing student interest and setting the stage for practical application during the lesson.

Problem-Based Situations

1. Imagine you have $100.00 and decide to divide the money equally among four friends. Each of your friends will receive an amount of $25.00. How could you calculate this division?

2. A farmer needs to divide a field into equal plots to plant different types of vegetables. Knowing that he can plant 3/4 of a certain type of vegetable in each plot and that the field must be divided into 5 parts, how could he calculate the area of each plot in fraction and decimal?

Contextualization

Operations with decimals and fractions are fundamental not only in mathematics but also in many everyday situations, such as cost calculations, measurements, and resource sharing. For example, when preparing a recipe that calls for 1/2 cup of flour, it is necessary to know how to convert this quantity into decimals if the measure of the cup is not standard. Furthermore, understanding these operations is crucial for handling money, such as calculating the correct change during a purchase.

Development

Duration: (75 - 80 minutes)

The Development phase aims to consolidate and deepen students' knowledge of operations with decimals and fractions through practical and contextualized activities. The proposed activities are designed to stimulate logical reasoning, group collaboration, and the application of mathematical concepts in real-life and enjoyable situations. This phase is crucial for students to not only understand but also effectively apply what they have learned, ensuring meaningful and lasting learning.

Activity Suggestions

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

Activity 1 - The Challenge of Fractions and Decimals in the Market

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of operations with fractions and decimals in a buying and selling context, developing calculation and logical reasoning skills.

- Description: Students will be divided into groups of up to 5 people, and each group will have a 'market' set up in the classroom, with fictional items in different quantities and prices expressed in fractions and decimals. The challenge is for each group, using their 'fake money', to calculate how much they can buy of each item, ensuring they do not exceed the total available amount.

- Instructions:

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

• Explain that each group has a budget of $100.00 (in fake bills) to spend in the market set up in the classroom.

• Each item for sale will have its price in fraction or decimal, and students will need to calculate how many units of each item they can buy with their budget.

• Students should record their purchases and calculations on a provided worksheet.

• At the end, each group will present their purchases and calculations to the class, explaining the strategies used to maximize the use of their money.

Activity 2 - Constructors of Fractions and Decimals

> Duration: (60 - 70 minutes)

- Objective: Enhance understanding and application of fractions and decimals in division and planning situations, promoting teamwork and creativity in problem-solving.

- Description: In this activity, each group of students will become 'constructors', responsible for dividing a plot of land into equal fractions for different purposes, such as planting vegetables in specified quantities. The land and quantities will be represented in decimals and fractions, challenging students to apply their mathematical skills to solve the problem.

- Instructions:

• Form groups of up to 5 students and distribute a blueprint of a square or rectangular plot of land.

• In each plot, students must plan the division into equal fractions for different types of vegetables, expressed in fractions and decimals.

• Students will use a ruler and pencil to divide the land on paper, following the fractions and decimals established in the challenge.

• Each group will present their divided plot and explain the fractions and decimals used, as well as the reasoning behind the division.

• A classroom discussion will be held about the different approaches and solutions presented.

Activity 3 - MasterChef of Fractions and Decimals

> Duration: (60 - 70 minutes)

- Objective: Utilize fractions and decimals in practice, reinforcing mathematical learning through real and fun application.

- Description: Students, organized into groups, will participate in a culinary challenge where they must follow a recipe that uses both fractions and decimals. Each group will receive a recipe broken down into parts, and the challenge will be to calculate the correct quantities of ingredients to serve 20 people.

- Instructions:

• Divide the class into groups of up to 5 students and distribute a recipe that uses fractions and decimals for the measurements.

• Explain that each group must prepare the recipe to serve 20 people, and they will need to calculate the correct quantities of ingredients based on the fractions and decimals in the recipe.

• Provide each group with a kitchen equipped with basic ingredients and utensils.

• Students will prepare the recipe, applying the calculations of fractions and decimals.

• At the end, each group will present their dish and explain the calculations done and the difficulties encountered.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback stage is to consolidate learning, allowing students to articulate their acquired knowledge and reflect on the practical application of operations with decimals and fractions. Through the group discussion, students have the opportunity to verbalize and justify their thought processes, which helps strengthen understanding of mathematical concepts and develop communication and argumentation skills. Additionally, this stage allows the teacher to evaluate student understanding and identify any areas that may require further review.

Group Discussion

At the end of the practical activities, gather all students and promote a group discussion. Start the discussion with a brief introduction, highlighting the importance of sharing experiences and learnings. Encourage each group to present a summary of what they did, focusing on the challenges faced, the strategies used, and the results obtained. Use this opportunity for students to compare and contrast the different approaches and solutions found by each group, thus enriching collective understanding.

Key Questions

1. What were the biggest challenges in applying operations with decimals and fractions in the activities, and how did you overcome them?

2. Was there any situation where the theory studied previously did not seem to fit with the practical problem? How did you resolve that?

3. How did teamwork assist in solving the problems and applying mathematical operations?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the conclusion phase is to ensure that students have a clear and consolidated view of the topics discussed, integrating theoretical knowledge with the practical observed and executed during the lesson. Additionally, it seeks to reinforce the relevance of the content in practical life, motivating students to perceive mathematics as an essential and useful tool in their routines. This stage helps ensure that learning objectives have been achieved and that students are ready to apply the knowledge in future contexts.

Summary

To conclude, the teacher should summarize the key points addressed during the lesson, reiterating the basic operations with decimals and fractions, as well as exponentiation and exact root extraction. It is important to recap the strategies used by students in practical activities, such as the Challenge of Fractions and Decimals in the Market and the MasterChef of Fractions and Decimals, to solidify understanding of the content.

Theory Connection

Today's lesson established a strong connection between theory and practice, demonstrating how mathematical operations are essential in everyday situations, such as commerce, cooking, and agricultural planning. By applying theoretical concepts in real and simulated scenarios, students were able to visualize the immediate utility of what they learned, reinforcing the learning.

Closing

Finally, it is crucial to highlight the importance of operations with decimals and fractions in daily life. These skills are fundamental not only for academic success but also for students' autonomy in various practical situations, such as financial planning and understanding measurements. Understanding and applying these concepts enables students to be more critical and effective in solving real problems.