Lesson Plan | Active Learning | Fractions: Representation

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 establish the focus of the lesson and ensure that both the teacher and students are aligned on what will be learned. Clearly defining the objectives facilitates leading the activities and assessing the students' learning. In this lesson, the main goals are to ensure that students can identify and represent fractions effectively, using examples that facilitate comprehension, as well as to associate fractions with fundamental mathematical concepts such as division and part of a whole.

Main Objectives:

1. Enable students to identify and represent fractions smaller and larger than one, using practical examples to reinforce understanding.

2. Develop the students' ability to associate fractions with the result of a division or the idea of part of a whole, using manipulable materials and interactive exercises.

Side Objectives:

1. Encourage active participation of students through group discussions and presentations of their work.
2. Promote critical thinking and problem-solving through practical situations involving fractions.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and connect the content they studied at home with practice in the classroom. The proposed problem situations stimulate critical thinking and the application of prior knowledge, while the contextualization demonstrates the relevance of fractions in daily life and history, increasing students' interest and motivation.

Problem-Based Situations

1. Imagine a package of cookies is equally divided among 4 friends. Each one receives 1/4 of the total cookies. How many cookies does each friend have if the original package contained 16 cookies?

2. If a cake is cut into 8 equal pieces and one person eats 3/8 of the cake, how many pieces of the cake did they eat? And how many pieces of the cake remain?

Contextualization

Fractions are present in various everyday situations, from dividing a pizza among friends to calculating discounts on purchases. Knowing how to manipulate and understand fractions is crucial for effectively dealing with these situations. Furthermore, exploring the history of fractions, how they were developed to solve practical and theoretical problems, can be fascinating and motivating for students.

Development

Duration: (65 - 75 minutes)

The development stage is designed to allow students to practically and interactively apply the fraction concepts they studied previously. Through playful and contextualized activities, students can explore mathematics in an engaging and significant way. This approach not only reinforces learning fractions as part of a whole but also promotes skills such as teamwork, critical thinking, and problem-solving. Each activity is structured to be completed in groups, encouraging collaboration and communication among students.

Activity Suggestions

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

Activity 1 - Fraction Festival

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of fractions in the equitable division of resources for an event, developing teamwork and mathematical reasoning skills.

- Description: Students will plan a fictional party, where they will need to decide how many parts of a whole each festive item represents. For example, if the party has 3 types of sweets, 2 types of snacks, and 1 type of juice, students will need to decide how many parts of each item to serve for 10 guests.

- Instructions:

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

• Distribute colored cards representing each party item (sweets, snacks, juices) and ask each group to decide how to divide the total of each item for 10 guests, representing this in fractions.

• Each group will present their division and justify their choices, explaining how they arrived at the fractions used.

• Conduct a vote to evaluate which group managed to divide the items most equitably.

Activity 2 - Pizza Builders

> Duration: (60 - 70 minutes)

- Objective: Visualize and manipulate fractions in a playful and creative context, strengthening the understanding of the concept of fractions as part of a whole.

- Description: In this activity, students will design and 'build' miniature pizzas, using cardboard circles for the base and strips of paper to represent the ingredients. Each group should decide how to divide the pizza into equal fractions and visually represent the ingredients according to those fractions.

- Instructions:

• Distribute materials such as cardboard circles, strips of colored paper, and scissors.

• Instruct students to divide the circle into equal fractions, as if they were slices of pizza.

• Each group chooses the ingredients they wish to represent and decides how to divide the pizza to include all ingredients equitably.

• Present the completed pizzas and ask each group to explain their division choices and how fractions were used.

Activity 3 - Fraction Market

> Duration: (60 - 70 minutes)

- Objective: Develop financial math skills and the application of fractions in market situations, reinforcing the understanding of fractions as part of the whole.

- Description: Students will simulate a market where they will have to calculate prices and divide items into fractions for imaginary customers. Each group will receive a list of products and prices, and will have to decide how to divide the items based on fractions to meet customer needs.

- Instructions:

• Prepare 'merchandise' of items such as fruits, breads, vegetables, etc., with prices in fractions.

• Each group receives a shopping list from a customer and must calculate the total cost and the fraction of each item.

• Groups 'sell' their products to the class, which acts as customers, using fractions to represent the quantities bought.

• At the end, each group presents their division strategy and how fractions were used in transactions.

Feedback

Duration: (20 - 30 minutes)

This stage of the lesson plan is crucial for consolidating students' learning, allowing them to articulate and reflect on what they learned through practical activities. Group discussion helps develop communication and argumentation skills, while the key questions aim to deepen the understanding of the concepts of fractions and their practical application. This feedback also provides the teacher with valuable insights into the progress and challenges faced by students, guiding future pedagogical interventions.

Group Discussion

Start the group discussion by reminding students about the activities conducted, and ask each group how they applied the concept of fractions and what challenges they encountered. Use the following questions to guide the discussion: 'How did you decide the division of items at the Fraction Festival? Was there any specific strategy that helped you reach an agreement?' and 'In the Pizza Building, how did you manage to divide the pizza fairly among the ingredients?'

Key Questions

1. Which fraction concepts did you find most challenging during the activities and why?

2. How did you perceive the use of fractions in everyday life while carrying out the proposed activities?

3. What strategies do you think could have facilitated or improved the division in some of the activities?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage aims to consolidate the knowledge acquired by students during the lesson, linking practical activities to the theory studied. In addition, it seeks to reinforce the importance and applicability of fraction concepts in everyday life, preparing students to use them effectively in real situations. This final recap serves to ensure that students can retain and apply the learning continuously and meaningfully.

Summary

In this conclusion, let's recapitulate the main points addressed regarding fractions, from identifying and representing fractions smaller and larger than one to associating them with division and the idea of part of a whole. Let's revisit practical activities such as the Fraction Festival, Pizza Builders, and the Fraction Market, which allowed students to apply these concepts interactively and meaningfully.

Theory Connection

Today's lesson effectively connected theory to practice, using everyday situations and playful activities to solidify students' understanding of fractions. The practical activities helped visualize and manipulate fractions, reinforcing theoretical learning and demonstrating the relevance of fractions in various real applications.

Closing

Understanding fractions is essential not only for academic success in mathematics but also for daily life, where we encounter situations that regularly require the use of this concept, such as in cooking, dividing expenses, and measurements. The ability to work with fractions helps develop logical reasoning and the capacity to solve practical problems, becoming a valuable tool for students.