Lesson Plan | Active Learning | Fractions: Common Denominators

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 minutes)

This stage of the lesson plan is essential to establish the learning goals that students should achieve. By clearly defining the objectives, students have a guide to focus their efforts and attention on the proposed activities. This also helps align expectations and ensure that all involved are aware of what is expected as a result of the teaching-learning process.

Main Objectives:

1. Empower students to recognize when two fractions have different denominators and put them in a common denominator by applying the concept of equivalent fractions.

Side Objectives:

1. Develop logical and critical reasoning skills when solving mathematical problems involving fractions.

Introduction

Duration: (15 minutes)

The introduction aims to activate students' prior knowledge about fractions and prepare them for the practical activities they will perform in class. The problem situations encourage students to think critically and apply the concept of common denominators in real contexts. The contextualization aims to show the importance and applicability of fractions in everyday life, increasing engagement and the perceived relevance of the topic.

Problem-Based Situations

1. Imagine that in a cake recipe you need to double all the ingredients, but the original recipe asks for 1/2 cup of flour and 1/4 cup of sugar. How can you calculate how much of each ingredient should be used now that the recipe has been doubled?

2. Think of a pizza divided into 8 slices, where 3/8 is cheese and 2/8 is pepperoni. If a friend wants half of their portion, how can you calculate how much they will eat of cheese and pepperoni, considering that the pizza is now divided into 4 equal parts?

Contextualization

Fractions are often used in daily life, whether in the kitchen, in financial situations, or even in sharing a snack with friends. Understanding how to manipulate fractions, especially to find common denominators, is essential for carrying out everyday tasks and understanding more complex concepts in mathematics. Tidbits like the history of how ancient Egyptians used fractions to divide land and calculate taxes can spark students' interest and show the relevance of the subject in different cultural and historical contexts.

Development

Duration: (65 - 75 minutes)

The Development stage in the lesson plan is designed to allow students to practically and playfully apply the concepts of fractions with common denominators they studied previously. Working in groups, they will have the opportunity to solve problems and perform tasks that require not only mathematical knowledge but also teamwork and critical thinking skills. Each proposed activity aims to solidify students' understanding of how to manipulate and compare fractions, in addition to providing a dynamic and interactive learning environment.

Activity Suggestions

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

Activity 1 - The Race of Denominators

> Duration: (60 - 70 minutes)

- Objective: Practice identifying and ordering fractions with common denominators in a playful and competitive way.

- Description: In this activity, students will be divided into groups of up to 5 people to participate in a math race. Each group will receive a series of cards, each containing a fraction. The challenge will be to organize the cards in ascending or descending order, considering the common denominator. To make the activity more dynamic, each time a sequence is correct, the group will advance on a 'track' drawn on the classroom floor, simulating a race.

- Instructions:

• Divide the class into groups of no more than 5 students.

• Distribute fraction cards to each group. Each card must have a different fraction with varied denominators.

• Explain that the objective is to group the cards in ascending or descending order, considering placing the fractions in common denominators.

• Each time a group gets the sequence right, they advance one space on the track.

• The first group to complete the race will be the winner.

Activity 2 - The Festival of Half Pies

> Duration: (60 - 70 minutes)

- Objective: Develop negotiation and teamwork skills, in addition to practicing the manipulation of fractions with common denominators.

- Description: Students, in groups, will receive cards representing half pizzas divided into fractions. The challenge is to share these half pizzas among the groups in such a way that each receives the same amount of pizza, but the fractions are in common denominators. Groups will need to swap fractions among themselves until all pizzas are equally divided.

- Instructions:

• Organize students into groups of up to 5 people.

• Distribute cards representing half pizzas divided into different fractions to each group.

• Instruct students to divide the pizzas so that all groups receive the same amount, but with fractions in common denominators.

• Allow groups to negotiate and swap fractions among themselves to achieve the goal.

• The group that correctly divides the pizzas first, using fractions with common denominators, wins.

Activity 3 - Fraction Tower Builders

> Duration: (60 - 70 minutes)

- Objective: Encourage the use of equivalent fractions in common denominators to solve practical problems and develop problem-solving and collaboration skills.

- Description: In this activity, each group of students will receive building blocks that represent fractions with different denominators. The challenge is to construct the tallest possible tower using only blocks with equivalent fractions in common denominators. Each group will need to solve mathematical problems to obtain additional blocks, which will only be given if the fractions are correct.

- Instructions:

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

• Give each group building blocks that represent fractions with different denominators.

• Explain that to build the tower, they need to use only blocks with equivalent fractions in common denominators.

• Present a series of mathematical problems that the groups must solve to earn more blocks.

• The group with the tallest tower, built correctly with fractions in common denominators, wins.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to allow students to articulate what they learned and how they applied the concepts of fractions with common denominators. This reflection serves to consolidate knowledge, allowing students to identify the strengths and weaknesses of their approaches and learn from others' experiences. Moreover, by hearing colleagues' strategies, students can gain new perspectives and insights, promoting a deeper understanding of the topic.

Group Discussion

At the end of the activities, gather all students for a group discussion. Start the discussion with a brief introduction, explaining that the goal is to share what each group learned and the strategies they used to solve the challenges. Encourage each group to discuss not only what went well but also the mistakes they made and how they corrected them. This is a moment of collective reflection, where everyone can learn from each other.

Key Questions

1. What were the biggest challenges when trying to find common denominators among fractions during the activities?

2. How did equivalent fractions help you solve the proposed problems?

3. Was there any strategy that worked particularly well for your group?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage is to ensure that all key concepts covered during the lesson are clearly understood and internalized by the students. The recapitulation helps consolidate learning, while the discussion about the bridge between theory and practice and the relevance of fractions in everyday life reinforces the importance of studying beyond the classroom. This moment also serves to clarify any remaining doubts and ensure that students leave the lesson with a solid and applicable understanding of the content.

Summary

In conclusion, the teacher should summarize the main learnings on how to identify and work with fractions with common denominators, reinforcing the concepts of equivalent fractions and their applicability in practical situations. It is essential to recap the strategies discussed and utilized by students during the activities.

Theory Connection

During the lesson, the connection between the theory of fractions and the practices was emphasized through playful and contextualized activities, such as the 'Race of Denominators' and the 'Festival of Half Pies'. These activities not only reinforced the concept of equivalent fractions and common denominators but also showed how these concepts are applied in real and everyday situations.

Closing

Finally, it is important to highlight the relevance of studying fractions for everyday life, especially in contexts like cooking, resource sharing, and even financial planning activities. Understanding and applying fractions with common denominators is a fundamental skill that students can carry with them to solve practical problems in various areas.