Lesson Plan | Active Learning | Algebraic Expressions

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 direct the focus of students and the teacher to what will be essential during the lesson. By clearly establishing what students should achieve, this section serves as a map for subsequent activities, ensuring that all involved are aligned and understand the learning expectations. The listed objectives will guide the practical activities in the classroom, allowing students to apply prior knowledge effectively and engagingly.

Main Objectives:

1. Develop the ability to solve algebraic expressions by applying the properties of arithmetic operations in expressions that include variables, such as in the example 2x + 4x - 3x.

2. Enable students to identify and operate on algebraic expressions in various contexts, encouraging logical reasoning and the practical application of mathematical concepts.

Side Objectives:

1. Encourage the active participation of students through group discussions and collaborative problem-solving.
2. Promote students' self-confidence when dealing with mathematical problems involving algebraic expressions.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the lesson theme through problem situations that make practical use of the concept of algebraic expressions, acting as a bridge between theoretical knowledge and its application in the real world. Additionally, by contextualizing the subject, students can see the practical value of the content learned, thereby increasing interest and motivation for learning.

Problem-Based Situations

1. Imagine that a friend of yours is saving to buy a new video game that costs R$ 500. He already has R$ 200 and plans to save R$ x per month. After 3 months, he will have enough money to buy the video game. What is the value of x?

2. A company manufactures and sells x units of a product at R$ 20 each. If the fixed cost of production is R$ 1000 and the variable cost per unit is R$ 5, what should the value of x be for the company not to incur a loss?

Contextualization

Algebraic expressions are everywhere in our daily lives, from calculating personal expenses to analyzing profits in large companies. Understanding how to manipulate these expressions allows students not only to solve mathematical problems but also to develop analytical skills that are essential in various areas of life. Moreover, the ability to solve algebraic expressions strengthens logical reasoning, preparing students for more complex challenges in their academic and professional futures.

Development

Duration: (75 - 80 minutes)

The development stage is crucial to allow students to apply the concepts previously studied practically and engagingly. The proposed activities aim to consolidate students' understanding of algebraic expressions through interactive and collaborative methods. By working in groups, students also develop social and teamwork skills while practicing math in a fun and relevant way. Choosing only one activity allows for a significant deepening of the topic and ensures that all students actively participate in problem-solving.

Activity Suggestions

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

Activity 1 - The Great Race of Expressions

> Duration: (60 - 70 minutes)

- Objective: Practice solving algebraic expressions playfully and collaboratively, reinforcing the understanding of addition, subtraction, and simplification of algebraic terms.

- Description: In this activity, students will be divided into groups of up to 5 people to participate in a relay race with algebraic expressions. Each group will receive a set of cards containing incomplete algebraic expressions and must complete them correctly to advance to the next stage of the race. The expressions will involve addition, subtraction, and simplification of algebraic terms. The game will be set on a large board on the classroom floor, where each space will correspond to a stage of the race.

- Instructions:

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

• Explain the rules: each group starts at the same position on the board, and each correctly solved expression card allows the group to advance one space.

• Distribute the expression cards to each group.

• The first group to reach the end of the board, correctly completing all expressions, wins.

• Conduct a review of the expressions with the whole class at the end of the activity.

Activity 2 - Expressions in the Market

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of algebraic expressions in a financial management context, developing calculation and strategic reasoning skills.

- Description: Students will be challenged to manage a small fruit shop where they need to use algebraic expressions to calculate profits, losses, and restocking inventory. Each group will receive an initial amount of money and a list of buying and selling prices. They must decide on quantities to buy, calculate potential profit, and adjust their strategies as the game progresses.

- Instructions:

• Form groups of up to 5 students and distribute the 'money' and price list.

• Explain that they need to calculate profit based on the algebraic expressions provided for different buying and selling scenarios.

• Allow groups to make simulated purchases and sales and adjust their strategies throughout the game.

• At the end, discuss the strategies that led to the best results and the expressions used.

Activity 3 - Mathematical Mystery

> Duration: (60 - 70 minutes)

- Objective: Develop skills in solving algebraic expressions in a mystery game context, promoting teamwork and logical thinking.

- Description: In this mystery-solving activity, students will use their skills to solve algebraic expressions to uncover clues hidden in the classroom. Each clue resolves part of the mystery and leads to the next, with the final solution revealing 'who did it'. The puzzles will be related to the concepts of addition and subtraction of algebraic terms and simplification of expressions.

- Instructions:

• Prepare the classroom with hidden clues that can only be unveiled through solving algebraic expressions.

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

• Give each group the first clue to start the game.

• Groups must solve the expressions to advance to the next clue and eventually solve the mystery.

• Lead a discussion about resolution strategies after the activity.

Feedback

Duration: (10 - 15 minutes)

This stage of the lesson plan is essential to consolidate the learning acquired during the practical activities. By discussing in groups, students have the opportunity to reflect on their thought processes and resolution strategies, as well as learn from each other. This discussion helps reinforce understanding of mathematical concepts and promotes greater retention of knowledge. Interaction and idea sharing stimulate a collaborative and dynamic learning environment.

Group Discussion

Start the group discussion with a general review of the activities carried out. Ask students how they felt solving algebraic expressions through playful activities and what challenges they encountered. Encourage them to share their strategies and what they discovered about the use of algebraic expressions in everyday life. Use this opportunity for each group to report what they learned and how they applied the knowledge of algebraic expressions to solve the problems proposed in the activities.

Key Questions

1. What were the main difficulties encountered while solving algebraic expressions during the activities?

2. How did collaborating with peers help find solutions?

3. What lessons about algebraic expressions can you apply in real situations outside the classroom?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage serves to solidify students' understanding, providing a moment to review and reflect on what was learned. By summarizing the main concepts, the lesson reinforces students' memory and comprehension while the discussion about the practical application of the taught concepts highlights the relevance of the subject. This moment is also crucial for students to perceive the integration between the studied theory and the practical activities carried out, ensuring effective and meaningful learning.

Summary

To close the lesson, it is important to summarize and recap the concepts of algebraic expressions covered. During the lesson, students had the opportunity to explore the application of arithmetic operation properties in expressions that include variables, such as in the example 2x + 4x - 3x, and solved contextualized problems involving these expressions.

Theory Connection

Today's lesson was structured to connect theory with practice through diverse and interactive activities. Students applied theoretical knowledge in practical situations such as games and simulations, which facilitated understanding and retention of the mathematical concepts addressed.

Closing

The study of algebraic expressions is fundamental as it allows students to develop essential analytical skills to solve complex problems in various contexts, both academic and everyday. The ability to manipulate and understand algebraic expressions opens doors to understanding more advanced concepts in mathematics and other sciences.