Lesson Plan | Technical Methodology | Relationships and equations of magnitudes

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to ensure that students understand the relationships between quantities and how these can be represented mathematically. It is essential to develop practical skills that allow students to apply these concepts in real-life situations and in the job market, promoting a solid and usable understanding of mathematics in everyday life and future careers.

Main Objectives

1. Verify the type of relationship between two quantities and identify if they are directly or inversely proportional.

2. Express the relationship between quantities through algebraic sentences.

3. Associate first-degree linear equations with two unknowns to lines in the Cartesian plane.

Side Objectives

Introduction

Duration: (10 - 15 minutes)

Purpose: The purpose of this stage of the lesson plan is to contextualize and engage students about relationships and equations of quantities. By connecting the topic with everyday situations and examples from the job market, students can perceive the practical relevance of the content, which facilitates understanding and applying mathematical concepts in various fields.

Contextualization

Contextualization: The relationships between quantities are fundamental in everyday life and in various professions. For example, when cooking, the amount of ingredients needed is directly related to the number of servings one wishes to prepare. Understanding these relationships helps solve practical problems efficiently and accurately, facilitating everything from household chores to calculations in fields like engineering and economics.

Curiosities and Market Connection

Curiosities and Market Connection: Did you know that engineers use relationships between quantities to design safe and efficient structures? Additionally, data analysts often establish correlations between variables to predict market trends. Even in medicine, medication dosage is calculated based on the proportional relationship between the amount of medication and the patient's weight.

Initial Activity

Initial Activity: To spark the interest of students, show a brief 2-minute video on how civil engineers use proportional relationships to ensure the safety of bridges and buildings. Then, ask students: 'How do you think these mathematical relationships can influence other areas of our daily lives?'

Development

Duration: 70 - 75 minutes

The purpose of this stage of the lesson plan is to allow students to explore and apply the concepts of proportional relationships and linear equations in a practical and interactive way. Through constructing a model and solving fixation exercises, students will consolidate their understanding and be prepared to apply this knowledge in real-life situations and in the job market.

Covered Topics

1. Directly proportional relationships
2. Inversely proportional relationships
3. Algebraic sentences to represent relationships of quantities
4. First-degree linear equations with two unknowns
5. Graphical representation of linear equations in the Cartesian plane

Reflections on the Theme

Guide students to reflect on how relationships between quantities are present in everyday situations and professions. Ask how they think understanding these relationships can be useful in their lives and future careers. Encourage them to think of specific examples, such as calculating expenses in a family budget or forecasting sales in a business.

Mini Challenge

Building a Proportional Bridge

Students will build a scale model of a bridge using simple materials like popsicle sticks, string, and glue. They must calculate the amount of materials needed based on the proportion between the real bridge's dimensions and the model.

Instructions

1. Divide students into groups of 4-5 people.
2. Provide each group with a technical sheet containing the real dimensions of a bridge and the scale they should use to build the model (for example, 1:100).
3. Instruct students to calculate the number of popsicle sticks and string needed to build the model proportionally.
4. Allow students to construct the model using the provided materials.
5. After construction, ask each group to explain how they arrived at the proportion calculations and how they used these calculations to ensure that the model was proportional to the real bridge.

Objective: Develop the ability to apply proportional relationships in practical situations and stimulate teamwork and problem-solving skills.

Duration: 40 - 45 minutes

Evaluation Exercises

1. Given the directly proportional relationship between the amount of flour (in kg) and the number of loaves produced, if 2 kg of flour produce 10 loaves, how many loaves will be produced with 5 kg of flour? Write the algebraic sentence that represents this relationship.
2. A faucet fills a tank in 3 hours. If we use two identical faucets, how long will it take to fill the tank? Write the algebraic sentence that represents this inversely proportional relationship.
3. Write the first-degree linear equation that represents the relationship between the amount of fuel (in liters) and the distance traveled (in km) by a car that consumes 15 km/L. Graphically represent this equation in the Cartesian plane.

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to consolidate the knowledge acquired by students, reinforcing the connection between theory and practice and highlighting the relevance of relationships and equations of quantities for everyday life and the job market. This helps ensure that students recognize the importance of the studied content and feel motivated to apply what they learned in real situations.

Discussion

Promote a discussion in the classroom, encouraging students to reflect on how understanding the relationships and equations of quantities can be applied in different areas of the job market and daily life. Ask students how they felt doing the practical activity of building the model bridge and what difficulties and solutions they encountered. This will help consolidate learning and recognize the practical importance of the studied concepts.

Summary

Summarize the main content covered during the class, highlighting directly and inversely proportional relationships, expressing these relationships through algebraic sentences, and associating first-degree linear equations with two unknowns to lines in the Cartesian plane. Reinforce the importance of understanding these relationships to solve practical problems.

Closing

Explain how the lesson integrated theory and practice, showing students the relevance of relationships and equations of quantities in various areas of the job market. Emphasize that the skills developed are valuable both for everyday life and for their future careers. Conclude by highlighting the importance of continuing to explore and apply this knowledge in everyday situations.