Lesson Plan | Traditional Methodology | Inequalities: Introduction

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to provide students with a clear and detailed understanding of what inequalities are, how they differ from equations, and what methods are used to solve them. This theoretical and practical foundation is essential for students to move forward with confidence in solving more complex problems involving inequalities.

Main Objectives

1. Identify and understand the symbols and concepts of inequalities (>, <, ≥, ≤).

2. Solve basic first-degree inequalities using algebraic methods.

3. Interpret solutions of inequalities and represent them on the number line.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to provide students with a clear and detailed understanding of what inequalities are, how they differ from equations, and what methods are used to solve them. This theoretical and practical foundation is essential for students to move forward with confidence in solving more complex problems involving inequalities.

Context

To start the lesson on inequalities, it is important to establish a connection with the students' prior knowledge about equations. Explain that while an equation defines an equality between two expressions, an inequality establishes a relationship of inequality. Use simple examples to illustrate: 'If 2 + 3 = 5 is an equation, then 2 + 3 < 6 is an inequality.' Propose a daily situation, such as comparing heights among classmates or the amount of money needed to buy something, to contextualize the concept of inequality.

Curiosities

Did you know that inequalities are widely used in various areas of our daily lives? For example, engineers use them to ensure that bridges are safe by calculating the maximum stresses that materials can withstand. Economists use inequalities to forecast budgets and ensure that expenditures do not exceed revenues. Thus, understanding inequalities can help solve practical and important problems.

Development

Duration: 60 - 70 minutes

The purpose of this stage is to provide students with a detailed and practical understanding of solving inequalities. By addressing specific topics and solving problems in class, students are able to apply the concepts learned, consolidating their understanding and developing the necessary skills to solve first-degree inequalities with confidence.

Covered Topics

1. Definition and Symbols of Inequalities: Explain that an inequality is a mathematical expression that uses inequality symbols (>, <, ≥, ≤). Detail each symbol and its meaning, using practical examples to illustrate. 2. Transformation of Inequalities: Show how to manipulate inequalities similarly to equations, but with special attention to the inequality sign. For example, when we multiply or divide both sides of an inequality by a negative number, the inequality sign inverts. 3. Solving Basic Inequalities: Teach the steps to solve first-degree inequalities. Start with simple examples, such as 3x - 4 > 0, and guide the students step by step in the solution, highlighting the importance of maintaining balance in the inequality. 4. Representation on the Number Line: Demonstrate how to represent the solution of an inequality on a number line. Use practical examples and draw the number line on the board, showing how to identify and mark the solution intervals. 5. Interpretation of Solutions: Discuss how to interpret the solutions of inequalities. Explain that the solution of an inequality is a set of values that satisfy the given condition and that these values can be represented in intervals.

Classroom Questions

1. Solve the inequality 2x + 5 < 15 and represent the solution on the number line. 2. For what values of x is the inequality 4x - 7 ≥ 9 true? 3. Determine the solution of the inequality -3x + 6 ≤ 0 and represent it on the number line.

Questions Discussion

Duration: 15 - 20 minutes

The purpose of this stage is to review and consolidate the concepts and procedures learned during the lesson. By discussing the solutions to the proposed questions and addressing any difficulties encountered, students have the opportunity to clarify doubts and reinforce their understanding of solving inequalities. This moment of reflection and engagement also allows the teacher to evaluate the level of understanding of the students and identify points that may need greater emphasis or review.

Discussion

• Solve the inequality 2x + 5 < 15 and represent the solution on the number line:

• Subtract 5 from both sides: 2x + 5 - 5 < 15 - 5 results in 2x < 10.

• Divide both sides by 2: 2x / 2 < 10 / 2 results in x < 5.

• The solution is x < 5, which on the number line is represented by an open interval to the left of 5.

• For what values of x is the inequality 4x - 7 ≥ 9 true?

• Add 7 to both sides: 4x - 7 + 7 ≥ 9 + 7 results in 4x ≥ 16.

• Divide both sides by 4: 4x / 4 ≥ 16 / 4 results in x ≥ 4.

• The solution is x ≥ 4, which on the number line is represented by a closed interval to the right of 4.

• Determine the solution of the inequality -3x + 6 ≤ 0 and represent it on the number line:

• Subtract 6 from both sides: -3x + 6 - 6 ≤ 0 - 6 results in -3x ≤ -6.

• Divide both sides by -3 and invert the inequality sign: -3x / -3 ≥ -6 / -3 results in x ≥ 2.

• The solution is x ≥ 2, which on the number line is represented by a closed interval to the right of 2.

Student Engagement

1. What difficulties did you encounter when solving the inequalities? 2. Can anyone explain why the inequality sign inverts when multiplying or dividing by a negative number? 3. How would you represent the solutions of inequalities graphically? 4. Can you think of everyday situations where we use inequalities? 5. How can interpreting the solutions of inequalities help in solving practical problems?

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to review and consolidate the concepts learned, ensuring that students have a clear and cohesive view of the content addressed. By summarizing the main points, connecting theory to practice, and highlighting the relevance of the theme, students can reinforce their understanding and recognize the importance of inequalities in various areas.

Summary

• Inequalities are mathematical expressions that use inequality symbols (>, <, ≥, ≤).
• Manipulation of inequalities is similar to manipulation of equations, but attention must be paid to the inequality sign, especially when multiplying or dividing by negative numbers.
• The steps to solve first-degree inequalities include isolating the variable and adjusting the inequality sign as necessary.
• The solution of an inequality can be represented on a number line, indicating specific intervals.
• Interpreting the solutions of inequalities involves understanding that the solution is a set of values that satisfy the given condition.

The lesson connected theory to practice by using simple and everyday examples to illustrate the concepts of inequalities, showing how to solve problems step by step and represent them graphically. Students were able to see how theoretical methods apply to practical situations and how to interpret the results obtained.

Understanding inequalities is crucial for various fields of knowledge and everyday situations, such as in engineering to ensure the safety of structures, in economics to forecast budgets and control expenses, and even in simple situations like planning purchases or comparing heights. Inequalities are powerful tools for solving practical problems and making informed decisions.