Lesson Plan: Linear Inequalities in One Variable & Graphical Presentations of Solution of Linear Inequalities

Subject: Mathematics

Class: JSS 2

Term: Second Term

Week: 5

Topic: Linear Inequalities in One Variable, Graphical Presentations of Solution of Linear Inequalities

Sub-topic: Solving and Graphing Linear Inequalities in One Variable

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Behavioral Objectives

By the end of the lesson, students should be able to:

1. Define linear inequalities in one variable.
2. Solve linear inequalities in one variable.
3. Graphically represent the solutions of linear inequalities on a number line.
4. Understand and interpret solutions in the context of word problems.

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Keywords

• Linear Inequality
• Solution Set
• Number Line
• Greater Than (>)
• Less Than (<)
• Greater Than or Equal To (≥)
• Less Than or Equal To (≤)

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Set Induction (Lesson Introduction)

The teacher begins by drawing a simple number line on the board and asks:
“If I say that x is greater than 3, how would that be shown on the number line?”
After the response, the teacher explains that inequalities represent a range of values rather than a specific number and that they can be graphed.

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Entry Behavior

Students have prior knowledge of basic algebraic expressions and simple equations.

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Learning Resources and Materials

• Whiteboard and markers
• Number line charts
• Graphing tools (optional)
• Practice worksheets with inequalities

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Building Background/Connection to Prior Knowledge

• Students have previously learned about simple equations.
• The teacher connects solving linear inequalities to solving simple algebraic equations, emphasizing how inequalities differ by having multiple possible solutions.

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Embedded Core Skills

• Critical Thinking – Solving inequalities and interpreting solutions.
• Numeracy Skills – Correctly plotting points and reading number lines.
• Problem-Solving – Applying inequalities in real-world situations.

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Learning Materials

• Lagos State Scheme of Work
• Mathematics textbooks (JSS 2)
• Online resources: Khan Academy – Linear Inequalities

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Instructional Materials

• Number line printouts
• Graphing paper (if applicable)
• Practice exercises

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Lesson Presentation

Step 1: Introduction to Linear Inequalities

Teacher’s Activity:

• Defines a linear inequality as a mathematical expression that shows the relationship between two expressions using inequality signs (>, <, ≥, ≤).
• Provides examples:
  • x > 3
  • x ≤ 5
  • x ≥ -2

Learner’s Activity:

• Students give examples of linear inequalities they encounter in daily life (e.g., age restrictions, temperature limits).

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Step 2: Solving Linear Inequalities

Teacher’s Activity:

• Demonstrates how to solve linear inequalities, emphasizing the rules of inequality (e.g., when multiplying or dividing by a negative number, the inequality sign flips).
• Example 1: Solve x + 2 > 5
  • Subtract 2 from both sides: x > 3

Learner’s Activity:

• Students solve similar inequalities independently:
  • x – 4 ≤ 6
  • 2x > 10

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Step 3: Graphical Representation of Solutions on a Number Line

Teacher’s Activity:

• Explains how to graphically represent inequalities on a number line.
• Example 1: x > 3
  • The teacher draws an open circle at 3 and shades the area to the right.
• Example 2: x ≤ 5
  • The teacher draws a closed circle at 5 and shades the area to the left.

Learner’s Activity:

• Students graph the solutions of the inequalities:
  • x > 2
  • x ≤ -4
  • x ≥ 0

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Step 4: Solving Word Problems Involving Linear Inequalities

Teacher’s Activity:

• Presents word problems that involve linear inequalities.
  Example: “A school club has at least 30 members. Write an inequality to represent the number of members, and graph it.”
  • Solution: x ≥ 30

Learner’s Activity:

• Students work in pairs to solve similar word problems and represent the solutions graphically.

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Evaluation Questions

1. Which of the following is a linear inequality?
   a) x + 3 = 5
   b) 2x ≤ 7
   c) x – 4 = 0
   d) 3x + 2 > 8

2. What is the solution to the inequality x – 4 > 2?
   a) x > 6
   b) x < 6
   c) x ≥ 6
   d) x ≤ 6

3. Solve the inequality 5x ≤ 20.
   a) x ≤ 4
   b) x ≥ 4
   c) x < 4
   d) x > 4

4. Graph the solution of x > -2 on a number line.
   a) Open circle at -2, shading to the left
   b) Closed circle at -2, shading to the left
   c) Open circle at -2, shading to the right
   d) Closed circle at -2, shading to the right

5. Which of the following represents the inequality x ≤ 5 on a number line?
   a) Closed circle at 5, shading to the left
   b) Open circle at 5, shading to the right
   c) Open circle at 5, shading to the left
   d) Closed circle at 5, shading to the right

6. Solve the inequality 2x ≥ 12.
   a) x ≥ 6
   b) x ≤ 6
   c) x > 6
   d) x < 6

7. Graph the solution to the inequality x ≤ 3.
   a) Open circle at 3, shading to the right
   b) Closed circle at 3, shading to the left
   c) Closed circle at 3, shading to the right
   d) Open circle at 3, shading to the left

8. Solve the inequality 3x – 5 > 10.
   a) x > 5
   b) x < 5
   c) x ≥ 5
   d) x ≤ 5

9. Which of the following inequalities is represented by a solid line on the graph?
   a) x < 4
   b) x ≥ 2
   c) x > -3
   d) x < 0

10. What does the inequality x > 7 mean on a number line?
    a) The solution is all values less than 7.
    b) The solution is all values greater than or equal to 7.
    c) The solution is all values greater than 7.
    d) The solution is all values less than or equal to 7.

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Class Activity Discussion – FAQs

1. What is a linear inequality?
   A linear inequality is a mathematical statement that shows the relationship between two expressions using inequality signs (>, <, ≥, ≤).

2. How do we solve a linear inequality?
   Solve linear inequalities like equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.

3. What does the open circle represent on a number line?
   An open circle means the number is not included in the solution.

4. What does the closed circle represent on a number line?
   A closed circle means the number is included in the solution.

5. How do you graph x > 4?
   Draw an open circle at 4 and shade to the right of 4.

6. What happens if we multiply or divide an inequality by a negative number?
   The inequality sign flips.

7. Can inequalities be solved the same way as equations?
   Yes, but remember the special rule for multiplying or dividing by negative numbers.

8. Why is it important to understand inequalities?
   Inequalities are used to represent real-life situations like age restrictions, money, and measurements.

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Assessment – Short Answer Questions

1. Define linear inequality.
2. Solve the inequality x + 5 < 10.
3. Graph the solution of x ≥ 2 on a number line.
4. How would you solve 3x < 9?
5. What does the solution x > -1 mean in words?
6. Solve the inequality 5x + 3 ≥ 18.
7. Describe the difference between a solid and open circle on a number line.

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Conclusion

The teacher summarizes the lesson by revisiting key concepts such as solving and graphing linear inequalities. Practice problems are assigned for homework.

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