Further Mathematics - Senior Secondary 1 - Linear inequalities

Linear inequalities

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TERM: 3RD TERM

WEEK 1

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Linear Inequalities
Focus: Linear Inequalities in One Variable and Two Variables
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Solve linear inequalities in one variable.
  2. Solve linear inequalities in two variables.
  3. Represent the solutions of linear inequalities on a number line.
  4. Interpret the graphical representation of linear inequalities in two variables.

INSTRUCTIONAL TECHNIQUES: • Question and answer
• Guided demonstration
• Discussion
• Practice exercises
• Graphical representation
• Real-life applications

INSTRUCTIONAL MATERIALS: • Whiteboard and markers
• Number line charts
• Graph paper
• Worksheets with inequality problems
• Graphing calculators (if available)

 

PERIOD 1 & 2: Introduction to Linear Inequalities in One Variable
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of linear inequalities in one variable. Explains that inequalities involve a comparison between two expressions using symbols such as <, >, ≤, or ≥. Examples are provided: e.g., 2x - 5 < 9.

Students listen attentively and ask questions.

Step 2 - Solving One Variable Inequalities

Demonstrates how to solve simple linear inequalities by isolating the variable. For example, solving 2x - 5 < 9.

Students follow the example and solve similar problems individually.

Step 3 - Representing on a Number Line

Shows how to represent the solution on a number line, emphasizing open or closed circles for strict or inclusive inequalities.

Students practice representing solutions on a number line.

Step 4 - Practice Exercise

Provides practice problems for students to solve independently, then reviews the solutions as a class.

Students work on the exercises and present their answers for review.

NOTE ON BOARD:

  • Example: Solve 2x - 5 < 9
    Solution:
    2x - 5 < 9
    2x < 14
    x < 7
    The solution is x < 7, represented as an open circle at 7 on the number line.

EVALUATION (5 exercises):

  1. Solve: 3x + 4 < 10
  2. Solve: 5x - 6 ≥ 9
  3. Solve: 2x - 7 > 1
  4. Solve: 4x ≤ 16
  5. Solve: 3x + 2 < 11

CLASSWORK (5 questions):

  1. Solve: 7x - 3 > 18
  2. Solve: 5x + 8 < 23
  3. Solve: x - 2 ≤ 5
  4. Solve: 9x - 7 ≥ 20
  5. Solve: 6x + 3 < 15

ASSIGNMENT (5 tasks):

  1. Solve: 2x - 3 > 5
  2. Solve: 3x + 7 ≤ 16
  3. Solve: 4x - 1 < 3
  4. Solve: 5x ≥ 10
  5. Represent the solution of x < 4 on a number line.

 

PERIOD 3 & 4: Linear Inequalities in Two Variables
PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces linear inequalities in two variables, explaining the difference from one-variable inequalities. Examples are given: e.g., 2x + y ≤ 5.

Students take notes and ask clarifying questions.

Step 2 - Solving Two Variable Inequalities

Demonstrates how to solve and graph linear inequalities in two variables by first converting the inequality to an equation. For example, solving 2x + y ≤ 5.

Students observe the example and attempt similar problems.

Step 3 - Graphing the Inequalities

Shows how to graph the inequality on a coordinate plane, including how to differentiate between a solid and dashed line, depending on the inequality sign (≤, ≥ vs. <, >).

Students practice graphing inequalities on graph paper.

Step 4 - Guided Practice

Provides various two-variable inequalities for students to solve and graph, working in pairs.

Students solve and graph the inequalities with guidance.

NOTE ON BOARD:

  • Example: Solve and graph 2x + y ≤ 5
    Convert to an equation: 2x + y = 5
    Graph the line 2x + y = 5.
    Since the inequality is ≤, shade below the line (for values satisfying y ≤ 5 - 2x).

EVALUATION (5 exercises):

  1. Solve and graph: x + y ≤ 6
  2. Solve and graph: 3x - y ≥ 4
  3. Solve and graph: x - y < 2
  4. Solve and graph: 2x + y > 7
  5. Solve and graph: x + 2y ≤ 4

CLASSWORK (5 questions):

  1. Solve and graph: x + y ≥ 3
  2. Solve and graph: 2x - y < 4
  3. Solve and graph: 3x + y ≥ 9
  4. Solve and graph: x + 3y < 5
  5. Solve and graph: 4x - y ≥ 8

ASSIGNMENT (5 tasks):

  1. Solve and graph: x - 2y < 5
  2. Solve and graph: 2x + y ≥ 6
  3. Solve and graph: 4x + y > 8
  4. Solve and graph: 3x - y ≤ 2
  5. Graph the inequality: y > 2x + 1 on a coordinate plane.