Further Mathematics - Senior Secondary 1 - Linear inequalities

Linear inequalities

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TERM: 3RD TERM

WEEK 2

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Linear Inequalities
Focus: Graphs of Linear Inequalities in Two Variables, Identifying the Region that Satisfies Linear Inequalities

 

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

  1. Understand the concept of linear inequalities in two variables.
  2. Plot the graph of a linear inequality in two variables.
  3. Identify the region that satisfies the linear inequality.
  4. Solve problems related to linear inequalities.

 

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Discussion
• Practice exercises
• Use of real-life examples and applications

 

INSTRUCTIONAL MATERIALS:
• Graph board
• Graph books
• Ruler
• Flashcards with inequalities
• Example problems for class practice

PERIOD 1 & 2: Introduction to Linear Inequalities and Graphing

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of linear inequalities and explains how they relate to linear equations. Explains the difference between inequalities and equations.

Students listen attentively and ask clarifying questions.

Step 2 - Graphing Inequalities

Demonstrates how to graph a linear inequality (e.g., y > 2x + 1). Explains that the boundary line is plotted like a linear equation, but the region above or below the line is shaded, depending on the inequality sign.

Students observe and take notes on the method of graphing inequalities.

Step 3 - Identifying the Region

Demonstrates the use of shading to represent the solution set of the inequality. Emphasizes that the region above or below the line represents the values that satisfy the inequality.

Students observe and participate in the shading exercise on the graph.

Step 4 - Guided Practice

Provides several inequalities for the students to graph and shade in pairs. Offers guidance as needed.

Students work in pairs to graph and shade the solution set of inequalities.

NOTE ON BOARD:

  1. Plotting a linear inequality:
    • Graph the boundary line as if it were an equation (y = mx + b).
    • If the inequality is ">" or "<", use a dashed line.
    • If the inequality is "≥" or "≤", use a solid line.
    • Shade the region that satisfies the inequality.
  2. Example Inequalities:
    • y > 2x + 1
    • y ≤ -x + 3

EVALUATION (5 exercises):

  1. Graph y > x + 2.
  2. Graph y ≤ 3x - 1.
  3. Graph y < -x + 4.
  4. Identify the shaded region for the inequality y ≥ x - 2.
  5. Explain the difference between the graphs of y ≥ x + 1 and y > x + 1.

CLASSWORK (5 questions):

  1. Graph y < 2x + 1.
  2. Graph y ≥ -x + 3.
  3. Graph y > -2x + 4.
  4. Which region satisfies y ≥ 2x - 1?
  5. Draw the graph of y < -3x + 5.

ASSIGNMENT (5 tasks):

  1. Graph y > 3x + 2.
  2. Graph y ≤ x - 3.
  3. Solve and graph the inequality y > 4x - 2.
  4. Identify the region that satisfies y ≤ -x + 5.
  5. Create a real-life scenario that could be modeled with a linear inequality and graph it.

 

PERIOD 3 & 4: Solving Problems on Linear Inequalities

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Problem Introduction

Introduces a problem that involves linear inequalities in two variables. Shows how to model a word problem as a linear inequality and then graph it.

Students listen to the problem and take notes on the modeling process.

Step 2 - Guided Practice

Works through an example where students model a scenario and solve the linear inequality graphically.

Students follow along and solve a similar problem with teacher guidance.

Step 3 - Independent Practice

Provides several word problems for students to solve on their own, encouraging them to graph the inequalities and identify the solution region.

Students work independently or in pairs to solve the problems.

Step 4 - Class Discussion

Reviews the solutions to the problems, clarifying any difficulties and providing further explanations where necessary.#

Students discuss their solutions and ask for clarification if needed.

NOTE ON BOARD:
Steps to solve a linear inequality problem:

  1. Translate the word problem into a linear inequality.
  2. Graph the inequality on the coordinate plane.
  3. Shade the region that satisfies the inequality.
  4. Interpret the solution in the context of the problem.

EVALUATION (5 exercises):

  1. Solve and graph the inequality for a situation where the total cost y is less than 50, and each item x costs 5 units.
  2. Graph and solve the inequality y ≤ 2x + 1 for a scenario involving a budget constraint.
  3. Graph the inequality y ≥ 3x - 4 for a problem involving time and work.
  4. Solve and graph the inequality y < -x + 3 for a scenario involving speed.
  5. Write an inequality for a situation where you need to save at least $200 in a savings account.

CLASSWORK (5 questions):

  1. Solve and graph the inequality y ≥ x + 2 for a scenario where y represents the total amount saved and x represents the number of weeks.
  2. Solve and graph y > 4x - 1 for a problem involving distance and speed.
  3. Graph y ≤ -3x + 5 for a problem involving temperature.
  4. Graph y < -2x + 7 for a scenario involving time.
  5. Solve and graph y ≥ 2x - 3 for a problem involving sales targets.

ASSIGNMENT (5 tasks):

  1. Write and graph the inequality for a scenario where you are renting a room for a month, and the rent must be less than $500.
  2. Solve and graph the inequality y ≤ 4x + 3 for a scenario where y represents the number of books and x represents the price of each book.
  3. Graph and solve the inequality y > 5x - 2 for a scenario involving investments.
  4. Solve and graph y ≤ 2x + 6 for a problem involving resource allocation.
  5. Create and solve a word problem involving a linear inequality in two variables.