Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Third Term
Week: 2
Age: 15 years
Duration: 45 minutes
Subject: Further Maths
Curriculum Theme: Further Mathematics
Previous Lesson: Calculating and Processing Devices I.
Topic: LINEAR INEQUALITIES
Subject Matter: graphs of linear inequalities in two variables, region satisfying linear inequalities

Specific Objectives

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

Cognitive Domain:

Define linear inequalities in two variables.
State the steps involved in plotting the graph of a linear inequality.
Identify the region that satisfies a given linear inequality.

Affective Domain:

Appreciate the use of linear inequalities in solving real-world problems.
Show interest in accurately plotting graphs of inequalities.

Psychomotor Domain:

Accurately plot the graph of linear inequalities in two variables.
Correctly shade the region that satisfies a given linear inequality.

Work cooperatively with peers to solve graph-based inequality problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary Schools.
State Unified Scheme of Work for Further Mathematics SS 1.
New General Mathematics for Senior Secondary Schools 1.

Instructional Materials

The teacher will teach this lesson with the aid of:

Graph board
Graph books
Ruler
Pencil
Eraser
Chalk/Marker

Rationale for the Lesson

Understanding linear inequalities helps pupils solve problems where quantities are not exactly equal but have a range of possible values. This skill is important for various applications in science, economics, and daily decision-making, enabling pupils to interpret and represent real-life constraints graphically.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of plotting points on a Cartesian plane, solving linear equations, and basic understanding of inequalities.

Lesson Content/Board Summary

LINEAR INEQUALITIES

Definition of Linear Inequalities

A linear inequality in two variables (e.g., x and y) is a mathematical statement that compares two linear expressions using an inequality symbol (>, <, ≥, ≤). Unlike equations, inequalities represent a range of possible solutions rather than a single specific solution.

Graphing Linear Inequalities in Two Variables

To graph a linear inequality in two variables, the following steps are followed:

Step 1: Replace the inequality sign with an equality sign (=) to obtain the equation of the boundary line.
Step 2: Find at least two points that satisfy the equation (e.g., x and y-intercepts) and plot them.
Step 3: Draw the boundary line:
- Use a solid line if the inequality includes “or equal to” (≥ or ≤). This means points on the line are part of the solution.
- Use a dashed (broken) line if the inequality does not include “or equal to” (> or <). This means points on the line are NOT part of the solution.
Step 4: Choose a test point not on the boundary line (e.g., the origin (0,0) if it is not on the line).
Step 5: Substitute the coordinates of the test point into the original inequality.
Step 6: If the test point satisfies the inequality (makes it true), shade the region containing the test point. If it does not satisfy the inequality (makes it false), shade the region not containing the test point.

Identifying the Region Satisfying Linear Inequalities

The shaded region on the graph represents all the points (x, y) that satisfy the linear inequality. Every point within this shaded region is a solution to the inequality.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews their prior knowledge of linear equations and basic inequalities by asking: “What is the difference between an equation and an inequality?” and “How do you represent ‘x is greater than 5’?”
Pupils’ Activity: Pupils respond to the questions, recalling previous knowledge.
Learning Point: Pupils connect new learning with existing knowledge and are prepared for the lesson.

Step 2: Explanation of Linear Inequalities

Time: 5 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher introduces the topic “Linear Inequalities” and defines what a linear inequality in two variables is, using simple examples like x + y > 3. The teacher writes the definition on the board.
Pupils’ Activity: Pupils listen attentively, take notes, and ask questions for clarification.
Learning Point: Pupils understand the definition of linear inequalities in two variables.

Step 3: Steps for Graphing Linear Inequalities

Time: 10 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher outlines and explains the step-by-step procedure for plotting the graph of a linear inequality in two variables, emphasizing the difference between solid and dashed lines and the use of a test point. The teacher writes these steps on the board.
Pupils’ Activity: Pupils listen, observe, and copy the steps into their notebooks.
Learning Point: Pupils learn the systematic approach to graphing linear inequalities.

Step 4: Practical Demonstration

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Using the graph board, the teacher demonstrates how to plot the graph of a linear inequality, for example, 2x + y ≤ 4. The teacher works through all the steps, showing how to draw the boundary line and shade the correct region.
Pupils’ Activity: Pupils observe the demonstration carefully, asking questions about specific steps.
Learning Point: Pupils see a practical application of the steps and understand how to visually represent an inequality.

Step 5: Pupil Practice

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher gives pupils another inequality, e.g., x - y > 2, and asks them to attempt to plot it in their graph books. The teacher moves around the classroom, providing guidance and correcting errors.
Pupils’ Activity: Pupils work independently or in pairs to plot the given inequality in their graph books.
Learning Point: Pupils practice the graphing process and solidify their understanding.

Step 6: Discussion of Solutions

Time: 3 minutes
Teaching Skill: Feedback/Correction
Teacher’s Activity: The teacher invites a pupil to present their graph or discusses common challenges observed during the practice session, providing clear explanations and corrections. The teacher ensures pupils correctly identify the solution region.
Pupils’ Activity: Pupils compare their work with the discussed solution and make necessary corrections.
Learning Point: Pupils receive feedback and clarify any misconceptions.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a linear inequality in two variables.
State two steps you would take to graph the inequality 3x + 2y < 6.
Explain when a dashed line is used as a boundary for an inequality.
How do you determine which region to shade after drawing the boundary line?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of accurately drawing the boundary line and correctly shading the solution region. The teacher assigns homework involving plotting various linear inequalities.
Pupils’ Activity: Pupils listen and copy the homework assignment.
Learning Point: Pupils consolidate their learning and are given tasks for further practice.

Lesson Keywords

Inequality – A mathematical statement comparing two expressions using symbols like >, <, ≥, or ≤.
Linear – Referring to an expression or equation whose graph forms a straight line.
Variables – Symbols (usually letters) that represent unknown values.
Graph – A visual representation of data or a mathematical relationship.
Region – An area on a graph representing the set of all solutions to an inequality.
Boundary Line – The line that separates the coordinate plane into two regions, determined by the associated linear equation.
Shade – To colour or mark the region on a graph that satisfies an inequality.

Differentiation

For pupils who grasp the concept quickly, the teacher will provide more complex inequalities involving negative coefficients or ask them to graph systems of linear inequalities. For pupils needing more support, the teacher will provide additional guided practice, simpler examples, and one-on-one assistance, focusing on one step at a time.

Note for teachers using this lesson plan

Ensure that pupils have ample graph paper and appropriate drawing tools. Emphasize the distinction between solid and dashed lines and the importance of using a test point to correctly identify the solution region. Encourage pupils to clearly label axes and lines on their graphs.