Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: Third Term
Week: 1
Age: 15 years
Duration: 45 minutes
Subject: Further Maths
Curriculum Theme: Further Mathematics
Previous Lesson: Linear Inequalities II.
Topic: LINEAR INEQUALITIES
Subject Matter: linear inequalities in one variable, linear inequalities in two variables

Specific Objectives

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

Cognitive Domain:

Define linear inequalities.
Distinguish between linear inequalities in one variable and in two variables.
State the rules for solving linear inequalities.
Solve problems involving linear inequalities in one and two variables.

Affective Domain:

Appreciate the importance of linear inequalities in real-life problem-solving.
Show interest in solving problems related to linear inequalities.

Psychomotor Domain:

Accurately plot the solution sets of linear inequalities on a number line.
Graph the solution regions for linear inequalities in two variables on a Cartesian plane.

Collaborate with peers to solve linear inequality problems.
Communicate their solutions and reasoning clearly to others.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Further Mathematics.
State Unified Scheme of Work for Further Mathematics SSS 1.
New Further Mathematics for Senior Secondary Schools by P.N. Okeke et al.
Essential Further Mathematics for Senior Secondary Schools by A.J.S. Akubuilo.

Instructional Materials

The teacher will teach this lesson with the aid of:

Number line diagrams.
Whiteboard or chalkboard.
Markers or chalk.
Rulers.
Graph paper.

Rationale for the Lesson

This lesson helps pupils understand mathematical relationships where quantities are not exactly equal, which is common in daily life. Understanding linear inequalities enables pupils to solve practical problems involving limits, budgets, and resource allocation in various fields.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of solving linear equations, basic algebraic operations (addition, subtraction, multiplication, division), and plotting points on a number line.

Lesson Content/Board Summary

LINEAR INEQUALITIES

Definition of Linear Inequalities

A linear inequality is a mathematical statement that compares two expressions using an inequality symbol instead of an equality sign. The inequality symbols are: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Types of Linear Inequalities

Linear inequalities can be classified based on the number of variables they contain:

Linear Inequalities in One Variable: These involve only one variable, usually ‘x’. Examples include x + 3 < 7, 2y – 5 ≥ 1. Their solutions are often represented on a number line.
Linear Inequalities in Two Variables: These involve two variables, usually ‘x’ and ‘y’. Examples include x + y > 5, 2x – 3y ≤ 6. Their solutions are typically represented as regions on a Cartesian plane.

Rules for Solving Linear Inequalities

The rules for solving linear inequalities are similar to those for solving linear equations, with one important exception:

Adding or subtracting the same number from both sides of an inequality does not change the direction of the inequality sign.
Multiplying or dividing both sides of an inequality by a positive number does not change the direction of the inequality sign.
Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality sign.

Graphing Linear Inequalities on a Number Line (for one variable)

To graph a linear inequality in one variable on a number line:

Draw a number line.
Locate the critical value (the number on the other side of the inequality).
If the inequality is < or >, use an open circle (o) at the critical value to show that the value is not included in the solution.
If the inequality is ≤ or ≥, use a closed circle (•) at the critical value to show that the value is included in the solution.
Draw an arrow from the circle in the direction that satisfies the inequality. For > or ≥, the arrow points right; for < or ≤, the arrow points left.

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 the previous lesson on linear equations, asking questions like, “What is a linear equation?” and “How do we solve linear equations?”. The teacher then introduces the topic of linear inequalities by asking pupils if all mathematical relationships involve exact equality.
Pupils’ Activity: Pupils respond to the teacher’s questions, recalling previous knowledge, and listen attentively to the introduction of the new topic.
Learning Point: Pupils recall prior knowledge of linear equations and are introduced to the concept of inequalities.

Step 2: Definition of Linear Inequalities

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines linear inequalities, explaining the meaning of symbols like <, >, ≤, and ≥. The teacher provides simple examples to illustrate.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification. They attempt to define linear inequalities in their own words.
Learning Point: Pupils understand the definition of linear inequalities and recognize the inequality symbols.

Step 3: Types of Linear Inequalities

Time: 8 minutes
Teaching Skill: Elucidation/Differentiation
Teacher’s Activity: The teacher explains the two main types: linear inequalities in one variable and linear inequalities in two variables. The teacher gives examples for each type and highlights their differences.
Pupils’ Activity: Pupils identify and differentiate between linear inequalities in one and two variables based on the examples provided. They write down the examples.
Learning Point: Pupils can distinguish between linear inequalities in one and two variables.

Step 4: Rules for Solving Linear Inequalities

Time: 8 minutes
Teaching Skill: Demonstration/Rule Application
Teacher’s Activity: The teacher presents the rules for solving linear inequalities, emphasizing the rule about reversing the inequality sign when multiplying or dividing by a negative number. The teacher demonstrates with simple examples.
Pupils’ Activity: Pupils pay close attention to the rules and the demonstration. They note down the rules and try to apply them mentally.
Learning Point: Pupils learn and understand the rules governing the manipulation of linear inequalities.

Step 5: Solving Linear Inequalities in One Variable

Time: 7 minutes
Teaching Skill: Problem-Solving/Guidance
Teacher’s Activity: The teacher guides pupils through solving various linear inequalities in one variable, such as “Solve 3x – 4 > 5” and “Solve 7 – 2x ≤ 1”. The teacher ensures pupils correctly apply the rules.
Pupils’ Activity: Pupils actively participate by suggesting steps and solving problems on their notebooks as guided by the teacher.
Learning Point: Pupils can solve linear inequalities in one variable.

Step 6: Graphing Solutions on a Number Line

Time: 5 minutes
Teaching Skill: Demonstration/Visualisation
Teacher’s Activity: The teacher demonstrates how to represent the solution sets of linear inequalities (e.g., x > 3, x ≤ -2) on a number line using open and closed circles and arrows. The teacher uses number line diagrams.
Pupils’ Activity: Pupils observe the teacher’s demonstration and practice drawing number line graphs for the solutions of the inequalities solved in Step 5.
Learning Point: Pupils can graphically represent the solution of a linear inequality in one variable on a number line.

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.
State any two symbols used in linear inequalities.
What is the main difference between linear inequalities in one variable and in two variables?
Solve the inequality: 2x + 3 < 9.
Graph the solution for the inequality x ≥ -1 on a number line.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization/Consolidation
Teacher’s Activity: The teacher briefly summarizes the key points of the lesson, reiterating the definition, types, rules for solving, and graphing of linear inequalities. The teacher assigns homework involving solving and graphing various linear inequalities.
Pupils’ Activity: Pupils listen to the summary and copy down the assigned homework.
Learning Point: The lesson is consolidated, and pupils are given further practice.

Lesson Keywords

Inequality – A mathematical statement comparing two expressions using symbols like <, >, ≤, or ≥.
Variable – A symbol (usually a letter) representing an unknown quantity.
Number line – A line on which numbers are marked at regular intervals, used to represent solutions of inequalities.
Solution set – The set of all values that make an inequality true.
Greater than – Indicated by the symbol >.
Less than – Indicated by the symbol <.

Differentiation

For pupils who are struggling, the teacher will provide additional simpler examples and work through them step-by-step. For advanced pupils, more complex inequalities involving fractions or multiple steps will be provided as challenge questions.

Note for teachers using this lesson plan

Teachers should ensure active pupil participation through questioning and guided practice. Emphasize the rule for reversing the inequality sign when multiplying or dividing by a negative number, as this is a common area of error. Encourage pupils to always check their solutions.