Class: Junior Secondary School 2 (JSS2, JSS 2)
Term: 1st Term
Week: 9
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Cartesian Plane, Axes, and Plotting Points on Graphs
Topic: Linear Inequalities
Subject Matter: Identifying linear inequality in one variable, Solving linear inequalities, Graphical representation of solution of linear inequalities, Word problems involving linear inequalities.

Specific Objectives

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

Cognitive Domain:
(a) Identify and represent linear inequalities in one variable.
(b) Solve linear inequalities using mathematical operations.
(c) Interpret and represent solutions of inequalities on a number line.
Affective Domain:
(a) Appreciate the importance of inequalities in daily decision-making situations.
Psychomotor Domain:
(a) Draw number lines and shade regions to represent inequality solutions accurately.
Social Domain:
(a) Collaborate in solving and discussing word problems involving inequalities in groups.

Reference Materials

The following resources was used in planning this lesson:

9 Years Basic Education Curriculum
Lagos State Unified Scheme of work for Junior Secondary Schools
CK-12 Foundation – “Linear Inequalities” (https://www.ck12.org/algebra/linear-inequalities/)
Relevant Textbooks

Instructional Materials

The teacher will teach this lesson with the aid of:

Number line charts
Flash cards showing inequality symbols
Graph paper and ruler
Marker and whiteboard
Exercise sheets containing word problems

Rationale for the Lesson

Understanding linear inequalities helps students make informed decisions in real-life situations involving limits, comparisons, and possible ranges of values.

Prerequisite/Previous Knowledge

Pupils already know how to solve simple linear equations and can perform basic arithmetic operations such as addition, subtraction, multiplication, and division.

Lesson Content/Board Summary

Linear Inequalities

Identifying Linear Inequality in One Variable

An inequality shows that two expressions are not equal. It compares quantities using inequality symbols such as:

> (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to).

The following are examples of linear inequalities in one variable:

x+4>7x + 4 > 7
2x≤102x ≤ 10
5−x≥25 – x ≥ 2
3x<93x < 9

Each inequality involves one variable (x) and has a degree of one, which makes it linear.

Solving Linear Inequalities

To solve a linear inequality, perform the same operation on both sides of the inequality sign just like in equations, but remember that:

When multiplying or dividing both sides by a negative number, the inequality sign changes direction.

The following are steps to solve linear inequalities:

Simplify both sides of the inequality.
Collect like terms.
Isolate the variable on one side.
If division or multiplication by a negative occurs, reverse the inequality sign.
Express the solution clearly.

Example:
Solve 2x+3<72x + 3 < 7
Subtract 3 from both sides: 2x<42x < 4
Divide both sides by 2: x<2x < 2
Solution: x<2x < 2

Graphical Representation of Solutions of Linear Inequalities

Linear inequalities can be shown on a number line.
Open circles represent < or >, while closed circles represent ≤ or ≥.
The shaded part shows the range of possible values that satisfy the inequality.

Example:
For x≤4x ≤ 4, draw a closed circle on 4 and shade to the left.
For x>3x > 3, draw an open circle on 3 and shade to the right.

Word Problems Involving Linear Inequalities

Linear inequalities can be used to solve problems involving limits, costs, ages, or quantities.

Example:
A boy wants to buy pens costing ₦150 each with at most ₦900.
Let the number of pens be xx.
Then 150x≤900150x ≤ 900.
Dividing both sides by 150 gives x≤6x ≤ 6.
Interpretation: He can buy a maximum of 6 pens.

Teaching Methods/Instructional Techniques:

Discussion, Lecture, Explanation, Demonstration, Guided Discovery, Question and Answer, Group Work

Instructional Procedures

To deliver this lesson, the teacher will adopt the following steps:

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: Teacher reviews the previous lesson on linear equations and asks pupils to compare equations and inequalities.
Pupils’ Activity: Pupils respond and recall that inequalities use signs like >, <, ≥, ≤.
Learning Point: Pupils connect prior knowledge of equations to the new concept of inequalities.

Step 2: Identifying Linear Inequalities

Time: 8 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher explains and writes examples of linear inequalities in one variable on the board.
Pupils’ Activity: Pupils identify the inequality signs and note examples.
Learning Point: Pupils recognize linear inequalities and their symbols.

Step 3: Solving Linear Inequalities

Time: 10 minutes
Teaching Skill: Demonstration
Teacher’s Activity: Teacher demonstrates solving examples of linear inequalities step-by-step.
Pupils’ Activity: Pupils solve similar problems on the board.
Learning Point: Pupils learn to solve inequalities correctly and interpret the results.

Step 4: Graphical Representation

Time: 8 minutes
Teaching Skill: Visualization
Teacher’s Activity: Teacher shows how to represent inequalities on a number line using open and closed circles.
Pupils’ Activity: Pupils draw and shade number lines for given inequalities.
Learning Point: Pupils can represent solutions graphically.

Step 5: Word Problems

Time: 7 minutes
Teaching Skill: Application
Teacher’s Activity: Teacher presents real-life examples and guides pupils in forming and solving inequalities from word problems.
Pupils’ Activity: Pupils participate in solving and interpreting results in groups.
Learning Point: Pupils apply inequalities to practical situations.

Step 6: Note-Taking

Time: 3 minutes
Teaching Skill: Explanation
Teacher’s Activity: Teacher dictates or writes the board summary for pupils to copy.
Pupils’ Activity: Pupils copy the notes.
Learning Point: Pupils have a record of the key lesson points.

Step 7: Evaluation/Review

Time: 3 minutes
Teaching Skill: Questioning
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Mention three inequality symbols.
Solve 3x−5≥73x – 5 ≥ 7.
Draw a number line for x<2x < 2.
Form an inequality for this statement: “A person’s age is not more than 18 years.”
Pupils’ Activity: Pupils answer the questions orally.
Learning Point: Pupils demonstrate understanding of linear inequalities.

Step 8: Conclusion

Time: 1 minute
Teaching Skill: Reinforcement
Teacher’s Activity: Teacher summarizes the lesson and emphasizes key points about solving and representing inequalities.
Pupils’ Activity: Pupils listen and ask questions for clarity.
Learning Point: Pupils understand the relevance and application of linear inequalities.

Lesson Keywords

Inequality – a mathematical statement comparing two expressions using <, >, ≤, or ≥.
Variable – a symbol (usually a letter) that represents an unknown number.
Solution – a value that satisfies an inequality.
Number Line – a straight line used to represent numbers and solutions graphically.
Graph – visual representation of a solution on a number line.

Differentiation

Teacher simplifies examples for slower learners, gives moderate tasks to average learners, and provides challenging word problems for fast learners.

Note for teachers using this lesson plan

Encourage pupils to use accurate symbols when writing inequalities. Remind them to reverse the sign only when multiplying or dividing by a negative number. Provide enough practice for mastery.