Mathematics - Junior Secondary 2 - Linear inequalities (continued)

TERM: 2^ND TERM

WEEK 3
Class: Junior Secondary School 2
Age: 13 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Linear Inequalities Continued
Focus: Graphical Representation, Graphs of Cartesian Plane

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

Define linear inequalities and their graphical representation.
Plot linear inequalities on the Cartesian plane.
Understand the axes and quadrants of the Cartesian plane.
Apply linear inequalities to real-life situations such as budgeting and population distribution.
Solve graphical inequalities and interpret their solutions.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Discussion
• Graphing exercises
• Real-life application

INSTRUCTIONAL MATERIALS:
• Graph paper
• Whiteboard and markers
• Ruler
• Flashcards with inequalities
• Graphing software (optional)

PERIOD 1 & 2: Graphical Representation of Linear Inequalities

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Introduces the concept of linear inequalities and the significance of graphical representation.	Pupils listen and ask questions.
Step 2 - Explanation	Demonstrates how to graph a linear inequality on the Cartesian plane (e.g., y > 2x + 1).	Pupils observe and take notes.
Step 3 - Demonstration	Uses graph paper and ruler to plot linear inequalities, explains shaded regions.	Pupils practice plotting the graph with guidance.
Step 4 - Practice	Pupils plot given inequalities on graph paper.	Pupils complete individual graphing exercises.

NOTE ON BOARD:

Graph of y > 2x + 1: Draw the boundary line y = 2x + 1, then shade the region above it to represent y > 2x + 1.
Graph of y ≤ 3x – 2: Draw the boundary line y = 3x – 2, then shade below it to represent y ≤ 3x – 2.

EVALUATION (5 exercises):

Plot y > x + 2 on the Cartesian plane.
Plot y ≤ 4x – 1.
Find the shaded region for y ≥ 2x + 3.
Plot y > -x.
Graph y ≤ -x + 2.

CLASSWORK (5 questions):

Plot y ≤ 2x + 1.
Graph y > 3x – 2.
Draw the graph of y ≥ -2x + 4.
Shade the region of y > -x.
Plot the inequality y ≤ x – 1.

ASSIGNMENT (5 tasks):

Graph y ≥ x + 5.
Find the boundary line for y > -3x + 2.
Solve the inequality y > -2x – 1 by graphical method.
Shade the region representing y ≤ x + 3.
Plot the inequality y ≥ 2x – 4.

PERIOD 3 & 4: Graphs of Cartesian Plane – The Axes

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Explains the Cartesian plane, axes, and quadrants. Demonstrates how to identify coordinates.	Pupils listen and engage in discussions.
Step 2 - Explanation	Shows how to plot points on the Cartesian plane and explain their meaning in relation to inequalities.	Pupils observe and take notes.
Step 3 - Demonstration	Plots various points on the graph (e.g., (2, 3), (-1, -4), etc.) and explains their relevance to linear inequalities.	Pupils practice plotting points individually.
Step 4 - Practice	Pupils plot different points on the Cartesian plane.	Pupils complete plotting tasks.

NOTE ON BOARD:

Cartesian Plane: X-axis (horizontal), Y-axis (vertical).
Quadrants:

Quadrant I: (+, +)
Quadrant II: (-, +)
Quadrant III: (-, -)
Quadrant IV: (+, -)

Points: (x, y) represent a point’s location in relation to the axes.

EVALUATION (5 exercises):

Plot the point (4, 2).
Find the quadrant of the point (-3, 5).
Plot (-2, -3) and name its quadrant.
Identify the point on the graph where x = 0.
Plot the points (0, -4) and (5, 1).

CLASSWORK (5 questions):

Plot the point (3, -5).
Identify the quadrant of the point (-1, 6).
Plot (-2, 2).
Mark the origin (0, 0) on the graph.
Plot the points (4, 4) and (-1, -2).

ASSIGNMENT (5 tasks):

Plot the point (-4, 3).
Identify the quadrant of (2, -6).
Plot the points (0, 0), (1, 4), (-3, -2).
Find the coordinates of a point that lies on the X-axis.
Plot (5, -5) and explain its location.

PERIOD 5: Applying Graphs to Real-Life Situations

PRESENTATION:

Step	Teacher’s Activity	Pupil’s Activity
Step 1 - Introduction	Discusses the application of linear inequalities and graphs to real-life problems such as budgeting and population growth.	Pupils listen and participate.
Step 2 - Explanation	Uses an example like budgeting (y ≤ 100x + 200) to demonstrate how to apply inequalities in real-life situations.	Pupils ask questions and take notes.
Step 3 - Problem-Solving	Solves word problems involving linear inequalities and graphs.	Pupils solve problems with guidance.
Step 4 - Practice	Pupils solve a set of real-life word problems using linear inequalities.	Pupils complete individual exercises.

EVALUATION (5 questions):

A company earns 50x + 200 in a month. Graph the inequality for earnings greater than or equal to 1,000.
A car rental company charges 30x + 50 for rental. Graph the inequality for rental greater than or equal to 500.
A family’s monthly budget is constrained by y ≤ 2x + 300. Graph the budget and shade the region.
Find the solution to y > 3x – 50 when x = 20.
Apply linear inequalities to the problem of population growth of a city: y ≤ 2x + 5000.

CLASSWORK (5 tasks):

Solve the inequality y ≥ 2x – 100 using graphing.
Graph the inequality y ≤ 3x + 200.
Apply the inequality y ≥ x + 50 to a savings account balance scenario.
Solve the problem of profit from selling a product, where profit = 10x – 50, and graph the inequality for profit greater than 200.
Represent the population of a country growing at a rate of y = 1000x + 5000 on a graph.

ASSIGNMENT (5 tasks):

Graph the inequality y ≤ x + 150 for a monthly rent payment.
Solve and graph y ≥ 2x + 100 for a business revenue scenario.
Solve the inequality 5x – 3y = 20 using graphical representation.
Use linear inequalities to model the cost of a phone plan with a fixed base fee and variable rate.

Create a word problem where linear inequalities are used to determine pricing or budgeting constraints.