Lesson Plan Math Class X (Ch- 3) | Pair of Linear Equations in Two Variables

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10

lesson plan for maths class 10 chapter 3  pair of linear equations in two variables, lesson plans for mathematics teachers,  Method to write lesson plan for maths class 10, lesson plan for maths in B.Ed.

TEACHER  :   DINESH KUMAR	SCHOOL :  RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR
SUBJECT   :   MATHEMATICS	CLASS                  :   X  STANDARD BOARD                 :  CBSE
LESSON TOPIC / TITLE   :  CHAPTER 1: Pair of linear equations in two variables	ESTIMATED DURATION:  This lesson is divided into nine modules and it is completed in 10 class meetings.

PRE- REQUISITE KNOWLEDGE:-

Chapter  4 Linear equations in two variables class 9^th

Ability to solve the equations, ability to draw graphs.

TEACHING AIDS:- 

Green Board, Chalk,  Duster, Charts, smart board, projector, laptop  etc.

METHODOLOGY:-  

Demonstration and Lecture method.

LEARNING OBJECTIVES:

• Introduction of pair of linear equations in two variables.
• Graphical method of solving the pair of linear equations in two variables.
• Discuss the nature of solution, types of graphs, consistency or inconsistency of the pair of equations.
• Substitution method, Elimination method, and cross multiplication method  of solving the equations.

LEARNING OUTCOMES:

After studying this lesson students should know  

• All important concepts related to the pair of linear equations in two variables.
• Students should know the graphical method for solving pair of linear equations
• Students should know the substitution method, elimination method and cross multiplication method to solve the pair of linear equations in two variables.
• Students should know the  implementation of these formula's in simple and word problems.

RESOURCES

NCERT Text Book,
NCERT Exemplar Book of mathematics,

Resource Material : 

Worksheets , E-content, Basics and formulas from  (cbsemathematics.com)

KEY WORDS:

Linear equations, variables, unique solution, co-incident lines, parallel lines, intersecting lines, consistency, in-consistency etc.

LEARNING ACTIVITIES:

   INTRODUCTORY ACTIVITY

Mathematics Activity No 03  Class X

EXPERIENTIAL ACTIVITY

Mathematics Activity No 03  Class X

ART INTEGRATED ACTIVITY

Mathematics Activity No 03  Class X

PROCEDURE :

FOR COMPLETE EXPLANATION 

Start the session by checking their previous knowledge, by asking the questions of linear equations in two variables. After this explain the topic to the students. 

Introduction

Teacher will write the general pair of linear equations in two variables on the board and then explain all the components of the equations i.e. coefficients and variables .

a₁x + b₁y = c₁

a₂x +b₂y=c₂

Here a₁, a₂ are the coefficients of x,

b₁, b₂ are the coefficients of y,

c₁, c₂ are the constant terms ,

x and y are the variables.

Graphical Solution

Teacher will take an example of pair of linear equations in two variables and explain to the students the method of finding at least three solutions of each of the equation. Now on the board teacher will draw the graph of two equations on the single graph.

Teacher will also give the knowledge to the students that

• Point of intersection of two lines is called the solution of the equations.
• Graph of linear equations is always a straight line.
• If two lines intersect at a point then the pair of equations have unique solutions and the equations are called consistent.
• If two lines have same graph line then the pair of equations have Infinitely many solutions and the equations are called consistent.
• If two lines have parallel graph line then the pair of equations have no solutions and the equations are called Inconsistent.

Now by comparing the ratio of the coefficients, discuss the nature of solution, types of graphs and consistency or inconsistency of equations. Teacher can take some examples to explain this concept.

Substitution Method

Now teacher will explain the Method of solving the pair of linear equations in two variables by Substitution Method. Teacher will explain the topic by taking 3 - 4 examples.

After giving complete knowledge to the students teacher will give some problems to the students to check whether they understand the concept or not.

Types of graphs, nature of solutions, consistency/ inconsistency all are discussed in the following table.

Conditions	Nature of Solution	Type of Graph	Consistent /Inconsistent
	Unique Solution	Two intersecting lines	Consistent
	Unique Solution	Two intersecting lines	Consistent
	Infinitely many solutions	Coincident lines	Consistent
	No Solution	Two Parallel Lines	Inconsistent

Explanation of Algebraic Methods of solving Pair of Linear Equations in two Variables

Substitution Method of solving

Pair of linear equations in two variables

Let Given Pair of linear equations in two variables

        x + y = 3………………(1)

2x + 3y = 10…………..(2)

From equation (1)

x = 3 – y………….(3)

Putting eqn. (3) in eqn. (2) we get

2(3 - y) + 3y = 10

  6 - 2y + 3y = 10

           6 + y = 10

                      y = 10 - 6

             y = 4

Putting y = 4 in eqn. (3) we get

   x = 3 - y

    x = 3 - 4

x = -1

x = -1 and y = 4 is the required solution.

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Elimination method

Now teacher will explain the Method of solving the pair of linear equations in two variables by Elimination method. Teacher will explain the topic by taking 3 - 4 examples.

After giving complete knowledge to the students teacher will give some problems to the students to check whether they understand the concept or not.

Elimination Method of solving

Pair of linear equations in two variables

x + y = 3…………(1)

2x + 3y = 10…………..(2)

Eqn. (1) x 2 – eqn. (2) x 1 we get

y = 4

Putting y = 4 in equation (1)

x + 4 = 3

                   x = 3 - 4 = -1

x = -1 and y = 4 is the required solution.

Cross Multiplication Method

Now teacher will explain the Method of solving the pair of linear equations in two variables by Cross Multiplication Method. Teacher will explain the topic by taking 3 - 4 examples.

After giving complete knowledge to the students teacher will give some problems to the students to check whether they understand the concept or not.

Applications

After giving complete knowledge of different methods of solving pair of linear equations in two variables teacher will help the students to apply these methods in solving the word problems.

Teacher may also give some problems to the students for practice.

Equations Reducible to the Pair of Linear Equations

Now teacher will explain the method of solving the pair of equations which are not linear equations but can be made linear by making some substitutions. Such equations are called Equations Reducible to the Pair of Linear Equations.

Teacher may provide some problems from exercise 3.6 of NCERT book for practice and better understanding

Special Equations

Now Teacher will explain the method of solving some special types of equations given in exercise 3.7 (optional exercise) of NCERT Book

STUDENTS DELIVERABLE:-

• Students Should review questions given by the teacher. 
• Students should prepare the presentation on the basic concepts and formula's on pair of linear equations in two variables. 
• Students should Solve N.C.E.R.T. problems with examples, 
• Students should solve the assignment on Multiple Choice Questions (MCQ) given by the teacher.

MIND MAP

EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at  cbsemathematics.com

ASSESSMENT TECHNIQUES:-

Assignment sheet will be given as home work at the end of the topic. Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.

Class Test , Oral Test , MCQ worksheet and Assignments can be made the part of assessment.

Re-test(s) will be conducted on the basis of the performance of the students in the test.

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