9TH MATHS E/M LESSON PLAN (OCT 17 - 21) - ALGEBRA

        THEME  : Algebra                                                                           CLASS :  9                               

SUB-THEME  : Simultaneous Linear Equations                        SUBJECT : Mathematics

 PRE-KNOWLEDGE:

§  Making The  Student To  Remember an equation of the form ax+b=0 ( where a,b are real numbers and a ≠0 ) is called a linear equation in one variable x. §  The solution of an equation is the set of all values that, whensubstituted for unknowns, make the equation true. §  A linear equation in two variables is of the form ax + by + c = 0 where a, b and c are real numbers, both a and b are not zero (The two variables are denoted here by x and y and c is a constant).

INTRODUCTION:

                A system of linear equations consists of two or more linear equations with the same  variables.   Then such equations are called Simultaneous linear equations or System of inear equations or a Pair of linear equations.

 KEY CONCEPT:

             * When a system of linear equation has one solution, the system is said to be a consistent system.

            * When a system of linear equation has no solution, the system is said to be an inconsistent system.

             * There are different methods to find the solution of a pair of simultaneous linear           equations.

                Geometric way - 1.Graphical method  

                 Algebraic ways- 1. Substitution method

                                              2. Elimination method

                                              3. Cross multiplication method

ACTIVITIES:

     TEACHER ACTIVITIES :

           Solving the system of linear equations y = 2x + 1; −4x + 2y = 2  by all the four methods  and explaining the steps to follow in each method .

  STUDENTS GROUP  ACTIVITY :

Splitting  the  students  into Groups and giving the  problems to solve  under  guidance  Like   ‘Solve the system of linear equations x+y=7; x-y=3  by all the four methods’

TEACHER  DOING SAMPLE  PROBLEMS:

            *  The sum of the digits of a given two digit number is 5. If the digits are reversed,  the new number is reduced by 27. Find the given number.

            *  Solve for x and y:  8x -3y=5xy ; 6x -5y=-2xy  by the method of elimination.     

 CONCEPT MAP:

              

RE-INFORCEMENT:

                 Teaching  the  most  important concepts  again and again using simple examples and working model on geogebra   https://www.geogebra.org/m/z8txppjn#material/eqzktUFP                                                       

EVALUATION:

   LOT’s : 1. Which condition does not satisfy the linear equation ax+by +c = 0

                      (1) a  ≠ 0 , b = 0 (2) a = 0 , b ≠0 (3) a = 0 , b = 0 , c ≠ 0 (4) a  ≠0 , b  ≠ 0    

                 2.  A  pair of expression set equal to each other is  --------------

   MOT’s  :

               1.   The value of k for which the pair of linear equations  4x+6y −14=0 ; 2 x + ky −7=0   represents  parallel lines  is

                     (1) k = 3 (2) k = 2 (3) k = 4 (4) k = −3  

               2. Which of the following statement is true for the equation 2 x +3y =15                                                 (1) the equation has unique solution             (2) the equation has two solution                                 (3) the equation has no solution                     (4) the equation has infinite solutions

   HOT’s   : 

           1. The sum of two children is ‘a’. The age of the father is twice the ‘a’. After  twenty years, his age will be equal to the addition of the ages of his children. Find the age of father.

               2. What will be the solution of these equations  ax + by = a - b ; bx - ay = a + b  

                    (a)  x =1, y =2   (b)  x = 2,y = -1  (c)  x = -2, y = -2  (d)  x =1, y = -1

REMEDIAL TEACHING:

             Finding the concepts which are not understandable by most of the students and             teaching  them again using some QR CODE VIDEOS  from                     https://www.geogebra.org/m/qampr4ta                                                              

FOLLOW UP WORK:

             Instructing students to do the problems that are not worked out in class room-  activities as home work.

 FOLLOW UP ACTIVITY:

         Instructing the students to frame 2 pairs of linear system of equations from  found on their  practical life situations. And say to solve them by using all the 4 ways.  Which is the easiest method to you?  ( E.g., Ravi bought 3 pens and 5 pencils for Rs.25 in a shop at the  same time  Rani  bought 4 pens  and 4 pencils for Rs.28. Find the cost of each item)  

LEARNING OUTCOMES:    Students  able    *  To draw graph for a given linear equation.    *  To solve simultaneous linear equations in two variables by          ◊ Graphical method              ◊ Algebraic method          ◊  Substitution method         ◊ Elimination method   ◊ Cross multiplication method    *  To understand consistency and inconsistency of linear equations in two variables.