Lesson Plan Math Class 12 Ch- 4 | Determinants

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10+2

Lesson Plan, Class XII Subject Mathematics, chapter 4, Determinants , for Mathematics Teacher. Effective way of Teaching Mathematics. Top planning by the teacher for effective teaching in the class. E lesson planning for mathematics.

NAME OF THE TEACHER				DINESH KUMAR
CLASS	10+2	CHAPTER	04	SUBJECT	MATHEMATICS
TOPIC	DETERMINANTS			DURATION : 15 Class Meetings

PRE- REQUISITE KNOWLEDGE:-

Knowledge of matrices, chapter 3, class 10+2, 

Pair of linear equations in two variables class 10^th .

TEACHING AIDS:- 

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

METHODOLOGY:-   Lecture cum demonstration and Learning by doing method.

LEARNING OBJECTIVES:-

• Introduction and determinants of a square matrices up to 3 x 3 matrices.

• Properties of determinants.(DELETED FROM CBSE SYLLABUS)

• Minors and cofactors of determinants.

• Application of determinants in finding the area of triangle.

• Adjoint and inverse of the square matrices.

• Consistency, inconsistency and the number of solutions of system of linear equations.

• Method of solving system of linear equations in two or three variables having unique solutions using inverse of matrix method.

LEARNING OUTCOMES:

By the end of this chapter, students should be able to:

• Define what a determinant is and understand its significance in linear algebra.
• Compute determinants of 2 x 2 matrices and 3 x 3 matrices using the cross-product rule.
• Identify and explain various properties of determinants, such as scalar multiplication, row/column operations, and switching rows/columns.
• Apply cofactor expansion to calculate the determinant of larger matrices by recursively breaking them into smaller submatrices.
• Understand how determinants can be used to find the area of a triangle or parallelogram in two dimensions.
• Learn how to find the inverse of a matrix using determinants and adjoint matrices.
• Solve Systems of Linear Equations:
• Apply determinant calculations to real-world problems, such as finding solutions to systems of linear equations representing real-life scenarios.

RESOURCES

NCERT Text Book,
NCERT Exemplar Book of mathematics,

Resource Material : 

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

KEY WORDS

Determinants, Matrices, Rows, Column, Consistency, Inconsistency, System of linear equations, Minors, Cofactors, Adjoint, Singular matrix, Non singular matrix, Invertible matrices, Inverse of matrices.

CONTENT OF THE TOPIC

• Method of calculating the determinants of 2 x 2 matrix and 3 x 3 matrix.
• Explanation of properties of determinants and their implementation in different problems.
• Method of finding the area of triangle and parallelogram by using matrix method.
• Concept of minors and cofactors.
• Consistency and inconsistency of matrices.
• Method of finding the Adjoint of matrix.
• Matrix method of finding the inverse of a matrix.
• Solving system of equations by using matrix method.

LEARNING ACTIVITIES:

Introductory Activity

• Arrange the students in groups.
• Now explain the method of finding the determinants of 2 x 2 matrix.
• Now give different problems related to the 2 x 2 matrix to the different groups.
• Every group find the determinant of the problem assigned to them.
• Now in the presence of teacher each group will make the discussion on the result.

Conclusion : With this activity students able to understand that determinant is a number associated with the square matrix.

PROCEDURE & EXPLANATION OF LESSON PLAN

Start the session by asking the questions related to the matrices and system of linear equations in two variables. Now introduce complete topic determinants as follows.

PROCEDURE & EXPLANATION 

Click Here for : Complete Explanation

First of all teacher will start the session by asking certain questions of matrices. Then introduce the topic determinant.

Now teacher will help the students in finding the determinant of 2 x 2 matrices and  3 x 3 matrices.

Definition of Determinant

Determinant is a number associated with the square matrix.

To every square matrix A = [a_ij]  of order n, we can associate a number (real or complex) called determinant of the square matrix  A.

Determinant of matrix  [A] is denoted by |A|

Properties of Determinants

Now teacher will explain all the properties of determinants with the help of examples and apply them in different problems. Teacher will provide sufficient number of problems to the students for practice.

Concepts of minor and cofactor

Now teacher will introduce the concept of minor and Determinant  and will explain the method of finding the minors and cofactors. Students will be given sufficient method of finding the determinants by using the cofactors.

Area of Triangle

Now teacher will explain the method of finding the area of the triangles by using determinants.

Adjoint and Inverse of a Matrix

First of all teacher will explain the definition of Singular matrices, invertible matrices and Adjoint of a matrix.

Singular Matrix: A matrix whose determinant is equal to zero is called a singular matrix. If determinant is not equal to zero then it is called Non-Singular Matrix. 

Invertible Matrix: A matrix is said to be invertible if it is non-singular.

Now teacher will explain the method of finding the Adjoint and inverse of the square matrices.

Consistency and and Inconsistency of system of linear equations.

Teacher will Discuss and Explain the consistency, inconsistency and the number of solutions of the system of linear equations with two or three variables.

Solution of System of Linear Equations

Now teacher will explain the method of solving the system of linear equations in two or three variables by using Adjoint method of finding inverse of matrix method.

REFLECTION OF THE ACTIVITY

After these activities and explanations students will start 

• Making discussion on on determinants, minors, cofactors, adjoint and inverse of matrices.
• Students start reflecting the method of finding the determinants of 2 x 2 and 3 x 3 matrices.

IMMEDIATE FEEDBACK

After the completion of each topic teacher will conduct a simple quiz or simple MCQ test for the students.
From the responses of the students teacher will understand the degree of understanding of the students.

CREATION (e.g. MIND-MAP, COLLAGE, GRAPH, MAP etc.)

MIND MAP / CONCEPT MAP 

APPLICATIONS OF DERIVATIVES

STUDENTS DELIVERABLES:-

• Review questions given by the teacher. 
• Students should prepare the presentation on the properties of determinants. 
• Solve NCERT problems with examples.
• Solve assignment given by the teacher.

SUBJECT INTEGRATED:

Science : With this topic students are able to find the area of triangle, parallelogram and volume of parallelepiped. These concept are very useful in explaining many concepts in Physics and Physical Chemistry.

Economics : Knowledge of solving the system of linear equations with matrix method help students to solve the problems in economics very easily.

DIFFERENTIAL LEARNING

For Below Average Students

• Mind/ Concept maps
• Charts , Models and activity
• Simple questions

For Average Students

• Learning situations through watching video, creating collage, completing puzzles, assignment (click here)

For Above Average Students:

• Group Discussion
• Higher Order Thinking  Skill questions

SKILLS ENHANCED

Observation  skill,  analytical skill,  critical thinking, team work, constructive approach, interpersonal skill,  engagement  in learning process etc.

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 , 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.

Competency based assessment can be taken so as to ensure if the learning outcomes have been achieved or not. e.g.

• Puzzle
• Quiz based on MCQ
• Misconception check
• Peer check
• Students discussion
• Competency Based Assessment link: Case Study Based Questions

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