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Lesson Plan Math Class 12 (Ch-1) Relation & Functions
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E- LESSON PLAN SUBJECT MATHEMATICS CLASS 10+2
E-LESSON PLAN MATHEMATICS
CLASS-XII
CHAPTER-1 RELATIONS & FUNCTIONS
NAME OF THE TEACHER |
DINESH KUMAR |
||||
CLASS |
10+2 |
CHAPTER |
01 |
SUBJECT |
MATHEMATICS |
TOPIC |
RELATIONS & FUNCTIONS |
DURATION : 15 Class Meetings |
To explain the
- Cartesian
product and different types of relations.
- Reflexive,
symmetric, transitive and equivalence relations.
- Different
types of functions their domain and range.
- One-one(injective)
functions, onto (surjective)functions, bijective functions.
- Composite functions.
- Invertible and inverse of functions.
After studying this
lesson students should know the
- concept
Cartesian product,
- different
types of relations,
- domain
and range of relations,
- different
types of functions their domain and range,
- bijection of functions and inverse of functions
- composition of functions.
Cartesian Product, Domain, Range, Reflexivity, Symmetry , Transitivity, One-One, Onto, Injective, Surjective , Bijective, composition
CONTENT
OF THE TOPIC
1) Cartesian Product of two sets
2) Relation, Domain, Range and Co-domain of relation.
3) Different types of relations :- Reflexive, symmetric, transitive and
equivalence relation.
4) Functions, Different types of functions like :- one-one, onto, many
one and bijective functions.
5) Composite functions and Invertible functions.
6) Properties of Inverse Functions
INTRODUCTORY ACTIVITY
Start the session with little description of the set theory, definition of Cartesian product relations and functions, their domain, co-domain and range.
Set :- A well defined collection of objects is called a set.
If A and B are two non-empty sets, then the Cartesian product A x B is defined as the set of all the ordered pairs of the elements from A to B such that
If A and B are two non-empty sets, then relation R from A to B is a subset of the Cartesian product A x B. This means that number of subsets is equal to the number of relations.
The set of all the first elements of the ordered pairs in a relation R from a set A to a set B is called the domain of the relation R.
The set of all second elements in a relation R from a set A to a set B is called the range of the relation R.
The whole set B is called the co-domain of the relation R.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B.
Different types of relations:
If (a, a) ฯต R(relation) ∀ a ฯต A, then the relation is called a reflexive relation.
If (a, b) ฯต R ⇒ (b, a) ฯต R, ∀ a ฯต A, then the relation is called a symmetric relation.
If (a, b) ฯต R and (b, c) ฯต R, ⇒ (a, c) ฯต R, ∀ a ฯต A, then the relation is called transitive relation.
A relation which is reflexive, symmetric and transitive is called an equivalence relation.
Definitions of one-one, onto, many one and bijective functions and their arrow diagrams.
A function f from A to B is said to be one-one function or an injection if different elements of A have different images in B i.e. f(a) = f(b) ⇒ a = b for all a, b ฯต A
A function f from A to B is said to be many one function if two or more elements of set A have the same image in B.
A function f from A to B is said to be onto function if every element of B is the image of some element in A or
A function which is one one and onto is called bijective function.
Explain the Method of finding the domain and range of different functions.
Definition of Composite functions:
Let f: A→B and g:B→C be two functions. Then the function gof: A→C defined by gof(x) =g(f(x)), for all x ∊ AComposition is possible only if co-domain of first function is = domain of second function.
Note:
The composition of function is not commutative i.e. fog ≠ gof
Composition of bijection is also a bijection.
Invertible function:
A function which is one one and onto is called an invertible function.Properties of inverse of a function:
Students will be able to know the
CREATION (e.g. MIND-MAP, COLLAGE, GRAPH, MAP etc.)
DIFFERENTIAL LEARNING
- Mind/ Concept maps
- Charts , Models and activity
- Simple questions
- Learning situations through watching video, creating collage, completing puzzles, assignment (click here)
- Group Discussion
- Higher Order Thinking Skill questions
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.
- Puzzle
- Quiz
- Misconception check
- Peer check
- Students discussion
- Competency Based Assessment link: M C Q
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Comments
Lot of thanks , sir Ji
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ReplyDeleteThank you sir
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