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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 |
METHODOLOGY:-
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.
LEARNING ACTIVITIES: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) ϵ R(relation) ∀ a ϵ A, then the relation is called a reflexive relation.
If (a, b) ϵ R ⇒ (b, a) ϵ R, ∀ a ϵ A, then the relation is called a symmetric relation.
If (a, b) ϵ R and (b, c) ϵ R, ⇒ (a, c) ϵ R, ∀ a ϵ 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 ϵ 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 ∊ A
Composition 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
PLEASE COMMENT BELOW
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Comments
Lot of thanks , sir Ji
ReplyDeleteExcellent work👍
ReplyDeleteThank you sir
ReplyDeleteExcellent work 👍
ReplyDeleteIt's very nice and useful to every maths teacher..
ReplyDeleteThanks🌹
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