DETAILED LESSON PLAN IN MATHEMATICS FOR GRADE VIII
By Ma. Jessamine Valerie C. Cortez
I.
Objectives:
a. Differentiate the different types of correspondence of a relation.
b. Give examples in each type of correspondence.
c. Appreciate correspondence in real life situation.
II.
Subject Matter:
Topic: Correspondence of Relation
Reference: Mathematics Learner’s Module for Grade 8 by DepEd pp. 147-148
Materials: Laptop, projector, cartolina, marker,
Methods: Demonstration method and Activity method
Values Integrated: Appreciation, cooperation
III.
Procedure:
Teacher’s Activity
A. Preliminary Activities
1. Daily Routine
-Greetings
-Prayer
-Checking of Attendance
2. Review
Last meeting, our discussion
is all about relation. Again,
what is relation?
Learner’s Activity
Relation is a relationship between
quantities.
How do we represent a
relation?
We can represent a relation in different
ways like ordered pairs, table form,
mapping diagram, and through graph.
What is the difference
between domain and range?
The domain of a relation is the set of all
first coordinates or x-coordinates and the
range is the set of all second coordinates
or y-coordinates.
3. Motivation
The class will be divided into
three groups. Each group will
choose two representatives.
One of each group will pick a
relation and they will
represent it in table form
and mapping diagram. The
group who will finish it first
will get an incentive
afterwards.
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For example:
A relation between the
grade 8 and the sections.
y
Descartes
x
Hoffman
Grade 8
Euler
Gauss
Pascal
B. Lesson Proper
1. Presentation of the Lesson
The game that is being
executed has something to
do with our topic for today
which is the types of
correspondence of a
relation.
2. Discussion Proper
In relation, there is what we
called correspondence
wherein this correspondence
is classified into three types,
the one-to-one
correspondence, one-tomany correspondence, and
many-to-one
correspondence.
In one-to-one
correspondence, every
element in the domain is
paired into a unique element
in the range. For example:
1
4
2
5
3
6
Domain
Range
2
Let’s have an example in real life
situation. Say for instance, we
have a relation between the
student and its I.D. number. No
student have the same I.D.
number since, it is a one-to-one
relation.
X
y
Russel
001
Janesen
025
Angelo
154
Now, give me another example.
Another type of correspondence
is one-to-many correspondence.
In this type of correspondence,
every element in the domain is
mapped in any two or more
elements in the range. For
example:
y
x
2
1
3
2
4
5
3
The relation between a car and the
company.
Fortuner
Toyota
Montero
Mitsubishi
MU-X
Isuzu
CR-V
Honda
x
y
In real life, let’s have the relation
between the teacher and the
students.
y
x
Miller
Sir Daren
Rochelle
Sherwin
Who can give another example
of one-to-many
correspondence?
The relation between the principal and
the teachers.
Ma’am Raquel
Ma’am Rhea
Sir Tito
Sir Frank
x
Sir Buts
y
The last type of correspondence
of a relation is many-to-one
correspondence. If two or more
elements in the domain are
paired into a single element in
the range, it is called many-toone correspondence. See this
example.
x
1
y
2
5
3
6
4
4
As in real life, let’s have the
relation between the students
and their class rank.
x
Jhandy
y
Yvan
1st
Eroll
3rd
Reymond
Now, give another example of
many-to-one correspondence.
The relation between the student and
section.
x
y
Jasmine
Queen
Hoffman
Zip
Descartes
Rioben
C. Application
Given the following relation,
determine what type of
correspondence it is; One-to-one,
many-to-one, or one-to-many.
1. It is a many-to-one
correspondence since, two
elements in domain are paired
with the same element in the
range.
1. { (3,3), (1,3), (2,5), (0,2) }
2.
3.
x
y
0
-2
-2
0
2
1
1
3
7
2
4
2. It is a one-to-one correspondence
since, every element in the
domain is paired with unique
element in the range.
-5
-1
8
9
1
3. It is a one-to-many
correspondence since, one
element in the domain is paired
with two elements in the range.
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D. Generalization
What are the three types of
correspondence?
IV.
The three types of correspondence are
one-to-one correspondence, one-to-many
correspondence, and many-to-one
correspondence.
What is a one-to-one
correspondence?
One-to-one correspondence means that
every element in the domain is paired
with a unique element in the range.
What is one-to-many
correspondence?
When we say one-to-many
correspondence, it is a type of
correspondence wherein one element in
the domain is mapped with two or more
element in the range.
What is many-to-one
correspondence?
It is many-to-one correspondence when
two or more elements in the domain are
paired with just one element in the range.
What values have you gained
during our discussion?
We learned to appreciate correspondence
by relating it to our real life situation.
Evaluation:
Consider the sets of ordered pairs below.
1. Set A: { (3,4), (4,5), (5,6), (6,7), (7,8) }
2. Set B: { (2,2), ( 2,-2), (3,3), (3,-3), (4,4), (4,-4) }
3. Set C: { (0,1), (1,1), (2,1), (3,1), (4,1), (5,1) }
Questions to ponder:
a. What is the domain of each set of ordered pairs?
b. What is the range of each set of ordered pairs?
c. What type of correspondence is each set of ordered pairs?
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V.
Assignment:
A. Enrichment of the lesson
Determine the domain, range, and the type of correspondence of each mapping
diagram.
1.
-2
-5
0
-1
1
0
2
6
2.
1
0
2
3
4
3.
0
1
1
2
2
3
3
4
B. Future Lesson
1. What is a function?
2. What is/are the graph of a function?
Reference: Mathematics Learner’s Module for Grade 8, by Department of Education,
page 149-152.
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