QUARTER I
Week 1
Subject: General Math Grade Level: 11
Date: ______________ Day 2
Content Standard: Demonstrates understandings of key concepts of functions.
Performance Standard: Be able to accurately construct mathematical models to
represent real-life situations using functions.
Competency: Represents real-life situations using functions, including
piece-wise functions.
Code: (M11GM-Ia-1)
I. OBJECTIVES
Given a 60-minute activity, the students will be able to:
Knowledge: Define and understand relation and function correctly.
Skills: Solve problems involving relation and function in 15
minutes.
Attitude: Differentiate the different types of relation and determine
the types of relation that are function.
II. CONTENT
Topic: Relations and Functions
III. LEARNING RESOURCES
A. General Mathematics Learner’s Module
B. General Mathematics Teacher’s Guide
C. General Mathematics (for SHS) Textbook (Authors: Garvida, et. al)
D. Online Sources:
a. https://www.mathsisfun.com/sets/function.html
b. https://www.mathsisfun.com/sets/domain-range-codomain.html
c. http://mathonweb.com/help_ebook/html/functions_6.htm
IV. PROCEDURES
Teacher’s Activity Student’s Activity
A. Preliminary Activity
Greetings! (Students’ stand up)
Before we start, let us stand and pray. (Students’ raise their hands while the
To see who is absent let us check the teacher called their names)
attendance first, and then we go on our
lesson.
B. Mind Breaker to Present the New
Lesson
The students actively participate on the
ACTIVITY 1: PIC-REVIEW discussion.
Examine the images below. What can you
observe?
The students answer the question.
Possible Answer/s: Water, Batteries,
Gasoline, Pedals, Tree, Cellphone and Car.
“Very Good!”
C. Establishing a Purpose for the Lesson
The students raised their hands to answer
Motivation Questions:
the question.
1. What is the relation of the images in column Possible Answer/s:
1 with the images in column 2? 1. Tree needs water to grow.
2. Cellphone needs battery to function.
“Great!” 3. Car needs battery, gasoline and
pedals to work properly.
The students raised their hands to answer
the question.
2. What do you think if these objects have no Possible Answer: The objects in the right
relation with each other? side will not function.
“Very well said!”
The students raised their hands to answer
3. Do you think, finding their relation will the question.
Possible Answer/s: Yes or No.
determine whether they are functioning or
not?
“WE WILL ANSWER THAT IN OUR
LESSON FOR TODAY.”
D. Reviewing Some Definitions: The students listen attentively.
A SET is the collection of objects.
Examples:
1. Set of Vowels:
V = { a , e , i, o ,u }
2. Set of Integers:
I={… ,−2 ,−1 , 0 , 1, 2 , … }
ORDERED PAIR
- It is the composition of x-coordinate and
y-coordinate written in a fixed order
within parenthesis.
- It contains the coordinate of a point in
the Cartesian plane.
- It is in the form: (x , y ).
The set of x-values is called the DOMAIN and
it is written as:
X ={ x 1 , x 2 , x 3 ,… , x n } .
The set of y-values is called the RANGE and it
is written as:
Y = { y1 , y2 , y3 , … , yn } .
The set of ordered pairs is written as:
O=¿
The students listen attentively.
Participate by reading the definition.
E. Discussing New Concepts and Practicing
New Skills #1
RELATION
Definition: Relation is the relationship between
the set of x−values (domain) and
the set of y−values (range).
“Good.”
In other words, relation is the set of ordered
pairs. Let’s take a look with the example below:
Let: a={ ( 1 , 2 ) , ( 4 ,3 ) , ( 8 , 10 ) }
Thus, x= {1 , 4 , 8 }
y={2 ,3 , 10 }
To see the relation of our set of x with the set of
our y , we make use of the “mapping diagram.”
The students will solve the problem:
Answer:
Note: The set of y is the set of image of
X ( set of x ) .
Solve: Using mapping diagram, see the relation
of the set of ordered pairs:
b={ ( 1 , 4 ) , ( 1 ,1 ) , ( 2 ,1 ) ,(2 , 5) } The students listen attentively.
Participate by reading definitions.
F. Discussing New Concepts and Practicing
New Skills #2
FOUR TYPES OF RELATION:
1 - to - 1: Each element of the domain has a
unique image.
1 – to - many: At least 1 element in the
domain has many images.
many - to - 1: At least 2 elements in the
domain have the same
image.
many-to-many: Many elements in the
domain have many images,
The students raised their hands to answer
vice versa. the activity.
Answers:
1. Many-to-Many
2. 1-to-1
3. Many-to-1
4. 1-to-Many
ACTIVITY 2: BE OSERVANT!
Tell their relation:
The students listen attentively.
Participate by reading the definition.
“Good job!”
G. Discussing New Concepts and Practicing
New Skills #3
The students raised their hands to answer
FUNCTION the activity.
Answers:
Definition: Function is a relation where each I. Many-to-Many is not a function.
element in the domain is related to II. 1-to-1 is a function.
III. Many-to-1 is a function.
only one value in the range. IV. 1-to-Many is not a function.
Denoted as: f ( x ) = y
Read as: “ f of x is equal to y .”
ACTIVITY 3: LET’S EXAMINE! The students may ask questions/inquiries.
Using the given in Activity 2, examine the types
of relation.
“Very Good!”
H. Making Generalizations and Abstractions
About the Lesson
• 1 – to – 1 and many – to – 1 is a:
FUNCTION
• 1 – to – many and many – to – many is:
NOT a FUNCTION
A function is always a relation but a relation is
not always a function. The students answer the activity silently.
The students answer the activity silently.
I. Evaluating Learning
INDIVIDUAL WORK!
Tell whether the following relations are
functions or not. Explain.
1. f = {(−10 , 3 ) , ( 5 , 4 ) , (−10 ,5 ) , ( 15 , 6 ) }
2. g= { (−10 ,3 ) , ( 5 , 4 ) , (−10 , 3 ) , ( 15 ,6 ) }
3. h={ (−10 , 3 ) , ( 10 , 5 ) , ( 9 ,6 ) }
J. Additional Activities for Application or
Remediation
INDIVIDUAL WORK!
Tell whether the following relations are
functions or not. Explain.
1. t={ ( 3 , 4 ) , ( 10 , 5 ) , ( 35 , 4 ) , ( 17 , 6 ) ,(35 , 6) }
2. u={ (−3 , 60 ) , ( 4 , 20 ) ,(−5 ,−10) }
3. v={ ( 7 , 6 ) , ( 3 ,6 ) , ( 5 , 5 ) ,(6 , 3) }
V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80% in the
evaluation.
B. No. of learners who require additional
activities for remediation.
C. Did the remedial lessons work? No. of
learners who have caught up with the
lesson.
D. No. of learners who continue to require
remediation.
E. Which of my teaching strategies
worked well? Why did these work?
F. What are the difficulties I encounter
when teaching this topic?
G. What could I do to be more effective in
the next topic?
H. What innovation or localized materials
did I use/discover which I wish to share
with other teachers?
Prepared by:
MELANIE V. VALENZUELA
