daily lesson plan math grade 8 Week-4.docx

dll week 4

1. GRADE 8
DAILY LESSON
LOG
School SURABAY NATIONAL HIGH SCHOOL Grade Level 8
Teacher B. CHIONG Learning AreaMATHEMATICS
Week 4 (October 14-18, 2024) Quarter SECOND
Session 1 Session 2 Session 3 Session 4 Session 5
I. OBJECTIVES
1.Content StandardsThe learner demonstrates understanding of key concepts of linear functions.
2.Performance StandardsThe learner is able to formulate and solve accurately real-life problems involving linear functions.
3.Learning Competencies /
Objectives
The learner illustrates a relation and a
function. (M8AL-IIc-1)
a.Define relation and function.
b.Represent a relation in four
ways:
1.Table
2.mapping diagram
3.graph
4.rule method
c.Develop the value of
perseverance in studying.
The learner verifies if a given relation is a
function. (M8AL-IIc-2)
a.Differentiate a relation from a
function.
b.Determine if a relation is a
function or not using the vertical
line test.
c.Appreciate the concept of relation
and function in real-life situation.
The learner verifies if a given relation is a
function. (M8AL-IIc-2)
a. Determine if a relation is a function given:
1. ordered pairs,
2. mapping, and
3. rules/equations.
b. Express real-life situations into:
1. ordered pairs,
2. mapping, and
3. rules/equations.
c. Appreciate the concept of relation and
function in real-life situations.
The learner performs determines
dependent and independent
variables. (M8AL-IIc-3)
a. Define dependent and independent
variables.
b. Determine the dependent and
independent variables.
c. Appreciate new understanding on
dependent and independent
variables of a given function.
The learner finds the domain and
range of a function.(M8AL-IId-1)
a. Differentiate domain from
range.
b. Identify the domain and range
of a function given:
1. the ordered pairs, and
2. mapping.
c. Appreciate the concept of
domain and range in real-life
situations.
II. CONTENT
Representations of Functions and
Relations
Representations of Functions and
Relations
Representations of Relations and
Functions
Dependent and Independent
Variables
Domain and Range of
Function
III. LEARNING
RESOURCES
A.References
1. Teacher’s
Guide
155-182 168- 169
2. Learner’s
Materials 138-144
151-152
pages148-152 pages 155-156
3. Textbook
None None
Lapinid and Buzon, Advanced Algebra,
Trigonometry and Statistics: Patterns and
Practicalities, pp. 22-23;
Valtoribio, Advanced Algebra,
Trigonometry and Statistics, pp. 4-5.
Lapinid and Buzon, Advanced Algebra,
Trigonometry and Statistics: Patterns
and Practicalities, pp. 27-28
Lapinid and Buzon, Advanced
Algebra, Trigonometry and
Statistics: Patterns and
Practicalities, pp. 11-12.
4. Additional
Materials
https://www.youtube.com/watch?https://www.youtube.com/watch?

2. from Learning
Resource (LR)
portal
v=C5xcpNGeKCQ v=l4265qSL914
B.Other Learning
Resources Laptop, Projector,Speaker
LCTG Grade 8 by DepEd Cavite
Mathematics,2016
Laptop, Projector,Speaker
LCTG Grade 8 by DepEd Cavite
Mathematics,2016
Grade 8 LCTG by DepEd Cavite Mathematics
2016, projector, laptop, power point
presentation
Grade 8 LCTG by DepEd Cavite
Mathematics 2016, projector, laptop,
power point presentation
Grade 8 LCTG by DepEd Cavite
Mathematics 2016, laptop,
projector, powerpoint
presentation, “Cabbage of
Knowledge”
IV. PROCEDURES
A.Reviewing
previous
lesson or
presenting
the new
lesson
Where do I belong???
Description: This activity will enable you to write
ordered pairs. Out of this activity, you can describe
the relation of the products to its respective places.
Directions: Group the following products in such a way
that they are from the same places in Cavite.
Kesong putiSee
weeds
Pastillas
de leche
Smoked fish
(tinapa)
coconutDried fish
(tuyo)
Coffee
beans
Fresh
milk
Banana
shrimpBlack
pepper
Choco
milk
Strawberry
milk
crabpineapple
General
Trias
RosarioAmadeo
SPOTTING ERRONEOUS COORDINATES
Do the task as directed
A. Lea indicated that A has coordinates (-
3,2)
1.Do you agree with Lea?
2.What makes Lea wrong?
3.How will you explain to her that
she is wrong in a subtle way?
B. Cris insisted that B has coordinates (-2,-4)
while C has coordinates (-2,2). If yes, why?
If no, state the correct coordinates of points
of B and C
“Find your Match!”
Call on 8 volunteers. Give each student a
strip of paper and instruct them to find their
match.
Teacher-students
Boyfriend-girlfriend
Parent-child
God-creation
1. What did each pair represents?
2. How can you make your relationship with
others work/function?
Can you live without your

parents?
Who among you lives with their

parents?
Therefore, are you dependent or

independent individual?
Cabbage of Knowledge
Let the students pass around the
“cabbage of knowledge” while a
music is playing. Once the music
stops, the student holding the
cabbage will uncover a leaf and
will have to define or describe the
word written on each leaf.
Dependent Function
Independent Domain
Relation Range
B.Establishing Presentation of ObjectivesPresentation of ObjectivesA function is a relation where there is noVariables may be dependent orThe domain of a function refers to

3. a purpose for
the lesson
repetition of the first element.
dependent. Dependent variable
depends on the independent variable
while the independent variable
controls the dependent variable.
the first or x values in a set of
ordered pairs, while the range is
the set of the second or y values
in a set of ordered pairs.
C.Presenting
examples/
instances of
the lesson
Exploratory Activity
From the previous activity, form some
ordered pairs using the format:
( product, place )
a. Column 1: __________
b. Column 2: __________
c. Column 3: __________
Based on the coordinates you have
formulated, is there a repetition of the first
coordinates?
How about the second coordinates?
Try to present the ordered pairs formed in
table form.
PRODUCTSMUNICIPALITY
Now, try to make a mapping diagram to
show the relation.

What can you say about the
diagram you have formed?
What elements belong to the first set? To
the second set?
Is there a repetition of the first
Plot the following points in five separate
Cartesian Plane.
The relation between time and pay is an
example of a function.
Example:
Notice that there is no repeated value for
the first element. So, this is a function.
This can also be represented through
A.Ordered pairs
{(2,200), (4,400), (6,600), (8, 800), (10,
1000)}
B.Mapping
This is an example of one-to-one
correspondence.
A correspondence may be classified as one-
to-one, many-to-one, or one-to-many.
One-to-One Correspondence
Student I.D. No.
- Developmental Activity
If you study hard, what will

happen?
If you spend much of your

allowance, what will happen?
If you eat much, what will happen?

If you travelled long distance,

what will happen?
From the previous questions given to
you, we can determine the dependent
and independent variable.
In the first question, if you study
hard, you said you will get high
scores on tests, so you will get high
grades.
In the second question, if you spend
much of your allowance, you said you
will lose your money.
In the third question, if you eat
much, you said you will gain weight.
In the fourth question, if you
travelled long distance, there is
larger amount of gasoline to be
consumed.
From those given situations, can you
determine the dependent and
independent variables? How did you
identify the dependent and
independent variables?
Let’s have other examples. Classify
the variables as dependent or
independent.
1. cost of chicken and its weight
2. income of a worker and number of
hours of work
3. perimeter of a square and its side
Given the following set of ordered
pairs, identify the x values and y
values.
1. (4,5), (5,-4), (8,5), (-3,2), (6,1)
2. (0,3), (-1,5), (2,-4), (3,6), (4, -7)
3. (2,0), (0,9), (1,3), (-1,9), (3,7)
4. (-8,1), (4,-5), (6,0), (-7,8), (-5,2)
5. (-2,6), (4,-3), (-5,1), (4,0), (5,3)
In the previous activity, how did
you determine the domain and
range?
In mapping diagram, like
What is the domain? What is
the range?

4. coordinates? How about the second
coordinates?
The relations you have formed in the previous
activities are all examples of a
FUNCTION, as they are many-to-one correspondence.
If the relation shows one-to-one correspondence it is
also a function, but if the relation is one-to-many
correspondence, then it is not a function.
Aside from these three methods, function can also be
represented by picture
or graph, by equation and by rule.
Situation: Suppose Tenten is working in Gen. Trias
Dairy Raisers Multi-Purpose
Cooperative at Santiago, Gen. Trias, Cavite and he
earns ₱43 per hour.
Questions:
a.How much will Tenten earn if he works
for
4 hours a day?
5 hours a day?
6 hours a day?
7 hours a day?
8 hours a day?
b. Is his earnings related to the number of hours
of work? How?
Tenten’s earnings can be represented by some other
way like graph, equation or rule.
By graph
By equation or by rule, Tenten’s earnings
can be represented by y=43(h)
Many-to-One Correspondence
One-to-Many Correspondence
C.Rule/Equation
As the number of time (x) increases, the
amount of pay (y) also increases.
-What will be your pay if you worked for 1
hour? 15 hours? 20 hours? n hours?
So, the rule for this function is y= 100x.
4. In mathematical equation, like for
example, the linear function, y =3x-
5. If x=1, what will be the value of y?
If x=0, what is y? If x=1, what is y?
In these cases, which are the
dependent and independent
variables?
D.Discussing
new concepts
and
Video Presention diffentiating a relation and a
function.
From the previous activity, Is there a repetition of the
first coordinates? The second coordinates?
 Connect the given points from the first given point
up to the last.
1. Among the types of correspondence, which ones are
functions? Why?
2. Does one-to-one correspondence between elements
always guarantee a function? How about one-to-one?
What is dependent variable?
What is independent variable?
How can you differentiate the dependent
and independent variable?
How can you describe the domain and
range of a function given the:
a. ordered pairs
b. mapping diagram?

5. practicing
new skills
#1
 How can you describe each graph?
 Draw vertical lines through the graph.
 Does the vertical lines touch the graph?
 How many times does the vertical line touch the
graph?
Justify your answer.
3. Does one-to-many correspondence between
elements always guarantee a function? Justify your
answer.
E.Discussing
new concepts
and
practicing
new skills
#2
A.What can you say about
relation?
B.Can you determine whether a
relation is a function or a mere
relation? How?
C.What will be your reference that
a relation is a function?
D.Give real-life examples/
situations that can describe a
function.
A.Does each graph represent a
function? Why or why not?
B.If you are only given the graph,
how can you determine if the
graph represents a function?
C.What do you call this method?
Tell whether the following relations as
function or not.
1.
2.
3.
4. y = 3x+9
5. x
2
+ y
2
=16
6. (-1,2), (1,3), (1,5), (2,7)
7. (0,6), (-3,4), (3,5), (4,0), (6,-3)
Fill in the blanks.
1. I consider the weight of chicken as
a/an ________ variable because it
________ the cost of chicken.
2. I consider the cost if chicken as
a/an ________ variable because it
________ on the weight of the
chicken.
3. I consider the income of a worker
as a/an _______ variable because
it ________ on the number of
hours the worker worked.
4. I consider the number of hours
worked as a/an ________
variable because it ________ the
income of the worker.
5. I consider the perimeter of a
square as a/an ________ variable
because it ________ on the length
of its side.
6. I consider the length of the side of
a square as a/an ________
variable because it ________ the
perimeter of the square.
Determine the domain and range
given the following.
1. (2,0), (3,1), (3,7), (6,-1)
2. (3,0), (4,0), (5,0), (6,0)
3. (-1,9), (4,-1), (-4,1), (1,-1)
F.Developing
mastery
Determine whether a given mapping
diagram is a function or NOT a function.
Given the following graphs of relation,
determine whether each describes a
function or not a function.
Determine whether the following relations
as functions or not.
1. (-6,-4), (-4,-2), (-1,0) , (1,1), (4,2), (3,3)
(Group Activity)
Think of two quantities related to
each other. Identify the dependent
Determine the domain and range
given the following.
1. (9,10), (8,10), (-9,10), (6,10)

6. -5
-1
-9
10
(Leads to
Formative
Assessment
3)
2. (-4,0), (0,3), (4,0), (0,-3)
3. 3x + y = 4
4. 2x
2
+ y2

= 8
6.
7.

and independent variables. Give three
examples. (You may choose real life
situations.)
2. (3,2), (4,4), (5,6), (6,7)
3. (-7,9), (-6,-1), (-5,1), (-4,-1)
G.Finding
practical
applications
of concepts
and skills in
daily living.
Situation: Suppose you are working in a fast
food company. You earn ₱48 per hour.
Questions:
a. How much will you earn if you work
for
4 hours a day?
5 hours a day?
6 hours a day?
7 hours a day?
8 hours a day?
Plot the following points in five separate
Cartesian Plane and use vertical line test to
determine if is a function or not.
If a kilo of mango costs ₱120, how much
are 2 kilos? 3 kilos? 4 kilos? 5 kilos?
Express this relation by
a.) ordered pairs;
b.) mapping; and
c.) through equation.
Determine if it describes a function.
From the three examples you have
made in “Independent Practice” (I Can
Do This!) choose one and conduct an
interview, then make a table of
values and set of ordered pairs that
will represent/illustrate the function.
Rewrite the following ordered
pairs in mapping form or diagram
and vice versa and determine the
domain and range.
1. (4,5), (6,6), (5,7), (6,8)
2. (-3,-2), (-4,-4), (-5,-6), (-6,-7)
3. (-7,2), (-6,2), (-5,2), (-4,2)
2
0
-2
1
2
3
0

7. b. Are your earnings related to the
number of hours of work? How?
( The learners will be instructed to represent
their answer in different ways.)
Group 1 – by ordered pairs
Group 2 – by table
Group 3 – by mapping diagram
Group 4 – by graph
Group 5 – by equation/rule
Questions to be used:
How did you write the set of ordered

pairs?
How did you make a table?

How did you make a mapping diagram?

How many elements are there in the set

of ordered pairs you have made?
What elements belong to the first set?

second set?
Is there a repetition of first coordinates?

How about the second coordinates?
Domain Range
1.
2.
3.
4.
5.
H.Making
generalizatio
ns and
abstractions
about the
lesson
A relation is any set of ordered pairs. The
set of all the first coordinates is called the
domain of the relation. The set of all the
second coordinates is called the range.
A function is a relation in which
1. for each first coordinate, there is
exactly one second coordinate, or:
2. for every first element x, there
corresponds a unique element y.
NOTE: Every function is a relation, but some
relations are not functions.
A function can be represented by using
a table, or a set of ordered pairs of
numbers, by mapping, by picture or graph,
by equation and by rule or correspondence
A function is a relation where there is no
repetition of the first element.
The vertical line test is used to determine
whether the graph is a function or not. If
any vertical line drawn through the graph
intersects the graph in exactly one point,
then the graph represents a function.
A function is a relation where there is no
repetition of the first element.
-A correspondence may be classified as one-
to-one, many-to-one, or one-to-many. It is
one-to-one if every element in the domain is
mapped to a unique element in the range; or
many-to-one if any two or more elements of
the domain are mapped to the same
element in the range; or one-to-many if
each element in the domain is mapped to
any two or more elements in the range.
Dependent variable is a
mathematical variable whose
value is determined by that of
one or more other variables in
a function. It depends on the
independent variable.
Independent variable is a
mathematical variable that is
independent on the other
variables in an expression or
function and whose value
determines one or more of the
values of the other variables. It
controls the dependent
variable.
-The domain of a function is the
set of all possible values of its
first coordinates and the range is
the set of all possible values of its
second coordinates.
-The domain and range of a
function or relation maybe
identified from the set of ordered
pairs, from mapping diagram,
from the graph or from a rule or
equation.

8. expressed in words. When pictures and
arrows are used in representing a function,
the function may be called mapping.
The kinds of pairing or matching are :
one-to-one correspondence, many-to-one
correspondence and one-to-many
correspondence.
Note: A one-to-one correspondence and a
many-to-one correspondence are called
functions while the one-to-many
correspondence is not.
The variable x is considered the
independent variable because any
value could be assigned to it.
However, the variable y is the
dependent variable because its value
depends on the value of x.
I.Evaluating
learning
State whether the given set of ordered
pairs is a function or NOT. Give the reason
for
your answer.
1. ( 1 ,2 ), ( 2, 3 ), ( 3 , 4 ), ( 4, 5 )
2. ( -1, 6 ), ( -2, 7 ), ( -3, 8 ), ( -4, 9 )
3. ( 1, 2 ), ( 0, 8 ), ( 1, 3 ), ( 2 , 7 )
4. ( -3, 8 ), ( -1, 8 ), ( 3, 8 ), ( 7, 8 )
5. ( 5, 4 ), ( 5, 8 ), ( 7, 2 ), ( 7, 3 )
If a kilo of mango costs ₱120, how much
are 2 kilos? 3 kilos? 4 kilos? 5 kilos? 6
kilos?
Express this relation by graphing and
through vertical line test determine if it
describes a function.
True or False.
1. All functions relations.
2. Some relations are functions.
3. A many-to-one correspondence is a
function.
4. A one-to-one correspondence is a
relation.
5. A relation is a function if there is a
repeated value in the first element.
Answer the following:
1. At a grocery store, the amount of
dressed chicken is Php 110 per
kilogram.
a. Find the cost of dressed chicken for
3 kilograms, and 2.5 kilograms.
b. Which is the dependent variable?
2. In a Rice Productivity Program, a
hectare of land in Buenavista, General
Trias, Cavite yields an average of 120
cavans. What is the dependent and
independent variable?
True or False.
1. The range in {(3,5), (2,6), (1,7),
(0,8)} is (5, 6, 7, 8).
2. The domain is the set of all x
values.
3. In {(6,2), (-6,2), (-5,0), (5,0)},
the domain is (-6, 6)
4. The first values in a diagram
below are called as range.
5. The correspondence in number
4 is many-to-one.
J.Additional
activities for
application
or
remediation.
Give a real life situation that can be an
example of function. Select any of the
methods to represent it.
On a piece of an oslo paper draw a figure
illustrating a relation and label it with
function or not function.
1. Follow Up:
On a piece of an oslo paper draw a figure
illustrating a relation and label it with
function or not function.
2. Study:
Define the following:
a. Dependent variable
b. Independent variable
1. Follow Up:
Give a situation that can help you
determine the dependent and
independent variables.
2. Study:
Define:
a. Domain
b. Range
Thumbs Up-Down-Sideways
1. How well can I determine the
domain and range given a set of
ordered pairs?
2. How well can I determine the
domain and range given a
mapping?
Remediate on those who
answered “down”.
V. REMARKS
VI. REFLECTION

9. 1.No.of learners who earned
80% on the formative
assessment
2.No.of learners who require
additional activities for
remediation.
3.Did the remedial lessons
work? No.of learners who have
caught up with the lesson.
4.No.of learners who continue
to require remediation
5.Which of my teaching
strategies worked well? Why
did these work?
6.What difficulties did I
encounter which my principal
or supervisor can help me
solve?
Prepared By: BEN YHAZEER S. CHIONG
Teacher-III
Checked By: Attested By: Noted By:
ARNOLD C. AYAON VENJIE G. BALIDAD RIZA D. MORADOS
Master Teacher I Head Teacher III Principal IV