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Bachelor of Secondary Education Major in Mathematics (Cor Jesu College)
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GRADES 9
DAILY LESSON LOG
School
Teacher
Teaching Dates and
Time
Grade Level 9
Learning Area MATHEMATICS
Quarter FIRST
Teaching Day and Time
Grade Level Section
Session 1
Session 2
Session 3
Session 4
I. OBJECTIVES
1. Content Standards The learner demonstrates understanding of key concepts of quadratic equations, inequalities and functions, and
rational algebraic equations.
2. Performance
The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real life
problems involving quadratic equations, inequalities and functions, and rational algebraic equations and solve them
Standards
using a variety of strategies.
3. Learning
Solve problems involving
Solve problems involving
Solves equations
Solve problems involving
quadratic equations and
Competencies/
transformable to quadratic quadratic equations and
quadratic equations and
Objectives
equations (including
rational algebraic equations. rational algebraic equations. rational algebraic equations.
(M9AL-Ie-1)
rational algebraic
(M9AL-Ie-1)
(M9AL-Ie-1)
equation). (M9AL-Ic-d-1)
a. Analyze and solve a
a. Translate mathematical
a. Analyze and solve a
a. Transform rational
variety of word problems in variety of word problems in
statements into algebraic
algebraic expression into equations
rational algebraic equations rational algebraic equations
quadratic equations
b. Analyze and solve a variety b. Synthesize all the
b. Appreciate the importance
b. Find the solutions of
of word problems involving
mathematical presentation of solving problem with
equations transformable to quadratic equations
of problems
rational algebraic equation in
quadratic equations
c. Realize the role of
c. Realize the role of
real-life situation
including rational algebraic
systematic planning in solving systematic planning in
expression
solving problems
problems
c. Appreciate the
importance of rational
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algebraic expressions in
real-life situation
II. CONTENT
Equations Transformable Solving Problems Involving
to Quadratic Equations
Quadratic Equations
Solving Problems
Involving Quadratic
Equations
Solving Problems
Involving Quadratic
Equations
III. LEARNING
RESOURCES
A. References
1.
2.
Teacher’s
Guide
pp. 50-53
pp. 54-57
pp. 54-57
pp. 54-57
Learner’s
Materials
pp. 77-87
pp. 88-95
pp. 88-95
pp. 88-95
Intermediate Algebra
pp. 58-60
Julieta G. Bernabe et.al.
Intermediate Algebra
pp. 61-65
Julieta G. Bernabe et.al.
Intermediate Algebra
pp. 95-101
Julieta G. Bernabe et.al.
Intermediate Algebra
pp. 95-101
Julieta G. Bernabe et.al.
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
3.
Textbook
4.
Additional
Materials from
Learning
Resource (LR)
portal
B. Other Learning
Resources
IV. PROCEDURES
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A. Reviewing previous Find the LCM of the
lesson or presenting following expressions:
the new lesson
1.
2.
3.
B. Establishing a
purpose for the
lesson
Translate the verbal phrases
into algebraic expressions.
a. The ratio of x and 4.
b. 3 less than thrice a number
c. The sum of twice a number
and 8
d. The ratio of a number x and
six increased by two
e. A certain number decreased
by two
Study the situation below.
Review:
The sum of two numbers is Analyze, study and solve the
36. Describe the following given problem.
representations:
1. Coco Martin has a
_________1. Let x be the
vacant lot in his
_________2. 36–x be the
backyard. He wants to
________ 3. x(36-x) be the
make as many
rectangular gardens
as possible such that
the length of each
garden is 3m longer
than its width. He also
wants the length of
the garden with the
smallest area to be
4m.
1. How did you find the 1. What words serve as clues to Cite an example or situation
what operation symbol is to be in real life where the concept
LCM of the following
used?
expressions?
of the quadratic equation
2. What mathematics
2. What must be considered in and rational algebraic
concepts or principles did translating verbal phrases to
equation is applied.
you apply?
mathematical phrases and vice
3. Did you find any
versa?
difficulty in performing
3. In translating a verbal phrase
the task?
to an algebraic expression, a
single word can make a
difference. Thus, every word in
the statement must be
interpreted correctly. In what
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1. Illustrate the different
rectangular gardens
that Coco Martin could
make.
2. What are the
dimensions of the
different gardens that
Coco Martin wants to
make?
3. What is the area of
each garden in item 2?
4. What is the area of the
smallest garden that
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way does it affect our dealings
with others?
C. Presenting
examples/
instances of the
lesson
Example 1: Solve the
rational Algebraic
equation
Coco Martin can
make? How about the
area of the largest
garden? Explain your
answer.
Example 1: if the square of a Example. A tank fitted with Example. The denominator
number is added to 3 times, the two pipes is to be filled with of a fraction is 4 more than
sum is 108. Find the number.
water. One pipe can fill it in the numerator. If both the
Solution: Let x be the number
15 hours. After it has been numerator and the
open for 3 hours, the second denominator of the fraction
pipe is opened and the tank are increased by 1, the
a. Multiply both sides
is filled in 4 hours more.
of the equation by
How long would it take the resulting fraction equals .
(x +12) (x – 9) = 0
the LCM of all
x + 12 =0
x – 9 = 0 second pipe alone to fill the Find the fraction.
denominators. In
tank?
x = -12
x=9
the given
Analysis:
Example 2. The speed at which
equation, the LCM
Let
x
be
the
time
in
hours
for
water travels in a pipe can be
Let x, the numerator of the
is 4x.
measured by directing the flow the second pipe alone to fill
fraction
through
an
elbow
and the tank.
measuring the height its spurts Then: Rate x Time = Part Filled Then, x + 4 is the
out on the top. If the elbow
Rate x
Part denominator.
height is 10cm, the equation
Time
Filled Increasing both of these
relating the height of the water
b. Write the resulting
expressions by 1, the
7
above the elbow (in cm) and its First
quadratic equation
resulting equation is
velocity v (in cm/sec) is given by Pipe
in standard form.
(h + 10). Find v if h = Second
4
Pipe
2cm.
c. Find the roots of
the resulting
equation using
Solution: substitute the
value of h in the formula:
Solution:
Solution:
The LCD is (x + 5)(2).
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any of the
methods of
solving quadratic
equations. Try
factoring in finding
the roots of the
equation.
Multiplying both sides by the
LCD
= 1960 (12)
= 23520
= 153.36 cm/sec.
2 (x +1) = x + 5
8x = 60
2x + 2 = x + 5
x=3
x – 3 = 0 or x – 8 = 0
x = 3 or x = 8
The second pipe alone can the fraction is
fill the tank in
hours. The
product of the roots of
D. Discussing new
Solve the following.
concepts and
practicing new skills
1.
2.
3.
+
7x – 18 = 0 is -18
What are my Dimensions? Solve the following.
Analyze and solve the
1. What positive number following problem.
Use the situation below to
exceeds 3 times its
answer the questions that follow.
1. The perimeter of a
reciprocal
by
2?
The length of a rectangular floor
rectangular swimming
Representation: Let x
is 5m longer than its width. The
pool is 86m and its
be the number and its
area
of
the
floor
is
area is 450m2. What is
reciprocal.
the length of the
.
2. The length of a
swimming pool? How
rectangle is 7 inches
Questions:
more
than
its
width,
1. What expression
about its width?
its
area
is
228
square
represents the width of
Explain how you
inches.
What
are
the
the floor? How about the
arrived at your
dimensions of the
expressions represent its
answer.
rectangle?
width?
2. The length of a
Representation: Let x
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2. Formulate an equation
relating the width, length
and the area of the floor.
Explain how you arrived
at the mathematical
sentence.
3. How would you describe
the equation that you
formulated?
4. What is the width of the
floor? How about its
length?
5. How did you find the
length and width of the
floor?
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be the width of the
rectangle and
x+7
be the length
3. Mrs. Cesa can finish
checking 40 item test
ahead
of
Mrs.
Saburao by 1 min.
Together they can
finish 27 papers in 1
hour. How long does
it take each to finish
checking one paper?
Representation: Let x
be the time it takes
for Mrs. Cesa to finish
checking a 40-item
test paper. x + 1 be
the time it takes for
Mrs. Saburao to finish
checking a 40-item
test paper.
rectangular parking lot
is 36m longer than its
width. The area of the
parking lot is 5,152m2.
What equation
represents the area of
the parking lot?
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E. Discussing new
concepts and
Solve this equation:
practicing new skills
#2
Use the situation below to
In word problems, what we Use the situation below to
answer the questions that follow. need is to set a certain
answer the questions that
quadratic equation related to follow.
The length of rectangular board the condition of the problem.
is 36 inches longer than its
To facilitate the formulation A projectile that is fired
width. The area of the board is of the quadratic equation, as vertically into the air with an
576 square inches.
well as the solution, we need initial velocity of 120ft. per
second can be modeled by
a. Multiply both
to draw a rough diagram for
the equation s = 120t – 16t2.
sides of equation Questions:
the condition of the problem.
In the equation, s is the
by 2x(x+3) to get 1. What expression represents
In some problems, a root
the
width
of
the
board?
How
distance in feet of the
the quadratic
derived may be discarded. projectile above the ground
about
the
expression
that
equation
What do you think are the
represents its length?
after t seconds.
b. Solve for x
reasons why? Explain.
2.
Formulate
an
equation
using any method.
(Examples 1 – 3)
relating the width, length
1. How long will it take
and the area of the board.
for a projectile to
Explain how you arrived at
reach 216 feet?
the mathematical sentence.
2. Is it possible for the
3. How would you describe the
projectile to reach 900
equation that you
feet? Justify your
formulated?
answer.
4. Using the equation, how will
you determine the length
and width of the board?
5. What is the width of the
board? How about its
length?
6. How did you find the length
and width of the boar
F. Developing mastery View Me in Another Way! Let each student get the area of
Let Me Try!
Let each student get the area
the front page cover of their
of the blackboard Represent
(Leads to Formative
Solve the following.
Transform each of the
Math Learners Manual book.
the width of the board by x
Assessment 3)
following equations into a Represent the width of the book 1.Find the two consecutive and then find the expression
quadratic equation in the by x and then find the
even integers if one – third that represents its length.
form
expression that represents its
of the smaller one is equal to Formulate an equation
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.
1.
length. Formulate an equation one – fourt of the larger one. relating the width, length and
relating the width, length and the 2. the ten di of a two – digit the area of the board.
area of the book. Explain how number is one more than the Explain how you arrived at
you arrived at the mathematical units’ digit. If the number is the mathematical sentence.
sentence. Use cm as a unit of divide by the sumof the
Use m as a unit of
measurement.
digits, the quotient is equal measurement.
to seven.what is the
number?
2.
3.
4.
5.
G. Finding practical
What is the agricultural
product that is usually
applications of
concepts and skills in known as source of
income of
daily living
Maragondonians?
Use a variable to represent the Make a design or sketch
unknown quantity, and then plan of a table than can be
write an equation from the given
information. Explain how you made out of
arrived at your answer. (Group plywood and 2” x 3” x 8’
students into 5 and let them wood. Using the design or
Solve the following
work on these for 20 min)
sketch plan, formulate
equations. Copy the
Group 1 – Find the area and problems that involve
letter corresponding to perimeter of one rectangular quadratic equations, then
each equation and write pathway in your school campus. solve in as many ways as
it above the
Group 2 – Find the length of possible.
corresponding answer in fencing materials needed to
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Play the role of….
By Group:
Cite and role play a situation
in real – life situation where
the concept of quadratic and
rational algebraic equation is
applied. Formulate and solve
problems out of these
situations.
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the boxes below that
enclose a rectangular lot of
contain the answer code. administration building in your
school campus.
Group 3 – Find the area and
perimeter of any rectangular
garden in your school campus.
Group 4 – Find the area and
perimeter of the tarpaulin
needed that will fit to the wall of
the stage in your school
campus.
Group 5 – Number of hollow
blocks (5” x 4”) needed to
concretize the 3 walls of your
school campus Pavilion
including the 2 layered hollow
blocks below the ground.
There are conditions in a given There are conditions in a There are many types of
H. Making
STEPS IN
problem which when translated given problem which when applied problems involving
generalizations and TRANSFORMING
abstractions about RATIONAL ALGEBRAIC to the equation form in one translated to the equation rational equation. Success in
variable lead to a quadratic form in one variable lead to solving them depends upon:
the lesson
EXPRESSION INTO
1. Correct analysis of the
QUADRATIC EQUATION equation and two answers are a quadratic equation and
obtained.
In
some
problems,
a
two
answers
are
obtained.
In
problem
 Multiply both sides
set of answers can be some problems, a set of
2. Proper labeling of the
of the equation by
discarded.
For
instance, answers can be discarded.
variable(s)
the LCM of all
negative
dimensions
of For
instance,
negative
3. Accurate statement of
denominators. In rectangles and the negative time dimensions of rectangles
the
mathematical
the given
are disregarded.
and the negative time are
sentence
disregarded.
4. Systematic derivation
equation.
of the truth set, and
 Write the resulting
5.
Proper
translation into
quadratic equation
the solution set
in standard form.

Find the roots of
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the resulting
equation using
any of the
methods of
solving quadratic
equations. Try
factoring in finding
the roots of the
equation.
I. Evaluating learning
Find those missing!
Solve the following problems
involving rational algebraic
Solve the following problems equation.
involving quadratic equations
1. The denominator of a
1. A rectangular garden has
fraction is 4 more
2
an area of 84m and a
than the numerator. If
perimeter of 38m. Find its
both the numerator
length and width.
and the denominator
2. A car travels 20 kph
of the fraction are
faster than a truck. The
increased by 1, the
car covers 350km in two
resulting fraction
hours less than the time it
equals to ½. Find the
takes the truck to travel
fraction.
the same distance. What
2. The fifth, fifteen and
is the speed of the car?
fiftieth parts of a
How about the truck?
number
3. Filomena Resort rented a
together make43.
certain number of
Find the number.
function rooms for Php
3. The smaller of two
28, 800 when the price
numbers is two –
was reduced by Php 20
thirds of the larger,
per room, 6 more rooms
and the sum of their
were rented. How many
reciprocal is 1/6.
function rooms were
What are the
rented?
numbers?
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Solve
the
following
problems.
1. If an amount
of
money P in pesos is
invested at r percent
compounded
annually, it will grow
to an amount
A= P (l + r)2 in two
years. Suppose Vice
Ganda wants his
money amounting to
Php200,000 to grow
to Php228, 980 in two
years. At what rate
must he invested his
money?
2. Kathryn can type a
report in five hours
while Liza can finish
the same report in
four hours. If both
girls work on the
report together, how
long will it take to
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finish it?
J. Additional activities
for application or
remediation
Assignment:
Assignment:
Solve:
Two joggers leave the
starting point of a circular
course at the same time.
One jogger completes
one round in 6 minutes,
and the second jogger
finishes in 8 minutes.
After how many minutes
will they meet again at
the starting place,
assuming that they
continue to run at the
same pace?
Assignment:
Answer the problem below. Make a design or sketch
plan of a picture frame that
An amusement park wants can be made out of 6” x 12”
to place a new rectangular cardboard. Using the design
billboard to inform visitors of or sketch plan, formulate
their
new
attractions. problems that involve
Suppose the length of the quadratic equations, then
billboard to be placed is 4m solve in as many ways as
longer than its width and the possible.
area is 96m2. What will be
the length and the width of
the billboard?
V. REMARKS
VI. REFLECTION
a.
No. of learners who
earned 80% on the
formative assessment
b.
No. of learners who
require additional
activities for
remediation.
c.
Did the remedial
lessons work? No. of
learners who have
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Assignment:
Make a research about
quadratic inequalities.
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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 difficulties did I
encounter which my
principal or supervisor
can help me solve?
g.
What innovation or
localized materials did
I use/discover which I
wish to share with
other teachers?
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