School Calbayog City National High School Grade Level 9

GRADES 9 Teacher Rochele A. Santiago Learning Area MATHEMATICS

DAILY LESSON LOG
Teaching Dates and Time September 23 – 27, 2019 Quarter SECOND
September 10, 2019/ 8:15 – 9:15 September 11, 2019/ 8:15 – 9:15 am September 12, 2019/ 8:15 – 9:15 am September 13, 2019/ 8:15 – 9:15 am
Teaching Day and Time
am (Tuesday) (Wednesday) (Thursday) (Friday)

Grade Level Section 9 - Ellipse 9 - Ellipse 9 - Ellipse 9 - Ellipse

Session 1 Session 2 Session 3 Session 4

I. OBJECTIVES

1. Content Standards The learner demonstrates understanding of the keys concepts of variation and radicals.
2. Performance
Standards The learner is able to formulate and solve accurately problems involving variation and radicals

3. Learning Solves problems involving inverse Translates into variation Solves problems Translates into variation
Competencies/ variation. (M9AL-IIb-c-1) statement a relationship involving joint variation. statement a relationship
Objectives between two quantities (M9AL-IIb-c-1) between two quantities
given a mathematical given a mathematical
a. Translate into variation
equation. (M9AL-IIa-b-1) equation. (M9AL-IIa-b-1)
statement a relationship a. Translate into variation
involving inverse statement a relationship
a. Translate into variation a. Translate into variation
variation involving joint variation
statement a relationship statement a relationship
b. Solve problems involving b. Solve problems involving
involving joint variation involving combined
inverse variation inverse variation
b. Find the unknown in a variation
c. Appreciate the concept of c. Appreciate the concept of
joint variation equation b. Find the unknown in a
inverse variation in inverse variation in
c. Appreciate the concept joint variation equation
real-life situation real-life situation
of joint variation in c. Appreciate the concept of
real-life situation combined variation in
real-life situation
II. CONTENT
Inverse Variation Joint Variation Joint Variation Combined Variation
III. LEARNING RESOURCES

A. References

1. Teacher’s Guide
pp. 144-146 pp. 146-148 pp. 146-148 pp. 149 – 152
2. Learner’s
Materials pp. 211-214 pp. 215-219 pp. 215-219 pp. 220 – 223
 3. Textbook Mathematics III (Concepts, Mathematics III (Concepts,
Mathematics III (Concepts, Structures Structures and Methods Structures and Methods Mathematics III (Concepts, Structures and
and Methods for High School), pp. 367- for High School), pp. 373- for High School), pp. 373- Methods for High School), pp. 373-377,
369, Oronce, Orlando A., et.al 377, Oronce, Orlando A., 377, Oronce, Orlando A., Oronce, Orlando A., et.al
et.al et.al
4. Additional
Materials from
www.mesacc.edu/~pikeu/mat120/notes/ www.icoachmath.com/math_dictionary/joi www.burrillbrothers.com/algebrac/varia www.mesacc.edu/~pikeu/mat120/notes/vari
Learning Resource nt_variation.html
variation/inverse/inverse_practice.html tionwksht.doc ation/inverse/inverse_practice.html
(LR) portal

B. Other Learning Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite
Resources Mathematics 2016, Mathematics 2016, Mathematics 2016, Mathematics 2016,
activity sheets, laptop and monitor activity sheets, laptop and monitor activity sheets, laptop and monitor activity sheets, laptop and monitor
IV. PROCEDURES

A. Reviewing previous Preliminary Activity: Preliminary Activity: Preliminary Activity: Preliminary Activity:
lesson or presenting the Give the equation for each If the statement “y varies Give the equation for each of If the statement “z varies
new lesson of the following: jointly with respect to x and the following: directly as x and inversely
1.The lengths l of rectangles z” and the equation is in 1.The area A of a triangle as y” and the equation is in
with constant area 60 the form “y = kxz” (where k varies jointly as the base b
varies inversely as the is the constant), translate and the altitude h. the form “z = ” (where k is
width w. each statement into a 2. The appropriate lengths s
2. At a constant mathematical sentence of a rectangular beam the constant), translate
temperature, the volume using this pattern. varies jointly as its width w each statement into a
V of gas varies inversely 1. s varies jointly as r and its depth d. mathematical sentence
as the pressure P. and t 3. The volume V of a using this pattern.
3.The number of hours h in 2. V varies jointly as l, w, pyramid varies jointly as 1. P varies directly as L,
which a job can be and h the area of the base B and inversely as G
done varies inversely as and the altitude h. 2. y varies directly as x and
3. N varies jointly as
the number of men n 4. The force F applied to an inversely as the square
working. and of an object varies of z
4.The rate of vibration v of a jointly as the mass m and 3. P varies directly as t and
4. A varies jointly as b and the acceleration a.
string under constant inversely as V.
the square of c 5. The heat H produced by
tension varies inversely 4. A varies directly as the
5. The electrical voltage V an electric lamp varies
as the length l of the cube of b and inversely
varies jointly as the jointly as the resistance R
string. as the product of a and b.
current I and the and the square of the
5.The intensity i of light 5. W varies jointly as c and
resistance R. current i.
varies inversely as the square of a and
square of the distance d inversely as b.
from the source.
B. Establishing a purpose for a. Translate into variation a. Translate into variation a. Translate into variation a. Translate into variation
the lesson statement a relationship statement a relationship statement a relationship statement a relationship
involving inverse involving joint variation involving joint variation involving combined
variation b. Find the unknown in a b. Solve problems involving variation
b. Solve problems involving joint variation equation inverse variation b. Find the unknown in a
 inverse variation joint variation equation
C. Presenting examples/ Illustrative Example 1: Illustrative Example # 1: Illustrative Example # 1: Illustrative Example # 1:
instances of the The time (t) required to Find the equation of Find an equation of variation Translating statements into
lesson clean a classroom varies variation where a varies where a varies jointly as b mathematical equation
inversely to the number of jointly as b and c, and and c, and a = 24 when using k as the constant of
students (n) cleaning. If 7 a = 36 when b = 3 and b = 2 and c = 3. variation.
students can clean the room c = 4. Solutions: 1. T varies jointly as a and
in 40 minutes, in how many Solution: A = kbc inversely as b.
minutes can 10 students a = kbc 24 = k(2)(3) Solutions:
clean the room? 36 = k(3)(4) 24 = 6k
k = 36/12 k=4 T=
Solutions: k=3 Therefore, a = 4bc is the required
To express the statement, Therefore, the required equation of variation. 2. S varies directly as R
the time (t) varies inversely equation of variation is and inversely as the
to the number (n) of a = 3bc Illustrative Example 2: square root of V.
students cleaning, we write The area of a rectangle Solutions:
Illustrative Example # 2 varies jointly as the length
t= Assume a varies jointly and the width, and whose A = S=
with b and c. If b = 3 and 72 sq. cm when l = 12 cm
Therefore, by substituting c = 4, find the value of a. and w = 2cm. Find the area
the given values in the Given that a = 12 when of the rectangle whose length
derived equation, we have b = 1 and c = 6. is 15 cm and whose width
Solution: is 3 cm.
40 = Solving for k: Solutions:
k = 280 by k = 12/6 A = klw
Multiplication Property of k=2 72 = k(12)(2)
Equality (MPE) Solving for a: 72 = 24k
a = kbc k=3
Solving for the time t (in a = kbc Therefore, when l = 15 cm
minutes) for 10 students to 12= k(1)(6) and w = 3 cm,
clean the classroom a = (2)(3)(4) A = klw
a = 24 A = (3)(15)(3)
t= A = 135 sq.cm

t=
t = 28 minutes
D. Discussing new concepts Illustrative Example 2: Activity: What is Joint Illustrative Example 2:
and practicing new skills For a given mass and gas of Together? Solve Suppose the y varies
#1 constant temperature, the Translate each statement 1. If a varies jointly as b and inversely as x² and that of
pressure P varies inversely into mathematical the square root of c,
as the volume V. If P = 8 sentence. Use k as the and a = 21 when b = 5 and y =10 when x = . Find the
when V = 18, find V when constant of variation. c = 36, find a when b = 8
P = 4. 1. P varies jointly as q and c = 225. value of y when x = 4.
Solutions: and r. Solutions:
 2. V varies jointly as l, w,
P= k = PV and h. y= k = x²y
3. The area A of a
k = 8(18) parallelogram varies
k = 144 jointly as the base b k=( (10)
Solving for V: and altitude h.
4. The volume V of a k=( (10)
V= cylinder varies jointly as
its height h and the
V= square of the radius r. k=
5. The electrical voltage V
V= 36 varies jointly as the Solving for y:
current I and the
resistance R.
y=

y=

y=

y= ( )

y= or 2.5

E. Discussing new Work in small group in 1. What is joint variation? Question: Use the calculated value of
concepts and analyzing and solving the 2. How do we transform What are the steps in solving k in finding the unknown:
practicing new skills given problem: mathematical statement verbal problems involving If x varies directly as y and
#2 If the temperature is in joint variation joint variation? inversely as z. If x = 15
constant, the pressure of a equation? when y = 20 and z = 40,
gas in a container varies 3. What are the steps in find x when y = 12 and
inversely with the volume of finding the unknown in z = 20.
the container. If the joint variation equation? Solutions:
pressure is 10 pounds per
square foot in a container x=
which has a volume of 3
cubic feet, what is the
pressure in a container 15 =
which has a volume of 1.5 600 = 20k
cubic feet? k = 30
Therefore, when x = __
 and z = __

F. Developing mastery Solve the following Solve for the value of the Problem solving: Solve the following.
(Leads to Formative problems: constant k of variation, 1. y varies jointly as x and z. If b varies directly as c and
Assessment 3) 1. If 8 men can paint a then find the missing If y = 20 when x = 4 and inversely as the square of d,
house in 15 days, how value. z = 3, find y when x = 2 and b = 12, when c = 16
long will it take 12 men to 1. If y varies jointly as the and z= 3. and d = 2, find:
finish the same work? product of x and z, 2. The area A of a triangle 1. b when c = 2 and d = 4
2. The force F of attraction and y = 105 when x = 5 varies jointly as the 2. c when d = 3 and b = 4
between two opposite and z = 7, find y when base b and the altitude h of 3. d when b = 1 and c = 12
electrical charges vary x = 9 and z = 10. the triangle. If A = 65cm²
inversely as the square 2. If y varies jointly as the when b = 10 cm and
of the distance d between product of x and z, h = 13 cm, find the area of
them. If the force F = 18 and y = 1000 when x = a triangle whose b = 8 cm
when the distance d = 10, 10 and z = 20, find y and whose altitude h =
find F when d = 15. when x = 8 and z = 10. 11cm.
3. A varies jointly with l
and w, when A = 24,
l = 3 and w = 2. Find A
when l = 12 and w = 7.
G. Finding practical Solve the following .
applications of concepts problems: The volume V of a Activity: Solve the given problem:
and skills in daily living 1.The number of hours t pyramid varies jointly as (Work in small group in In Calbayog City National High
required to finish a its height h and the area A solving the given problem.) School, the number of
certain job varies of its base. A pyramid with The volume V of a cone girls varies directly as the
inversely as the number a height of 12 feet and a varies jointly as the height h number of boys and
of persons n on the job. base with area of 20 of the cone and the area of inversely as the number of
If 8 persons require 9 square feet has a volume the base B. A cone has a teachers. When there were
hours to finish the job, of 80 cubic feet. Find the volume of 140 with height 15 50 girls, there were 20
how long should it take volume of a pyramid with and base 28. Find the teachers and 10 boys. How
for 24 persons? a height of 17 feet and a volume of a cone with height many boys were there when
2.The bases b of triangles base with an area of 27 7 and base 12. there were 10 girls and 100
 having equal areas are square feet. teachers?
inversely proportional to
their altitudes h.
The base of a certain
triangle is 12 cm and its
altitude is 15 cm. Find
the base of a triangle
whose altitude is 20 cm.
H. Making generalizations How do we translate How do we translate joint How do we translate joint How do we translate
and abstractions about inverse variation variation statement variation statement inverse variation
the lesson statement into into equation? into equation? statement
mathematical equation? into mathematical
equation?
I. Evaluating learning Find the missing variable: Solve the following. Solve the following. Solve.
1. y varies inversely with x. If r varies jointly as p and 1. F varies jointly with D and 1. x varies directly as y and
If y = -4 when x = 2, q and r = 30 when p = 5 E. When F = 98, inversely as z. If x = 7
find y when x = -6. and q = 3 D = 2 and E = 7. Find F when y = 2 and z = 4,
2. y varies inversely with x. 1. Find r when p = 8 when D = 15 and E = 8. find x when y = 3 and
If y = 20 when x = 8, and q = 7 2. The strength S of the z = 6.
find x when y = -5. 2. Find p when r = 36 rectangular beam varies 2. x varies directly as y³
3. y varies inversely with x. and q = 2 jointly as its width w and and inversely as z. If
If y = 7 when x = -4, 3. Find q when r = 40 the square of its depth d. x = 8 when y = 2 and
find y when x = 5. and p = 4 If S = 1200 pounds per z = 4, find x when y = 3
4. y varies inversely with x. square inch and w = 3 and z = 9.
If y = 15 when x = -18, inches and d = 10 inches, 3. a varies directly as b and
find y when x = 27. what is the strength of a c and inversely as d²
5. y varies inversely with x. beam four inches wide and a = 12 when b = 4,
If y = 75 when x =25, and 6 inches deep? c = 9 and d = 6. Find a
find x when y = 25. when b = 3, c = 12 and
d = 4.

J. Additional activities for Study Reflection: Study: Solve.

application or remediation 1. What do you mean by What are the concepts to 1. What do you mean by the A variable u varies jointly
the word joint? remember about joint word combined? as x and y, and
2. What is joint variation? variation? 2. What is combined inversely as z, when
3. What mathematical variation? z = 14, x = 3, y = 7, and
statement represents 3. What mathematical u = 6. Find the value of
joint variation? statement represents y when x = 10, u = 5
combined variation? and z = 6.
Reference: Grade 9
Learner’s Materials,
pp. 215-216
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 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?

Checked by:

GLORIA M. ROSILLAS
Math Department Head