lOMoARcPSD|18826857
Calculus DLL WEEK 9
BS Secondary Education major in Mathematics (Eastern Samar State University)
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lOMoARcPSD|18826857
ADE 1 to 12 School Grade 11
AMADEO NATIONAL HIGH SCHOOL Level
DAILY LESSON
LOG Teacher Learning BASIC CALCULUS
ARTHUR E. GUAPO Area
Teaching Dates and Quarter THIRD
Time
SESSION 1 SESSION 2 SESSION 3 SESSION 4
I. OBJECTIVES
A. Content Standard The learner demonstrates an understanding of basic concepts of derivatives.
B. Performance The learner shall be able to formulate and solve accurately situational problems involving related
Standard rates.
C. Learning The learner illustrates The learner solves The learners solve
Competency/Objectiv implicit differentiation. problems (including situational problems
es (STEM_BC11D-IIIi-2) logarithmic and inverse involving related rates
Write the LC code for trigonometric (STEM_BC11D-IIIj-2)
each. functions) using
implicit differentiation
(STEM_BC11D-IIIi-j-
1)
II. CONTENT
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pp.168-179 pp 168-179 pp 180-190
pages
2. Learner’s
Materials pages
3. Textbook pages
4. Additional
Materials from
Learning
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Resource
(LR)portal
B. Other Learning http://tutorial.math.la http://tutorial.math.la http://tutorial.math.lamar
Resource mar.edu/terms.aspx mar.edu/terms.aspx .edu/terms.aspx
IV. PROCEDURE
S
A. Reviewing previous a. Teacher asks for Teacher asks: Teacher asks:
lesson or presenting reactions about the 1. What is implicit 1. When is your
the new lesson question: “Would differentiation? shadow longer,
separation yield to a 2. How does it at 11:30 am or
simpler or more differ from the 4:00 pm? Why?
complicated life?” basic 2. What happens to
differentiation the size of an
b. (optional) Teacher rules? object, when you
plays the first stanza At what kind of move away from
and chorus of the functions/equations it?
song “Bluer than 3. Why does it
do we apply implicit
Blue” by Barry become harder to
Manillow” differentiation?
pump air in a
balloon when the
balloon already
reached its fullest
size?
4. What happens
when you drop a
stone into a still
water?
B. Establishing a Teacher says: “so far, Teacher says: “Last Teacher says: “There is a
purpose for the we have determined time, you learned how variety of applications of
lesson the derivative of basic to obtain the derivative calculus. In this section,
functions of the form of functions and you will understand why
, in which and can be equations with we
separated. But in non-separable spend so much time
variables or variables taking calculus. We will
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other instances, and that are impractical to cover problems in
are inseparable or are separate. Today, we physics, engineering,
difficult to separate. will extend the concept biological and other
Sometimes, when they of implicit sciences through the use
are separated, the differentiation to other of basic and implicit
result is a more concepts in calculus. differentiations. I hope
complicated function that, after covering the
which is very difficult topic, you’ll develop a
to differentiate. greater appreciation of
Today, you will learn calculus.
how to differentiate
such kind of function. Let us jump right to a
problem and see how
calculus works.
C. Presenting a.Teacher a.Teacher Challenges a.Teacher poses the
examples/Instances of Challenges learners: learners: problem:
the new lesson “Find in the equation “Find in the equation A gas balloon is being
b.Teacher asks: filled at a rate of 100𝑢
“Why is it difficult to b.Teacher asks: “can cm3/sec. At what rate
find the derivative of you find any is the radius of the
with respect to . differentiation formula balloon increasing
c.Teacher entertains that will solve for the when the radius is 10
answers and queries derivative ? c.Teacher cm?
from learners. entertains answers and
d. Teacher asks queries from learners. b. Teacher asks:
learners to find for the d. Teacher asks 1. What quantities are
given function using learners to find for the given in the problem?
the basic rules with given function using 2. How do we solve for
separation of the basic rules of the volume of a sphere
variables. differentiation. in relation to its
e. Teacher says: “we e. Teacher says: “we radius?
can do it (faster) with can do it by simply 2. What does the quantity
minimal steps. Let’s revising the equation mean?
do it and analyze our
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solutions. I call this without violating any 3. What is the required
process “implicit rule of equality. Come quantity in the
differentiation”. on, let’s work on it problem? Represent it
f. Teacher and together. through symbols.
learners work on the c. Teacher guides the class
derivative using f. Teacher and learner in working with the
“implicit work on the derivative solution?
differentiation”. using “implicit
differentiation” and
other rules and
technique.
D. Discussing new (10 mins) Teacher asks Teacher provides worded
concepts and practicing learners to work in problems and tells the
new skills # 1 Teacher asks pairs: class to work on the
learners to work in 1. Find for the following problems in
pairs and find the function groups with three
derivative of , with 2. If , what is ? members.
respect to , for the
functions:
1. 2.
E. Discussing new concepts Teacher asks the Teacher asks the Teacher asks the
and practicing new following guide following guide following guide
skills # 2 questions: questions: questions:
1. What preliminary
1. Which between 1. In what other
steps did you do
the two equations is types of
in solving related
separable? functions/equa
rates problems?
Inseparable? tions do we use
2. After the
2. What is the implicit
preliminary
difference between differentiation?
steps, what did
finding the derivative 2. Do you find it
you do next?
using the basic rules convenient,
3. When does
and finding the working with
differentiation
derivative using implicit
enter in the
implicit differentiation?
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differentiation? Does implicit process?
3. What is implicit differentiation seem 4. How would you
differentiation? to be very different simplify the
related rates
from the other
problem so that
rules/techniques of you can solve for
differentiation we the required
have discussed? quantity?
5. How would you
check if your
answer is
logically correct?
F. Developing mastery Teacher asks Teacher asks Teacher asks learners to
(leads to Formative learners: learners: answer the problem: A
Assessment 3) Find in the equation If and , what is the tank is in the form of an
value of ? inverted cone having an
altitude of 16 cm and a
radius of 4 m. Water is
flowing into the tank at
the rate of 2 m3/min.
How fast is the water
level rising when the
water is 5 m deep?
G. Finding practical Two cars, one going east
application of concepts at a rate of 90 km/hr and
and skills in daily the other going south at a
living rate of
60 km/hr, are traveling
toward the intersection of
the two roads. At what
rate are the two cars
approaching each other
at the instant
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when the first car is
0.20 km and the second
car is 0.15 km from the
intersection?
H. Making Teacher and Teacher and Learners Teacher and Learners
generalizations and Learners discuss the discuss the following discuss the following
abstractions about following key key concepts: key concepts:
the lesson concepts: Uses of
Definition:
1. Implicit implicit
A “related rates”
Differentiation differentiation
problem is one
(or fake a. Equations
involving two or more
differentiation)- a containing two
variables that are
process of finding or more non-
mathematically
the derivative separable
related to each other
without separating variables.
and are both changing
the two variables in with respect to time.
an equation. The b. Equations
differentials of both containing Steps in
variables are taken logarithmic on Solving Related
simultaneously with both sides Rates
respect to the Problems:
independent c. Equations 1. Read the problem
variable. relating two or 2. Read the problem
more again, this time
2. In finding transcendental with understanding
derivatives with functions 3. List down given
respect to . quantities. Identify
variables and
constants.
4. Identify the
required quantity.
5. Draw diagram to
represent the
relationship
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between
variables.
6. Determine a
formula relating
the variables.
7. Limit the formula
to only two related
variables.
8. Differentiate the
formula with
respect to time.
9. Plug-in the given
quantities and rate
of change.
10. Solve for the
required quantity.
11. Check if your
answer is logically
correct.
I. Evaluating learning Teacher says: Take A. Find in each
time to study the equation. Teacher provides 6
lesson because 1. worded problems asks
tomorrow you will 2. learners to answer 4
make use of implicit 3. . problems from the
differentiation in 4. following:
other concepts of
B. Find the equation of
calculus.
the tangent line to the
curve at the point
.
J. Additional activities
for application or
remediation
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V. REMARKS Applications of implicit differentiation will be incorporated to the topic “related rates”
VI. REFLECTION
A. No. of learners who
earned 80% in the
evaluation
B. No. of learners who
require additional
activities for
remediation who
scored below 80%
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?
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Checked by: Noted by:
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