DAILY LESSON LOG OF STEM_BC11LC-IIIa-1 (Week One-Day One)
School
Teacher
Teaching Date and Time
I.
OBJECTIVES
A. Content Standards
B. Performance
Standards
C.
Learning
Competencies/
Objectives
II. CONTENT
III. LEARNING
RESOURCES
A. References
1.
2.
Teacher’s Guide
Learner’s
Materials
3. Textbook pages
4. Additional
Materials from
Learning
Resource (LR)
portal
B. Other Learning
Resources
IV. PROCEDURES
Grade Level
Grade 11
Learning Area
Basic Calculus
Quarter
Third
Objectives must be met over the week and connected to the curriculum standards. To
meet the objectives, necessary procedures must be followed and if needed, additional
lessons, exercises and remedial activities may be done for developing content
knowledge and competencies. These are assessed using Formative Assessment
Strategies. Valuing objectives support the learning of content and competencies and
enable children to find significance and joy in learning the lessons. Weekly objectives
shall be derived from the curriculum guides.
The learner is able to demonstrate the basic concepts of limit and continuity of a
function
The learner is able to formulate and solve accurately real-life problems involving
continuity of functions
Learning Competency: Illustrate the limit of a function using a table of values and the
graph of the function. (STEM_BC11LC-IIIa-1)
Learning Objectives:
1. Give the standard form of limit.
2. Illustrate the limit of a function using a table of values.
3. Display critical thinking in analyzing the concepts.
Limits and Continuity
Teacher’s Guide
Pages 3-16
These steps should be done across the week. Spread out the activities appropriately
so that pupils/students will learn well. Always be guided by demonstration of learning
by the pupils/ students which you can infer from formative assessment activities.
Sustain learning systematically by providing pupils/students with multiple ways to
learn new things, practice the learning, question their learning processes, and draw
conclusions about what they learned in relation to their life experiences and previous
knowledge. Indicate the time allotment for each step.
The teacher will give a pre-assessment about limits so that the teacher will know the
prior knowledge of the students about limits.
1.
2.
A. Review previous
lesson or presenting
the new lesson
3.
4.
Answer Key:
1.) 16
2.) 0
2
3.) 5
4.) a. 15 b. 5 c. 6 d.
B. Establishing a
purpose for the
lesson
2
3
The teacher will discuss the standard form of limit and how to read it. The teacher
will connect it though graphing and table of values for the students to understand it
further.
The teacher will divide the students into 4 groups. Each group will be assigned the
following function to make a table of values and graph. They will write their answer
on a manila paper and present it in the class.
Instructions: Create a table of values and graph. Provide values of x that is
approaching but will never be equal to the given
Group 1: lim(1 + 3𝑥) from the left
𝑥→2
Group 2: lim(1 + 3𝑥) from the right
𝑥→2
Group 3: lim (𝑥 + 1) from the left
𝑥→−1
C.
Presenting examples/
instances of the new
lesson
Group 4: lim (𝑥 + 1) from right
𝑥→−1
Questions:
1. What are the x values you consider on the table?
2. What have you observed to the value of the function as x approaches a certain
value from the left or from the right? How about the graph?
3. Based on your own assessment what can you infer about the concept of limit of a
function?
Answer Key:
1. The x values approaches to left or right.
2. As x approaches a certain value the corresponding y also approaches another
single value.
3. (Definition of Limits)
The teacher will present the formal definition of limits to the class.
D. Discussing new
concepts and
practicing new skills
#1
The teacher will explain the concept of the example. Here, f(x) = 1+3x and the
constant c, which x will approach, is 2. To evaluate the given limit, we will make use
of a table to help us keep track of the effect that the approach of x toward 2 will have
on f(x). Of course, on the number line, x may approach 2 in two ways: through values
on its left and through values on its right. We first consider approaching 2 from its
left or through values less than 2. Remember that the values to be chosen should be
close to 2.
Observe that as the values of x get closer and closer to 2, the values of f(x) get closer
and closer to 7. This behavior can be shown no matter what set of values, or what
direction, is taken in approaching 2. In symbols,
lim(1 + 3𝑥) = 7
𝑥→2
The teacher will further discuss the concepts through the graph of f(x) and will say, if
one knows the graph of f(x), it will be easier to determine its limits as x approaches
given values of c. Consider again f(x) = 1 + 3x. Its graph is the straight line with slope 3
and intercepts (0, 1) and (−1/3, 0). Look at the graph in the vicinity of x = 2.
The teacher will emphasize to the students that they can easily see the points.
(1, 4), (1.4, 5.2), (1.7, 6.1), and so on, approaching the level where y = 7.
The same can be seen from the right (from the table of values in page 4).
Hence, the graph clearly confirms that
lim(1 + 3𝑥) = 7
𝑥→2
E.
Discussing new
concepts and
practicing new skills
#2
In pair, the teacher will let the students investigate the following limit, by
constructing tables of values (for numbers 1 and 2 only).
1. lim (𝑥 2 + 1)
𝑥→−1
2. lim|𝑥|
𝑥→0
3. Find the limit of the function and graph.
lim
𝑋 →2
(2𝑥 2 −3𝑥−2)
𝑥−2
Answer Key:
1. We start again by approaching −1 from the left.
F.
Developing mastery
(leads to formative
assessment 3)
Now approach −1 from the right
The tables show that as x approaches −1, f(x) approaches 2. In symbols,
lim (𝑥 2 + 1) = 2
𝑥→−1
2. Approaching 0 from the left and from the right, we get the following tables:
3. Answer key: 5
G. Finding practical
applications of
concepts and skills in
daily living
(Contextualization and Localization)
Imagine that you are going to watch a Mandaue City Mayor’s Cup basketball game.
When you choose seats, you would want to be as close to the action as possible. You
would want to be as close to the players as possible and have the best view of the
game, as if you were in the basketball court yourself. Take note that you cannot
actually be in the court and join the players, but you will be close enough to describe
clearly what is happening in the game. This is how it is with limits of functions. We
will consider functions of a single variable and study the behavior of the function as
its variable approaches a particular value (a constant).
The variable can only take values very, very close to the constant, but it cannot equal
the constant itself. However, the limit will be able to describe clearly what is
happening to the function near that constant.
H. Making
generalizations and
abstractions about
the lesson
On students’ activity notebook, the teacher will let them answer the following
exercises.
Investigate the following limits through table of values and constructing its graph.
1. lim
2𝑥 2 −𝑥−1
𝑥→3
2. lim
𝑥→1
I.
Evaluating Learning
𝑥−1
2𝑥 2 −𝑥−1
𝑥−1
Answer Key:
1. Table: (Possible Response)
x
2.9
2.9997
2.999993
2.9999999
f (x)
6.82
6.9994
6.999986
6.9999998
x
3.1
f (x)
7.2
3.004
3.0001
3.000002
7.008
7.0002
7.000004
Graph
Therefore, the lim
𝑥→3
2𝑥 2 −𝑥−1
𝑥−1
=7
2. Table (Possible Response)
x
0.9
0.9998
0.999994
0.99999999
f (x)
2.82
2.9996
2.999988
2.9999998
x
1.1
1.003
1.0001
1.000007
f (x)
3.2
3.006
3.0002
3.000014
Graph:
J.
Additional activities
or remediation
V. REMARKS
VI. REFLECTION
A. No. of learners who
earned 80% of the
evaluation
B. No. of learners who
require
additional
activities
for
remediation
who
scored below 80%
C. Did the remedial
lesson work? No. of
learners who have
caught up with the
lesson.
D. No. of learners who
Reflect on your teaching and assess yourself as a teacher. Think about your students’
progress. What works? What else needs to be done to help the pupils/students learn?
Identify what help your instructional supervisors can provide for you so when you
meet them, you can ask them relevant questions.
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
Part G
DLL Writer: Melanie B. Garcia
DLL Editors: Hazel Mae C. Abay
Mark Ernesto A. Bacat
Fatima B. Inot
Catherine C. Mira
John Neil V. Semblante