Detailed Lesson Plan

1. GRADE 10
DAILY
LESSON
LOG
School LPNHS- GATCHALIAN ANNEX Grade Level 10
Teacher MR. MARK RAYMOND T. DOMINGO Learning Area MATHEMATICS
Teaching Dates and Time AUGUST 30, 2022- SEPTEMBER 2, 2022 Quarter FIRST
Session 1 Session 2 Session 3 Session 4
I. OBJECTIVES
1. Content Standards The student demonstrates understanding of key concepts of sequences.
2. Performance Standards The student is able to create, analyze and solve problems involving sequences and series in disciplines such as arts,
music, science, business, agriculture, etc. through appropriate and accurate representations.
3. Learning
Competencies/
Objectives
The learner generates
patterns. (M10AL-Ia-1)
a. Determining sequences
and series using sigma
notation.
The learner…
 illustrates an
arithmetic
sequence.
(M10AL-Ib-1)
 determines
arithmetic means
and nth term of an
arithmetic
sequence.
(M10AL-Ib-c-1)
 finds the sum of
the terms of a
given arithmetic
sequence.
(M10AL-Ic-2)
a. Using arithmetic
sequence.
b. Determining
arithmetic means.
The learner …
 apply their
learning on
sequences,
series and
arithmetic
sequences and
series.
 write an essay
demonstrates
unity, coherence,
and
completeness.
 support general
statements with
effective
examples.
 Develop
examples with
specific details to
illustrate a point.
The learner can
independently use their
learning to …
 find and generate
patterns.
 find the terms of a
given sequence-
arithmetic.
 solve problems
involving sequences,
series and arithmetic
sequences and
series.

2. c. Finding sums of
arithmetic series.
II. CONTENT Sequences and Series Arithmetic Sequences
and Series
PERFORMANCE
TASK
QUIZ
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
2. Learner’s Materials
pages
Mathematics Learner’s
Module pp. 1-8
Mathematics Learner’s
Module pp. 9-25
3. Textbook pages Simon L. Chua, DT,
Josephine L. Sy Tan, Arvie
D. Ubarro, Ma. Remedios
R. Cayetano, SPC, Renato
R. Guerrero
Soaring 21st Century
Mathematics 10 pp. 2-14
Simon L. Chua, DT,
Josephine L. Sy Tan,
Arvie D. Ubarro, Ma.
Remedios R. Cayetano,
SPC, Renato R. Guerrero
Soaring 21st Century
Mathematics 10 pp. 15-25
4. Additional Materials
from Learning
Resource (LR) portal
https://drive.google.com/fil
e/d/1wfh1tGplJkf0vXuQhs
KbfS6-
jDccfdxl/view?usp=sharing
https://drive.google.com/fil
e/d/1wfh1tGplJkf0vXuQhs
KbfS6-
jDccfdxl/view?usp=sharing
B. Other Learning
Resources / Materials
https://www.youtube.com/
watch?v=btKkchZRhzI&list
=PLPPsDIdbG32AXjKv2cr
_bKEM7YcEfR4iE
https://www.youtube.com/
watch?v=fLruSm66fY8&list
=PLPPsDIdbG32AXjKv2cr
_bKEM7YcEfR4iE&index=
2
https://www.youtube.com/
watch?v=_vp3ev0oRvk&li
st=PLPPsDIdbG32AXjKv2
cr_bKEM7YcEfR4iE&inde
x=4
https://www.youtube.com/
watch?v=TDpRJQ2fBc4&li
st=PLPPsDIdbG32AXjKv2
cr_bKEM7YcEfR4iE&inde
x=5

3. https://www.youtube.com/
watch?v=2GAB1vcQ4yg&li
st=PLPPsDIdbG32AXjKv2
cr_bKEM7YcEfR4iE&index
=3
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
TPS Activity!
Students to share their
drawn patterns and reflect
on each other’s designs.
Do a quick survey:
a. Who are Kapuso,
kapamilya, or kapatid?
b. What are their favorite
TV series and why?
B. Establishing a
purpose for the
lesson
Guide Questions:
1. What would happen if
there were no patterns,
routines, or guidelines?
2. Why do we need
patterns, routines, or
guidelines?
Guide Questions:
1. Have the students write
a reflection on looking
forward to “What’s next?”
Have a buzz session
wherein the students can
share their reflections.
2. How can you make
decisions that will leave a
lasting legacy?
C. Presenting examples/
instances of the
lesson
Present and discuss
Sequences and Series. Use
illustrative examples below:
Example 1: Find the first
four terms of the infinite
sequence defined by 𝑎𝑛 =
1
2𝑛+1
.
Solution:
Replacing n with 1, 2, 3, and
4 in the expression of 𝑎𝑛,
we generate the first four
terms.
Present and discuss
Arithmetic Sequences and
Series. Use examples as
illustrative examples.

4. 𝑎1 =
1
2(1)+1
=
1
3
First term
𝑎2 =
1
2(2)+1
=
1
5
Second
term
𝑎3 =
1
2(3)+1
=
1
7
Third term
𝑎4 =
1
2(4)+1
=
1
9
Fourth term
The sequence defined by
𝑎𝑛 =
1
2𝑛+1
can be written as
1
3
,
1
5
,
1
7
,
1
9
, … ,
1
2𝑛+1
, …
Because each term in the
sequence is smaller than
the preceding term, this is
an example of a decreasing
sequence.
Example 2: Find the first
four terms and the 47th term
of the sequence whose
general term is 𝑎𝑛 =
(−1)𝑛
(𝑛 + 1).
Solution:
Replacing n with 1, 2, 3, and
4, we generate the first four
terms:
𝑎1 = (−1)1(1 + 1) = −2
First term
𝑎2 = (−1)2(2 + 1) = 3
Second term

5. 𝑎3 = (−1)3(3 + 1) = −4
Third term
𝑎4 = (−1)4(4 + 1) = 5
Fourth term
The 47th term is found by
replacing n with 47.
𝑎47 = (−1)47(47 + 1) =
−48 47th term
The sequence defined by
𝑎𝑛 = (−1)𝑛
(𝑛 + 1) can be
written as -2, 3, -4, …,
(−1)𝑛
(𝑛 + 1),…
The factor (−1)𝑛
causes
the signs of the terms to
alternate between positive
and negative, depending
on whatever n is even or
odd.
D. Discussing new
concepts and
practicing new skills
#1
Facilitate discussion on
finding the General Term of
a Sequence. Showing
some examples and doing
seatwork/board work as
practice.
Facilitate discussion on
modeling using Arithmetic
Sequences. Showing
some examples and doing
seatwork/board work as
practice.
E. Discussing new
concepts and
practicing new skills
#2
Facilitate discussion on
Partial Sums and Infinite
Series, Summation
Notation. Showing some
examples and doing
seatwork/board work as
practice.
Facilitate discussion on
Arithmetic Series.
Showing some examples
and doing seatwork/board
work as practice.

6. F. Developing mastery
(Leads to Formative
Assessment)
Answer and discuss Warm-
up Practice of the textbook.
Answer and discuss
Warm-up Practice of the
textbook.
Call on students to explain
why the sequences are
arithmetic then, post on
the board the illustrative
examples of arithmetic
sequences and their
common differences.
G. Finding practical
applications of
concepts and skills in
daily living
Organize a “new year’s
countdown”
a. Ask: “Does history
repeats itself?”
b. Have a TPS activity
wherein the students
choose a past
experience and share
why they wish that
history can repeat itself
(lessons learned).
Ask the students to list
down day to day real life
activities that they can
associate with Arithmetic
Sequence and Series.
Essay:
Write the batch “Will and
Prophecy”.
H. Making
generalizations and
abstractions about the
lesson
 A finite sequence is
a function whose
domain includes only
the first n positive
integers.
 Terms of Sequence
 The nth term of a
sequence 𝑎𝑛 is
called the general
term of the
sequence.
 Consider the infinite
sequence
𝑎1, 𝑎2, 𝑎3, … , 𝑎𝑛, …
 An arithmetic
sequence or
arithmetic
progression is a
sequence in which
each term after the
first differs from the
preceding term by a
constant. The
difference between
consecutive terms
is called the
common difference
of the sequence.

7. The finite series 𝑆𝑛is
the sum of the first n
terms of the
sequence and is
called the nth partial
sum.
𝑆𝑛 = 𝑎1 + 𝑎2 + 𝑎3 +
⋯ + 𝑎𝑛
On the other hand,
the sum of all the
terms 𝑎1 + 𝑎2 +
𝑎3 + 𝑎𝑛 + ⋯ is
called an infinite
series.
 The nth term (the
general term) of an
arithmetic
sequence with first
term 𝑎1 and
common difference
d is 𝑎𝑛 = 𝑎1 + (𝑛 −
1)𝑑.
 The sum 𝑆𝑛 of the
first n terms of an
arithmetic
sequence is given
by 𝑆𝑛 =
𝑛
2
(𝑎1 + 𝑎𝑛)
or 𝑆𝑛 =
𝑛
2
[2𝑎1 +
(𝑛 − 1)𝑑] where 𝑎1
is the first term and
𝑎𝑛 is the nth term.
I. Evaluating learning The general term of a
sequence is given. For
each problem, write the
first four terms, the 10th
term 𝑎10, and the 15th term
𝑎15.
1. 𝑎𝑛 =
𝑛+2
𝑛+3
2. 𝑎𝑛 = (−1)𝑛
𝑛
3. 𝑎𝑛 = 1 −
1
𝑛
Expand each summation
notation.
4. ∑ (𝑥 + 𝑖)
5
𝑖=1
5. ∑
𝑥+𝑖
𝑥−1
5
𝑖=1
Expand each sum by
writing the first three terms
and the last term. Then,
use the formula for the
sum of the first n terms of
an arithmetic sequence to
find the indicated sum.
1. ∑ (5𝑖 + 3)
17
𝑖=1
2. ∑ (−3𝑖 + 5)
30
𝑖=1
Solve each problem.
1. Find the sum of the even
integers between 21 and
45.
2. Find the sum of the odd
integers between 30 and
54.
Which of the following is true?
1. Every sequence is a
relation, but some sequences
are not functions.
2. A general term for the
sequence -1, 1/3, -1/5, 1/7, …
is 𝑎𝑛 =
(−1)𝑛
2𝑛−1
.
3. The range of infinite
sequence is the set of integers.
4. It is possible to find the 51st
term of a sequence without
knowing all 50 preceding
terms.
5. The symbol Ʃ represents
sums and products.
Solve the problems.

8. 1. A sequence is formed by
writing the integers the
corresponding number of times
as follows: 1, 2, 2, 3, 3,3, 4, 4,
4, 4, 5, 5, 5, 5 5, …. What is the
800th term in this sequence?
2. The number 2000 is
expressed as the sum of 32
consecutive positive integers.
What is the largest of these
integers?
3. We want to find a sequence
of numbers, the first and the
last being zero and each
successive term differing from
the one before it by at most 1.
For the example, 0, 1, 2, 3, 3, 2,
3, 2, 2, 1, 0 is such a sequence
with a sum of 19. How many
terms are in a shortest of such
sequence whose sum is 2000?
J. Additional activities
for application or
remediation
In how many ways can 75
be expressed as the sum
of at least two positive
integers, all which are
consecutive?
A child playing with blocks
placed 35 blocks in the first
row, 31 in the second row,
27 in the third row, and so
on. Continuing in this
pattern can she end with a
row containing exactly 1
block? If not, how many
blocks will the last row
contain? How many rows
can she make in this
pattern?
V. REMARKS

9. VI. REFLECTION
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?
7. What innovation or
localized materials
did I use/discover

10. which I wish to share
with other teachers?