This document contains a daily lesson log for a Grade 10 mathematics class. It outlines the objectives, content, procedures, and activities for lessons on sequences over the course of a week. The lessons aim to help students understand key concepts of sequences, polynomials, and polynomial equations. Students will learn to define sequences, identify patterns in sequences, find the nth term of sequences, and solve problems involving sequences. A variety of examples and illustrative problems are provided to reinforce these skills.

1. GRADES 1 TO
12
DAILY LESSON
LOG
SCHOOL: TUOD INTEGRATED SCHOOL GRADE LEVEL: TEN (10)
TEACHER: MELANIE D. CALONIA LEARNING AREA: MATHEMATICS
TEACHING DATES &
TIME:
AUGUST22 – 26, 2022 (Week1)
8:50 – 9:40/10:50 – 11:40
QUARTER: FIRST QUARTER
I. OBJECTIVES MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
A.Content Standards: The learner demonstrates understanding of keyconcepts of sequences, polynomials, and polynomial equations.
B. Performance
Standards
The learner is able to formulate and solve problems involving sequences, polynomials, and polynomial equations in different disciplines through appropriate and
accurate representations.
C. Learning
Competencies/Objective
s: Write the LC code for
each.
The learner…
shall be able
determine the
schedule of classes,
school and
classroom rules and
regulations, and to
select class officers.
Thelearnergenerates
patterns. (M10AL-Ia-1)
a. Definesequence.
b. Identify the next
term of a
sequence
c. Value
accumulated
knowledgeas
meansof new
understanding.
Thelearnergeneratespatterns.
(M10AL-Ia-1)
a. Identify the first few
termsof a sequence
given the nth
term/equation.
b. Determinethepattern
of the given rule.
Value accumulatedknowledge
as meansof newunderstanding.
The learner generates patterns.
(M10AL-Ia-1)
a. Find the general or nth
term of a sequence
b. Identify the pattern of
each sequence
Value accumulated knowledge
as means ofnew understanding.
The learner generates
patterns. (M10AL-Ia-1)
a. Solve problems
involving
sequence.
b. Identify the nth
term of the given
problem.
Value accumulated
knowledge as means of
new understanding.
II. CONTENT Orientation Sequence IdentifytheFirstFewTermsof
a Sequencegiven thenth Term
of a Sequence
Find the nth term of a
Sequence
Problems involving
Sequence
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
Pages
pp. 14-15 14-16 14-16 14-16
2. Learner’s Materials
Pages
pp. 9-10 9-11 9-11 9-11
3. Text book Pages Next Century Mathematics,
MirlaS. Esparragoet.al.,
pp.2 and15
4. Additional Materials
from Learning
resources(LR)Portal
www.world.mathigon.org https://www.youtube.com/
watch?v=UuceRRQGk8E
B. Other Learning
Resources
School Handbook (if
any)
Grade10 LCTGsbyDepEd Mathematics
PPT,Laptop, Television,Activity Notebook
Grade10 LCTGsbyDepEd Mathematics
PPT,Laptop, Television,Activity Notebook

2. III. PROCEDURE
A. Reviewing Previous
Lesson or Presenting
New Lesson
With Pattern or Without
Pattern?
Identify if eachpicture
belowshowsa pattern or
not. If there is a pattern,
put a checkmark(✓)and
identifyit, otherwiseput a
crossmark(x).
1. Banderitas
2. Coffee beans
3. Tahongshells
4.
4. Stack of Stones In the
Beach
GROUP YOURSELF
Theteacherwillgivethe
pattern or sequenceandthe
students willidentifythe next
term by groupingthemselves.
Think-Pair-Share
Find the next three terms ofthe
given sequence.
Study and complete the
pattern given in each item.
1.
1.
2. 2. 2, 4, 8, 16, ___
3.
4. 3. Rosario, Novelata,
Kawit, Bacoor, Roario,
___
5.
6. 4. Jan, Apr, Jul, ____
7. 5. 5, 8, 11, 14, ____

3. B. Establishing a
Purpose for the
Lesson
Completethepattern
generatedfrom the
previous activity.
a. Colorof the Banderitas:
Green,Blue, Red,
Orange,Yellow,
Green,Blue,
Red, Orange,Yellow,
_____
b. Numberof Coffee beans
4, 6, 8, _____
C. TahongshellsClose,
Open,Close, Open,
Open,Close, Open,
Open,Open,_____
D. Numberof Stackof
Stones 1, 2, 3, 4, 5,
_____
f. Dates inthe calendar
for the monthof July3, 10,
17, 24, _____
Considerthe pictureat
below:
1. Do you see any pattern
form the given picture?
2. Write the terms of
coffeebean.
3. If the pattern continues
what willbe next term?
4. Canyou give an
equationthat will
satisfy the sequence
form by the coffee
bean?
From the previous activity:
1. What are the nextterms
of the given sequence?
2. Can you find the
pattern?
3. What is the general/nth
term of the sequence?
a.
E. Presenting
Examples/Instances
of the Lesson
The set objects in the
priming activity are called
sequences.
Illustrative Example:
Identify if the set of
each object shows a
pattern or not then find the
next term.
1.
2. 0, 4, 8, 12, 16, ___...
3. 9, 4, -1, -6, -11,
____
llustrative Example:
Considerthe ruleform of
the sequence
an = 7n– 4.
If we areasked to get the
first five termsof the
sequence,wehave
a1= 7(1) – 4 = 3
a2= 7(2) – 4 = 10
a3= 7(3) – 4 = 17
a4= 7(4) – 4 = 24
a5= 7(5) – 4 = 31
Therefore,thesequence
canalsobe denotedas
3, 10, 17, 24, 31.
8 10
A sequence is a function whose
domain is the finite set{1, 2,
3,…, n} or the infinite set{1, 2,
3,…}.
Example:
a 1 2 3 4 5
an 3 -1 1.5 10 𝜋
This finite sequence has 5 terms.
We may use the notation a1, a2,
a3, …, an to denote a(1), a(2),
a(3)…a(n) respectively.
Find the nth term ofeach
pattern.
1. 3, 7, 11, 15
2. 3, 9, 15, 21, 27

4. 4. 1, 3, 9, 27,81, _____
5. 160, 80, 40, 20,10,
___
In Grade 10, we often encounter
sequences that form a pattern
such as that found in the
sequence below.
Example: a 1 2 3 4…
an 4 7 10 13…
The above sequence is an infinite
sequence where
an = 3n + 1
F. Discussing New
Concepts and
Practicing New
Skills#1
Think Pair Share
Study the following
patterns then supplythe
missingterm to complete
the sequence.
1. Jan, Mar, May, Jul, Aug,
___, ____
2. 5, 8, 11, 14, ___, 20,
___...
3. 1/2, 1, 3/2, 2, 5/2, ___,
7/2, 4, ___,…
4. 3, -6, ___, -24, 48, ___
…
5. 1, 4, 9, 16, ___,36, 49,
64, ___
Howdo you generatea
sequencefrom agiven rule/nth
term?
Find the nth term ofeach
sequence
1. 6, 11, 16, 21, 26
2. 2, 10, 18, 26, 34
3. 8, 6, 4, 2, 10
The SSG Club proposed a
projecton collecting pet
bottles to lessen the trash
on our school. Ifthe
officers can collect25 pet
bottles on the first day, 45
on the second day , 65 on
the third day, and the
pattern continues, how
many petbottles can they
collectin the fifth
day?How many petbottles
they will collectin one
week?
G. Discussing New
Concepts and
Practicing New
Skills#2
GuideQuestions:
1. What pattern is shown
in every item?
2. If the pattern
continuesineachof
the item, whatwill
be the next item?
Given the followingnthterm,
supplyeachblankby a correct
answerfollowingthetask at the
right to generatethe pattern.
a. Given an = 2(n+1), list the first
5 termsof the sequence.
How did you find the activity?
Can you find the pattern?
How did you find the nth term of
each number?
Guide Questions:
3. What pattern is
shown in every item?
4. If the pattern
continues in each of
the item, what will
be the next item?

5. Solution: if n = 1
a__= 2(__+1)Substitute n
a1 = 2(__)Add the termsinside
the parenthesis
a1 = ___Multiplythe factors
Do the sameprocedureifn = 2,
n = 3, n = 4 and n = 5. Then,list
the sequencebelow.
___, ___, ___,___, ___
b. Given an = (12)−1, generate
a sequencewith4terms.
Solution:
if n = 1
a__= (12)___−1Substitutethe
value of n 4
a1 = (12)___Subtractthe
exponent
a1 = ____Simplifythe exponent
andthe fraction
Do the sameprocedureifn = 2,
n = 3 and n = 4 then, list the
sequencebelow.
___, ___, ___,___

6. H. Developing Mastery
(Leads To Formative
Assessment 3)
Find theNumber
Study the given sequence,
identifythe patternthen
find the missingnumber.
1. 1 3 5 7 9 ____
13 15 17
2. 0 5 10 ____ 20
25 30 35 40
3. 17 15 13 ____
9 7 5 3
4. 25 35 45 ___ 65
75
5. 34 44 54 64 ___
84 94
Completethetablebelowby substitutingthe given values of n to an
andlist down the termsof the sequence
What is the general term ofeach
sequence below:
1. -2, 1, 4, 7
2. 3, 6, 12, 24
3. -5, −
5
2
, −
5
3
, −
5
4
4. 4, 1, -4, -11
5. 64, 36, 16, 4
Find the nth term ofthe
given sequence.
1. 3, 5, 7, 9, 11, 13
2. 12, 19, 26, 33, 40
3. 9, 6, 3, 0, -3
I. Finding Practical
Application of
Concepts and Skills
in Daily Living
Answer the following
problems.
1. Thetablebelowshows
the costof rentingthe
Cavite Hall at IslandCove
Resort andLeisurePark
in Kawit, Cavite
dependingonthenumber
of attendees.
Numberof
Persons
Rental
Cost in
Peso
20 6200
25 6500
30 6800
35 7100
Jose bookedthe hall
for a birthday party
1. Emiliahelpshermotherin
selling“KalamayBuna”(a
delicacyfrom Indang). From the
moneythat her motherisgiving
her, she plansto save Php25
every weekfor seven weeks.
Form asequencethatwill show
the amountof moneyshe is
saving from the first to seventh
week.
2. Theincreaseinthepopulation
of Cavite Provincefollowsa
pattern. Thatis, 1.5% of its
previous year’s populationis
addedto the present to obtain
the next. If the current
populationofCavite is
3,000,000,list the province’s
populationforthe next 2 years.
Christian helps his mother in
selling “ Tinapang
Bangus” ( a productfrom
Rosario, Cavite). From the
money that his mother is giving
him, he plans to save Php30
every week for five weeks. Form
a sequence thatwill show the
amount of money he is saving
from the first to fifth week, and
identify the nth term of the given
situation.
A rabbit population ofMr.
Ricafrente grew in the
following pattern: 2, 4, 8,
16…If all the rabbits live
and the pattern continues,
how many rabbits will be
in the 8th generation?
Write the nth term of the
sequence.

7. for 40 persons. How
muchwillhepay?
1. A rabbitpopulation
grewin the following
pattern: 2, 4, 8, 16…if
allthe rabbits live and
the pattern continues,
howmanyrabbits will
be inthe 8th
generation?
2. Lewisis offered P20
000.00as starting
salaryfor a job, with
a raiseof P2 000.00
at the end of each
year of outstanding
performance.Ifhe
maintainscontinuous
outstanding
performance,what
willhis salarybe at
the endof 6 years?
H. Making Generalization
and Abstractions about
the lesson
A sequenceisa function
whosedomainisa finite
set of positive integers{1,
2, 3, …, n} or aninfiniteset
{1, 2, 3, …}. It is a string of
objects,likenumbers,that
followa particularpattern.
(world.mathigon.org)
Eachelementorobjectin
the sequenceiscalled
term.
When the sequencegoes
on forever it is calledan
infinitesequence,
otherwiseit is a finite
sequence.
A sequence isafunctionwhose
domainisa finite set of positive
integers{1, 2, 3, …, n} or an
infiniteset {1, 2, 3, …}
Eachelementorobjectinthe
sequenceiscalled term.
A sequencehavinglast term is
calledfinitesequence whilea
sequencewithnolast term is
calledinfinitesequence.
Sequencesmaycomeinrule
form. Thesearesequences
stated in generalornth terms.
A sequence is a function whose
domain is a finite setof positive
integers {1, 2, 3, …, n} or an
infinite set{1, 2, 3, …}
Each elementor objectin the
sequence is called term.
A sequence having lastterm is
called finite sequence while a
sequence with no last term is
called infinite sequence.
A sequence is a function
whose domain is a finite set
of positive integers {1, 2, 3,
…, n} or an infinite set {1, 2,
3, …}
Each element or object in
the sequence is called
term.
A sequence having last
term is called finite
sequence while a
sequence with no last term
is called infinitesequence.

8. Sequences may come in rule
form. These are sequences
stated in general or nth terms.
Sequences may comein
rule form. Theseare
sequences stated in
general or nth terms.
I. Evaluating Learning A. Study the following
patterns then supply
the missingterm to
completethe
sequence.
1. 2, 4, 7, 11, ____
2. 7, 9, 11, ____,____,
17, 19
3. 1, 8, 27, 64, 125, ____
4. 5, 10, 7, 14, 11, 22,
19, _____
Findthe first 5 termsof the
sequencegiventhe nth term.
1. an = n + 4
2. an = 2n – 1
3. an = 12– 3n
4. an = 3n
5. an = (-2)n
What is the nth term for each
sequence below:
1. 3, 4, 5, 6, 7,…
2. 3, 5, 7, 9, 11,…
3. 2, 4, 8, 16, 32,…
4. -1, 1, -1, 1, -1,…
5. 1,
1
2
,
1
3
,
1
4
,
1
5
,…
Ms May Ann Fuerte the
adviser ofRosario
National High School
newspaper “Ang Kronikel”
assigned her writers to
write news aboutBrigada
Eskwela. A writer wrote
890 words on the first day,
760 words on the second
day and 630 words on the
third day, how many
words did the writer wrote
on the fifth day?
J. Additional Activities for
Application or
Remediation
A. FollowUp
1. Observe the
thingsaround
you. Takea
pictureof objects
forminga
sequence.
B. Study
1. Write the
sequencethat
satisfy the given
equation:
an = 3n+ 1
A. Followup:
Cut out picturesthat showa
pattern andidentify the ruleof
the given pattern.
B. Study
Determinethenth term of the
given sequence
2, 4, 7, 11, ____
A. Follow up:
1. Find the nth term of
each sequence
a. 4, 7, 10, 13, 16
b. 4, 13, 28, 49, 76
Study:
Define Arithmetic
Sequence
V. REMARKS The lesson shall be
continued tomorrow.
The lesson shall be
continued tomorrow.
The lesson shall be
continued tomorrow.
The lesson shall be
continued on Monday.
VI. REFLECTION
A. No. of learners who
earned 80% in the
evaluation

9. B. No. of learners who
required additional
activities for remediation
C. Did the remedial
lessons work?
D. No. of learners who
continue to require
remediation
E. Which of my
teaching strategies work
well? Why did this work?
F. What difficulties did I
encounter which my
principal or supervisor
can help me solve?
G. What innovation or
localized materials did I
used/discover which I
wish to share with other
teachers?
Prepared by: Noted :
Melanie D. Calonia Jenefeir B. Denque
Math Teacher Principal I