GRADE 10 School Napindan Integrated School Grade Level 10

DAILY LESSON LOG Teacher Ms. Laurice C. Benal Learning Area MATHEMATICS

Teaching Dates and Time August 29- September 2, 2022 Quarter FIRST

Session 1 Session 2 Session 3

I. OBJECTIVES

1. Content Standards The learner demonstrates understanding of key concepts of sequences, polynomials, and polynomial equations.

2. Performance The learner is able to formulate and solve problems involving sequences, polynomials, and polynomial equations in different
Standards disciplines through appropriate and accurate representations.

3. Learning The learner generates patterns. (M10AL- The learner generates patterns. (M10AL- The learner generates patterns. (M10AL-
Competencies Ia-1) Ia-1) Ia-1)

Objectives a. Define sequence. a. Identify the first few terms of a a. Find the general or nth term of a
sequence given the nth sequence
b. Identify the next term of a sequence term/equation.
b. Identify the pattern of each
c. Value accumulated knowledge as b. Determine the pattern of the given sequence
means of new understanding. rule.
c. Value accumulated knowledge as
c. Value accumulated knowledge as means of new understanding.
means of new understanding.

Sequence Identify the First Few Terms of a Find the nth term of a Sequence
Sequence given the nth Term of a
II. CONTENT Sequence

III. LEARNING
RESOURCES

A. References

1. Teacher’s Guide pp. 14-15 14-16 14-16

2. Learner’s pp. 9-10 9-11 9-11

Materials

3. Textbook Next Century Mathematics, Mirla S.

Esparrago et.al., pp.2 and 15

4. Additional www.world.mathigon.org
Materials from
Learning
Resources (LR)
portal

B. Other Learning Grade 10 LCTGs by DepEd Cavite Grade 10 LCTGs by DepEd Cavite
Resources Mathematics 2016 Mathematics 2016
Grade 10 LCTGs by DepEd Cavite
Mathematics 2016 PPT, Laptop, Television PPT, Laptop, Television

PPT, Laptop, Monitor

IV. PROCEDURES

A. Reviewing previous With Pattern or Without Pattern? GROUP YOURSELF Think-Pair-Share

lesson or presenting the
new lesson
Identify if each picture below shows a Find the next three terms of the given
pattern or not. If there is a pattern, put a The teacher will give the pattern or sequence.
check mark (✓) and identify it, otherwise sequence and the students will identify the
put a cross mark (x). next term by grouping themselves.

1. Banderitas

2. Coffee beans

3. Tahong shells
 4. Stack of Stones In the Beach

B. Establishing a purpose Complete the pattern generated from the Consider the picture at below: From the previous activity:
for the lesson previous activity.
1. What are the next terms of the given
sequence?

a. Color of the Banderitas: 2. Can you find the pattern?

1. Do you see any pattern form the
Green, Blue, Red, Orange, Yellow, given 3. What is the general/nth term of the
Green, Blue, picture? sequence?

Red, Orange, Yellow, _____ 2. Write the terms of coffee bean.

3. If the pattern continues what will be

next term?
b. Number of Coffee beans 4, 6, 8,
_____ 4. Can you give an equation that will
satisfy the sequence form by the
coffee bean?
d. Tahong shells Close, Open, Close,
Open, Open, Close, Open, Open,
Open, _____

e. Number of Stack of Stones 1, 2, 3,

4, 5, _____
 f. Dates in the calendar for the month of
July 3, 10, 17, 24, _____

C. Presenting The set objects in the priming activity are A sequence is a function whose domain is
examples/Instances of the called sequences. the finite set {1, 2, 3,…, n} or the infinite set
new lesson llustrative Example: {1, 2, 3,…}.
Consider the rule form of
the sequence Example:
Illustrative Example: an = 7n – 4.
a 1 2 3 4 5
Identify if the set of each object If we are asked to get the
shows a pattern or not then find the next first five terms of the an 3 -1 1.5 10 π
term. sequence, we have
a1= 7(1) – 4 = 3 This finite sequence has 5 terms. We may
1. a2= 7(2) – 4 = 10 use the notation a1, a2, a3, …, an to denote
a3= 7(3) – 4 = 17 a(1), a(2), a(3)…a(n) respectively.
a4= 7(4) – 4 = 24
a5= 7(5) – 4 = 31 In Grade 10, we often encounter
2. 0, 4, 8,
sequences that form a pattern such as that
12, 16, ___... Therefore, the sequence
found in the sequence below.
can also be denoted as
3, 10, 17, 24, 31. Example:
3. 9, 4, -1, -6, -11, ____
a 1 2 3 4…

4. 1, 3, 9, 27, 81, _____

an 4 7 10 13…

5. 160, 80, 40, 20,10, ___

The above sequence is an infinite
sequence where

an = 3n + 1

D. Discussing new Think Pair Share How do you generate a sequence from a Find the nth term of each sequence
concepts and practicing given rule/nth term?
new skills # 1
 Study the following patterns then supply 1. 6, 11, 16, 21, 26
the missing term to complete the
sequence. 2. 2, 10, 18, 26, 34

3. 8, 6, 4, 2, 10

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, ___

E. Discussing new Guide Questions: Given the following nth term, supply each How did you find the activity?
concepts and practicing blank by a correct answer following the
new skills # 2 task at the right to generate the pattern.
1. What pattern is shown in every item? a. Given an = 2(n+1), list the first 5 terms Can you find the pattern?

2. If the pattern continues in each of the of the sequence.

item, what will
How did you find the nth term of each
be the next item? Solution: number?

if n = 1
 a__ = 2(__+1) Substitute n

a1 = 2(__) Add the terms inside the

parenthesis

a1 = ___ Multiply the factors

Do the same procedure if n = 2, n = 3, n =

4 and n = 5. Then, list the sequence
below.

___, ___, ___, ___, ___

b. Given an = (12)−1 , generate a sequence

with 4 terms.

Solution:

if n = 1

a__ = (12)___−1 Substitute the value of n 4

a1 = (12)___ Subtract the exponent

a1 = ____ Simplify the exponent and the

fraction

Do the same procedure if n = 2, n = 3 and

n = 4 then, list the sequence below. ___,
___, ___, ___

F. Developing mastery Find the Number What is the general term of each sequence
(leads to Formative Complete the table below by substituting the given
below:
Assessment 3) values of n to an and list down the terms of the
Study the given sequence, identify the sequence
pattern then find the missing number.
1. -2, 1, 4, 7

2. 3, 6, 12, 24
1. 1 3 5 7 9 ____ 13 15 17
−5 −5 −5
3. -5, , ,
2. 0 5 10 ____ 20 25 30 2 3 4
35 40
4. 4, 1, -4, -11
3. 17 15 13 ____ 9 7
5. 64, 36, 16, 4
5 3

4. 25 35 45 ___ 65 75

34 44 54 64 ___ 84 94

G. Finding practical Answer the following problems. 1. Emilia helps her mother in selling Christian helps his mother in selling
application of concepts “Kalamay Buna” (a delicacy from Indang). “ Tinapang Bangus” ( a product from
and skills in daily living From the money that her mother is giving Rosario, Cavite). From the money that his
her, she plans to save Php25 every week for mother is giving him, he plans to save
1. The table Number Rental
seven weeks. Form a sequence that will Php30 every week for five weeks. Form a
below shows of Cost in
show the amount of money she is saving sequence that will show the amount of
the cost of Persons Peso
from the first to seventh week. money he is saving from the first to fifth
renting the
Cavite Hall at 20 6200 2. The increase in the population of Cavite week, and identify the nth term of the given
Island Cove Province follows a pattern. That is, 1.5% of situation.
25 6500
Resort and its previous year’s population is added to the
Leisure Park in 30 6800 present to obtain the next. If the current
Kawit, Cavite population of Cavite is 3,000,000, list the
depending on 35 7100 province’s population for the next 2 years.
the number of
attendees.

Jose booked the hall for a birthday party for

40 persons. How much will he pay?
 2. A rabbit population 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?

3. Lewis is offered P20 000.00 as starting

salary for a job, with a raise of P2
000.00 at the end of each year of
outstanding performance. If he
maintains continuous outstanding
performance, what will his salary be at
the end of 6 years?

H. Generalizing and A sequence is a function whose domain is A sequence is a function whose domain is a A sequence is a function whose domain is
abstractions about the a finite set of positive integers {1, 2, 3, …, finite set of positive integers {1, 2, 3, …, n} a finite set of positive integers {1, 2, 3, …,
lesson n} or an infinite set {1, 2, 3, …}. It is a string or an infinite set {1, 2, 3, …} n} or an infinite set {1, 2, 3, …}
of objects, like numbers, that follow a
Each element or object in the sequence is Each element or object in the sequence is
particular pattern. (world.mathigon.org)
called term. called term.
A sequence having last term is called finite A sequence having last term is called finite
Each element or object in the sequence is sequence while a sequence with no last sequence while a sequence with no last
called term. term is called infinite sequence. term is called infinite sequence.
Sequences may come in rule form. These Sequences may come in rule form. These
are sequences stated in general or nth
are sequences stated in general or nth
When the sequence goes on forever it is terms.
terms.
called an infinite sequence, otherwise it is a
finite sequence.

I. Evaluating learning A. Study the following patterns then Find the first 5 terms of the sequence
supply the missing term to complete given the nth term. What is the nth term for each sequence
the sequence. below:
1. an = n + 4
1. 3, 4, 5, 6, 7,…
2. an = 2n – 1
 1. 2, 4, 7, 11, ____ 3. an = 12 – 3n 2. 3, 5, 7, 9, 11,…

2. 7, 9, 11, ____, ____, 17, 19 4. an = 3n 3. 2, 4, 8, 16, 32,…

5. an = (-2)n 4. -1, 1, -1, 1, -1,…

3. 1, 8, 27, 64, 125, ____ 1 1 1 1

5. 1, , , , ,…
2 3 4 5

4. 5, 10, 7, 14, 11, 22, 19,_____

J. Additional activities for

application or remediation
A. Follow Up A. Follow up: A. Follow up:

1. Observe the things around you. 1. Find the nth term of each sequence
Take a picture of objects forming a
sequence. Cut out pictures that show a pattern and a. 4, 7, 10, 13, 16
identify the rule of the given pattern.
b. 4, 13, 28, 49, 76

B. Study
B. Study
1. Write the sequence that satisfy the
given equation: Determine the nth term of the given
sequence
an = 3n + 1
2, 4, 7, 11, ____

Prepared by: Checked by:

MS. LAURICE C. BENAL MRS. NELDA ANDUYAN

Mathematics 10 Teacher Master Teacher II-In-Charge