QUARTER I
Week 1
Subject: MATH
Grade Level: 10
Date:
__________________
Day: 1
Demonstrates understanding of key concepts of
sequences, polynomials and polynomial equations.
Content Standard
Performance Standard
Is able to formulate and solve problems involving
sequences, polynomials and polynomial equations in
different disciplines through appropriate and accurate
representations.
M10AL-Ia-1
Generates patterns.
Competency
I. OBJECTIVES
Knowledge: 
Skill: 
Attitude: 
II. CONTENT
Generates and describes patterns using symbols and
mathematical expressions.
Finds the next few terms of a sequence.
Demonstrates cooperation in the given activity.
Patterns and Algebra
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide
Pages
2. Learner’s
Materials Pages
3. Textbook Pages
4. Additional
Materials
5. Learning
Resources (LR)
portal
B. Other Learning
Resources
Teacher’s Guide (TG) in Mathematics 10, pp. 14 - 15
Learner’s Module (LM) in Math 10, pp. 9 - 10
e-Math Worktext in Math by Orlando Oronce and
Marilyn O. Mendoza, pp. 1 – 3


Activity Sheets
Attachment

EASE Module 1 on Searching Patterns, Sequences
and Series, pp. 1 – 5
http.//www.mathisfun.com/algebra/sequencesseries.html
IV. PROCEDURES
A. Reviewing or
presenting the new
ACTIVITY: Guess My Rule
Note to the Teacher:
lesson


The teacher will show strips with four or five
numbers written in a sequence.
Example:
a. 1, 3, 5, 7, ……
b. 1, 4, 7, 10, ……
The teacher may ask the students what number
comes next. Usually a student will correctly guess.
Example:
a. 1, 3, 5, 7, …… (expected answer: 9)
b. 1, 4, 7, 10, ….. (expected answer:
13)



B. Establishing a
purpose for the
lesson
Ask for the next number in the sequence of
example a. Ask the student who answered how she
or he knew that was correct. Students will offer
explanations such as “You’re skipping a number
every time”. If they don’t bring it up themselves,
point out that these are odd numbers
Do the same for Example B.
Ask the students to explain the pattern.
Note:
The teacher may state this:
It is a common experience to be confronted with a set
of numbers arranged in some order. The order and
arrangement may be given to you or you have to
discover a rule for it from some data.
For example, the milkman comes every other day. He
came on July 17; will he come on Aug 12? Consider
that you are given the set of dates: 17, 19, 21, …
arranged from left to right in the order of increasing
time. Continuing the set, we have
July 17, 19, 21, …, 29, 31, August 2, 4, ….,28, 30…
so that the answer to our question is yes.
Any such ordered arrangement of a set of
numbers is called a SEQUENCE.
C. Presenting examples
of the new lesson
ACTIVITY: What’s Next
Each item below shows a pattern. Answer the
given questions.
1. What is the next shape? (expected answer:
, ,,
,
, _______
)
2. What is the next number? (expected answer: 20)
What is the 10th number? (expected answer: 36)
0, 4, 8, 12, 16, ____
3. What is the next number? (expected answer: 16)
What is the 8th number? (expected answer: -26)
9, 4, -1, -6, -11, ______
The set of shapes and the sets of numbers in the above
activity are called sequences.
A sequence maybe generated from shapes, patterns, or
rules. Each number in sequence is called a term. Each
term is identified by its position in the ordered list. The
terms are usually denoted by a1, a2, a3,…or t1,t2, t3, ….
D. Discussing new
concepts and
practicing new skills
#1
Discussion:
Look at this example. Lorna, a 2nd year student in a
certain public school, is able to save the money her
ninongs and ninangs gave her last Christmas. She then
deposits her savings of P1,000 in an account that earns
10% simple interest. The total amount of interest she
earned in each of the first 4 years of her saving is
shown below:
Year
1
2
3
4
Total amount
10
20
30
40
The list of numbers 10, 20, 30, 40 is called a
sequence. The list 10,20,30,40 is ordered because the
position in this list indicates the year in which that total
amount of interest is earned.
Now, each of the numbers of a sequence is
called a term of the sequence. The first term in the
sequence 10, 20, 30, 40 is 10, the second term is 20,
while the third term is 30 and the fourth term is 40. It is
also good to point out that the preceding term of a
given term is the term immediately before that given
term. For example, in the given sequence 20 is the term
that precedes 30.
E. Discussing new
concepts and
practicing new skills
#2
Note: The teacher may discuss about sequence.
(Please refer to attachment: discussion)
Ask the students to answer the following in pairs.
DIRECTION: Find the next two terms of each
sequence.
1. 4, 7, 10, 13, … (expected answer: 16, 19)
2. 15, 7, -1, -9, … (expected answer: -17, -25)
3. 7, 14, 28, 56, …. (expected answer: 112, 224)
3 3
4. 24, -12, 6, -3, …. (expected answer: , )
2 −4
F. Developing Mastery
Activity: Individual or Group Activity
Find the next term in each sequence.
1. 17, 22, 27, 32, …
2.
1 1 1 1
, , , …
2 5 8 11
3. 5, 10, 20, 40,…
4. 3, -3, 3, -3,…
Note: Refer to key answer for the solution and answer.
G. Finding practical
applications of
concepts and skills
in daily living
H. Making
Generalizations and
abstractions about
the lesson
I.
Under a normal condition, a newborn pair of rabbits
that are put in a field produces no offspring during the
first month. At the end of the second month, the female
rabbit produces a new pair of rabbit in the field. If a
female rabbit always produces one pair every month
from the second on, how many pair of rabbits will there
be at the end of one year?
Guide Questions for Generalization:
 How do you find the next few terms of a sequence?
(Given at least the first 3 terms of a sequence, you can
easily find the next term in that sequence by simply
discovering a pattern as to how the 3rd term is derived
from the 2nd term, and the 2nd from the 1st term. You
will find that either a constant number is added or
subtracted or multiplied or divided to get the next term
or a certain series of operations is performed to get the
next term. This may seem hard at first but with practice
and patience in getting them, you will find that it’s very
exciting.)
Evaluating learning
I. Find the next two terms of each sequence.
a. 15, 7, -1, -9, …. (expected answer: -17, -25)
b.
(expected answers:)
J. Additional
Activities for
application or
remediation
Please See Attachment for additional activities



V.
VI.
Supplementary Activity 1 – Why are Policeman
Strong?
Supplementary Activity 2 - Use patterns to
complete the table
or the Teacher may ask the student to use ICT
and search on the web using the URL
http.//www.mathisfun.com/algebra/sequencesseries.html
REMARKS
REFLECTION
A. No. of learners who
earned 80% in the
evaluation
B. No. of learners who
require additional
activities for
remediation
C. Did the remedial
lessons work? No. of
learners who have
caught up the lesson
D. No. of learners who
continue to require
remediation
E. Which of my
teaching strategies
worked well? Why did
these work?
A. _____ No. Of learners who earned 80% in the
evaluation
B. _____ No. Of learners who require additional
activities for remediation
C. Did the remedial lessons work? ____ No. Of
learners who have caught up the lesson
D. ____ No. Of learners who continue to require
remediation
Strategies used that work well:
_____ Group collaboration
_____ Games
_____ Powerpoint Presentation
_____ Answering preliminary activities/exercises
_____ Discussion
_____ Case Method
_____ Think-Pair-Share (TPS)
_____ Rereading of Paragraphs/Poems/Stories
_____ Differentiated Instruction
_____ Role Plying/Drama
_____ Discovery Method
_____ Lecture Method
Why?
_____ Complete Ims
_____ Availability of Materials
_____ Pupil’s eagerness to learn
_____ Group member’s Cooperation in doing their
tasks
F. What difficulties did I
encounter which my
principal and supervisor
help me solve?
_____ Bullying among pupils
_____ Pupils behavoir/attitude
_____ Colorful IM’s
_____ Unavailable Technology Equipment
(AVR/LCD)
_____ Science/Computer/Internet Lab
_____ Additional Clerical Works
_____ Reading Readiness
G. What innovation or
localized I
used/discover which I
wish to share with other
teacher?
ATTACHMENT
Session: 1 (Day 1)
Content: Patterns and Algebra
DISCUSSIONS:
A sequence is a set of numbers written in a specific order:
a1, a2, a3, a4, a5, a6,………, an
The number a1 is called the 1st term, a2 is the 2nd term, and in general, an is
the nth term. Note that each term of the sequence is paired with a natural
number.
Given at least the first 3 terms of a sequence, you can easily find the next
term in that sequence by simply discovering a pattern as to how the 3rd
SUPPLEMENTARY ACTIVITY 1
Note: The activities included here will be used only when needed.
B.
Answer the puzzle.
Why are Policemen Strong?
Find the next number in the sequences and exchange it for the letter which
corresponds each sequence with numbers inside the box to decode the answer to
the puzzle.
A
2, 5, 11, 23, __
N
2, 6, 18, 54, __
B
2, 4, 16, __
O
20, 19, 17, __
C
7, 13, 19, __
P
2, 3, 5, 7, 9, 11, 13, 15,
D
19, 16, 13, __
R
13, 26, 39, __
E
4, 8, 20, 56, __
S
5, 7, 13, 31, __
F
2, 2, 4, 6, 10, 16, __
T
1, 1, 2, 4, 7, 13, 24, __
H
1, 1, 2, 4, 7, 13, __
U
1, 1, 1, 2, 3, 4, 6, 9, 13,
I
3, 6, 12, 24, __
Y
1, 2, 2, 4, 3, 6, 4, 8, 5, 10,
L
10, 11, 9, 12, 8, __
__
__
__
256
164
25
47
24
14
13
10
19
85
19
164
17
44
44
24
164
52
47
6
26
25
26
47
162
48
25
SUPPLEMENTARY ACTIVITY 2
Note: The activities included here will be used only when needed.
DIRECTION: Use patterns to complete the table below.
Figurate Number
1st
2nd
3rd
4th
5th
Triangular
Square
Pentagonal
Hexagonal
Heptagonal
Octagonal
1
1
1
1
1
1
3
4
5
6
7
6
9
12
15
10
16
22
15
25
6th
7th
KEY ANSWER
Note: The answers are highlighted.
Developing Mastery Activity
Solutions:
1. Notice that 5 is added to 17 to get 22, the same is added to 22 to get 27, and
the same (5) is added to 27 to get 32. So, to get the next term add 5 to the
preceding term, that is, 32 + 5 = 37. The next term is 37.
2. Notice that 1 is the numerator of all the fractions in the sequence while the
denominators- 2, 5, 8, 11 form a sequence. 3 is added to 2 to get 5, 3 is also
added to 5 to get 8. So that 3 is added to 11 to get 14. The next term is
therefore 1/14.
3. For this example, 2 is multiplied to 5 to get 10, 2 is multiplied to 10 to get 20
and 2 is also multiplied to 20 to get 40. So, the next term is 80, the result of
multiplying 40 by 2.
4. It is easy to just say that the next term is 3 since the terms in the sequence is
alternately positive and negative 3. Actually, the first, second, and third terms
were multiplied by -1 to get the second, third and fourth terms respectively.
Supplementary Activity 1
(Answer: Because they can hold up traffic)
Supplementary Activity 2
Figurate Number
1st
2nd
3rd
4th
5th
6th
7th
Triangular
Square
Pentagonal
Hexagonal
Heptagonal
Octagonal
1
1
1
1
1
1
3
4
5
6
7
8
6
9
12
15
18
21
10
16
22
28
34
40
15
25
35
45
55
65
21
36
51
66
81
96
28
49
70
91
112
133
REFERENCES
A. DepEd INSTRUCTIONAL MATERIALS:
EASE Modules Year 2, Module 1: Searching for Patterns, Sequences and Series
B. BOOKS AND OTHER REFERENCES
Mendoza, M. and Oronce, O. (2007). e-Math Worktext in Mathematics. Quezon
City,
Philippines: Rex Book Store.
K to 12 Curriculum Guide Mathematics. (2012). Department of Education,
Philippines;
C. OTHER RESOURCES
http.//www.mathisfun.com/algebra/sequences-series.html