Subject: MATH Grade Level: 10
Date: __________________ Quarter 1-Week 1-Day 1
The learner demonstrates understanding of key
Content Standard concepts of sequences, polynomials and polynomial
equations.
The learner is able to formulate and solve problems
involving sequences, polynomials and polynomial
Performance Standard equations in different disciplines through appropriate
and accurate representations.
M10AL-Ia-1
Competency Generates patterns.
I. OBJECTIVES
Knowledge: generates and describes patterns using symbols
and mathematical expressions.
Skill: find the next few terms of a sequence.
Attitude: demonstrates cooperation in the given activity.
II. CONTENT Patterns and Algebra
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide Pages Teacher’s Guide (TG) in Mathematics 10, pp. 14 - 15
2. Learner’s Materials Pages Learner’s Module (LM) in Math 10, pp. 9 - 10
3. Textbook Pages e-Math Worktext in Math by Orlando Oronce and
Marilyn O. Mendoza, pp. 1 – 3
4. Additional Materials Activity Sheets
Attachment
5. Learning Resources (LR) EASE Module 1 on Searching Patterns,
portal Sequences and Series, pp. 1 – 5
B. Other Learning Resources http.//www.mathisfun.com/algebra/sequences-
series.html
IV. PROCEDURES
A. Reviewing or presenting the new ACTIVITY: Guess My Rule
lesson
Note to the Teacher:
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)
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.
B. Establishing a purpose for the Note: The teacher may state this:
lesson
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 ACTIVITY: What’s Next
lesson
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 a 1, a2, a3,…or
t1,t2, t3, ….
D. Discussing new concepts and Discussion:
practicing new skills #1
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 Note: The teacher may discuss about sequence.
practicing new skills #2
(Please refer to attachment: discussion)
Ask the students to answer the following in pairs.
DIRECTION: Find the next two terms of each
sequence.
4. 4, 7, 10, 13, … (expected answer: 16, 19)
5. 15, 7, -1, -9, … (expected answer: -17, -25)
6. 7, 14, 28, 56, …. (expected answer: 112,
224)
3 3
7. 24, -12, 6, -3, …. (expected answer: ,
2 −4
)
B. Developing Mastery Activity: Individual or Group Activity
Find the next term in each sequence.
17, 22, 27, 32, …
1 1 1 1
, , ,
1. 2 5 8 11 …
2. 5, 10, 20, 40,…
3. 3, -3, 3, -3,…
Note: Refer to key answer for the solution and
answer.
B. Finding practical applications Under a normal condition, a newborn pair of rabbits
of concepts and skills in daily that are put in a field produces no offspring during the
living 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?
C. Making Generalizations and Guide Questions for Generalization:
abstractions about the lesson
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.)
D. Evaluating learning I. Find the next two terms of each sequence.
a. 15, 7, -1, -9, …. (expected answer: -17, -
25)
b.
(expected answers:)
F. Additional Activities for Please See Attachment for additional activities
application or remediation
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/sequences-
series.html
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 3 rd
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.
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, __
24 14 13 10 19 17 44 52 47 26 26 48 25
256 164 25 47 19 85 164 44 24 164 6 25 47 162
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 6th 7th
Triangular 1 3 6 10 15
Square 1 4 9 16 25
Pentagonal 1 5 12 22
Hexagonal 1 6 15
Heptagonal 1 7
Octagonal 1
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 1 3 6 10 15 21 28
Square 1 4 9 16 25 36 49
Pentagonal 1 5 12 22 35 51 70
Hexagonal 1 6 15 28 45 66 91
Heptagonal 1 7 18 34 55 81 112
Octagonal 1 8 21 40 65 96 133
