Detailed Lesson Plan in Mathematics 10 sir ans
Principles and strategies in Math (Western Mindanao State University)
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Detailed Lesson Plan in Mathematics 10
I.
Objectives:
At the end of the lesson the students are expected to:
a. Identify if a sequence is geometric or not
b. Solve the nth term of geometric sequence; and
c. Write the importance of sequencing in real life
II.
Subject Matter: Mathematics-Algebra
Topic: Geometric Sequence
Reference: Mathematics-Grade-10 Learner’s Module by Melvin M. Callanta,et al
K to 12 Curriculum Guide –Mathematics
E-Math 10 by Orlando A. Oronce and Marilyn O. Mendoza, pp.42-57
Materials: PowerPoint Presentation, board, Pair of Scissors, Bond Papers, Cartolina and pilot
pen
Strategies/Methods used: Collaborative Learning, Interactive Method and Discovery
Method
Values Integration: Patience, Cooperation, Activeness, and Focus
III.
Procedure:
Teacher’s Activity
A.
Student’s Activity
PREPARATORY ACTIVITY
Introduction
Good day class! I am Miss. Reynacel Modal. I am your Math
teacher for today.
Good morning Ma’am Modal!
Before we begin with our discussion today, may I ask everybody
to please stand up for our prayer. Ms. (someone)
student leading the prayer
Please remain standing for our energizer to be played by
multimedia.
Thank you class…..
Before you take your seats please pick up any piece of scatterd
papers on the floor and check your desk alignment.
Class president is there absent for today’s session?
When I say “Eyes on me”
Are you ready for our discussion today?
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“None Ma’am”
“Eyes on you”
“Yes Ma’am.”
Setting of Standards
 The teacher introduces the classroom rules.
Before we will start to our new lesson, we should follow the
following rules:
1. Quite when there is someone talking or answering. (in
short be behave all time)
2. Listen attentively I may/might call names for some
questions.
3. You are not allowed to go out, stand up, and roam around
while the teacher is discussing.
4. If there are questions, clarifications, raise your hand to
identify you immediately.
(Students are listening)
5. Be honest during quiz time.
Do I make my rules clear?
(Yes Ma’am…)
Now, the class will be divided into two groups. (by counting 1,2)
All number 1 represent GROUP UNO. And all number 2 represent
GROUP DOS.
I have here three pictures,



SMILE is equivalent to 5 points.
STAR is equivalent to 3 points
Like is equivalent to 1 point.
(Students are listening.)
You only get points if you participate in our class discussion.
Yes Ma’am…
Did you get me?
Each group has already 25 points but if the group will
misbehaved during class discussion and did not follow the
rules I presented a while ago, I will deduct points from your
25 points. And if you are doing good and can follow my
instructions correctly, you will receive an additional points for
your group.
Yes Ma’am…
Is that clear?
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B. MOTIVATION (PROVIDE ME!)
 The teacher reviews the previous lesson which is the
“Arithmetic Sequence”.
Answer:
Who can define an arithmetic sequence?
Arithmetic sequence is a sequence of
numbers such that the difference
between two consecutive terms is
constant.
Very good.
Give me an example of an arithmetic sequence with 5
terms..
Answer:
4, 7, 10, 13, 16,… this series is an
example of arithmetic sequence.
Great..
Who can give me the formula on finding the nth term of an
Arithmetic Sequence
Answer:
=1+
− 1 , this is the
formula of finding the nth term of
an arithmetic sequence.
Excellent…
ACTIVITY: PERFORM AND YOU’LL FIND
General Instruction: At this point please get your pair of
scissors and a piece of short bond paper one bond paper each
group, and perform the following: (5 minutes)
Direction:
a.1. Cut the paper in half.
a.2. Stack the halves. Cut the stack in half.
a.3. Continue stacking and cutting the paper until you reach 5
cuts.
(student perform the activity)
B. Guide the class in filling out the table.
Number of cuts
1
2
3
4
5
Number of pieces
2
4
8
16
32
C. The teacher ask “what can you observe about the change in the
number of pieces with each cut after the first?”
Answer:
The number of pieces is multiplied
as we cut it continually.
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Very good….
2, 4, 8, 16, 32 is an example of what type of sequence?
Unscramble the following letters to identify the type of sequence.
Answer:
C
R
E
G
O
M
E
T
It is GEOMETRIC.
I
Based the activity that you perform What do you think is our
lesson for today?
(student answered)
Class,our lesson for today is about “GEOMETRIC SEQUENCE ”
(Present the title of The topic and the objectives.)
C. PRESENTATION:

Do you have any idea of what is geometric sequence?
Answer:
A sequence which each term that
multiply to the preceding term by
a fixed number.
Okay.. thank you for that.
GEOMETRIC SEQUENCE or GEOMETRIC
PROGRESSION—is a sequence in which each
term is obtained by multiplying the preceding term
by a fixed number.
The student listen attentively
Okay class, here is the formula for finding any term of a geometric
sequence.
GENERAL FORMULA:
= 1 ∙ −1
Where:
1
= ℎ 𝑖𝑠 𝑚 ℎ 𝑠𝑢
𝑖𝑠 ℎ ℎ 𝑚 ℎ 𝑠𝑢
n= is the number of terms
r = is the common ration
Yes ma’am
Get it class?
Very good!!!
Let’s know this one class, then after this let’s have a group
activity right after the discussion.
3,9,27,81,…
➜ this sequence is a geometric sequence, since it has first
term which is 3, common ratio which is 2. To get the
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common ratio just simple divide the second term to the
first term, then the quotient of that will be the r.
Did you get it, class?
Yes ma’am
Good job.
D. UNLOCKING DIFFICULTIES
IDENTIFY ME!
Direction: Identify whether the given sequence is geometric or not. If it
is, give the common ratio.
a.
b.
c.
d.
e.
11, 22, 44, 88,…
4, 8, 16, 32,…
5, 8, 12, 17, 26,…
32, 28, 24, 20,…
1, 8, 64, 512,…
(student are listening)
Answers:
a.
b.
c.
d.
e.
How do you find the activity class?
Okay let’s give them a hand…
Now, let’s talk further about geometric sequence by having
example.
E. DISCUSSION: SHOWING EXAMPLES WITH SOLUTION.
So, let’s have our example:
Example#1:
➜ Find the 6thterm in the geometric sequence 3,12,48,....
SOLUTION:
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Geometric r=2
Geometric r=2
Not
Not
Geometric r=8
(two student shared)
Example #2:
➜ Find the 9th term of the geometric sequence 3, 15, 75,
375, 1875,…
SOLUTION:
1
=
=
= (−1)
=
= ,𝟔
= 1, 11, 𝟏
Example #3:
➜ Determine the 12th term of geometric sequence whose
first term is -4 and whose common ratio is 2.
SOLUTION:
1
=− ,
= 1,
=
= 1 ∙ −1
1−1
1 =−
1
=−
1
11
=− ()
=− 1𝟔
Did you understand the process class?
Okay, now it’s your turn who can solve this one on the board?
➜ Solve for the 8 term of the given series 3, 6, 12, 24,…
Yes, ma’am.
th
Answer:
Given:
1 = 3r=2
solution:
8= 1−1
8
= 3(28−1)
8
8
Very good… Good Job!
= 3(27)
= 3(128)
8
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= 384
F. GENERALIZATION
Answers:
1. What is geometric sequence?
2. 2, 4, 8, 16, 32,…is an example of a geometric sequence or not?
3. To find the nth term of a geometric sequence, what will be the
formula to use?
1. a geometric sequence
is a sequence in which each
term is obtained by multiplying the
preceding term by a fixed number.
2. it is an example of geometric
sequence.
3. this will be the formula on
finding the nth term of geometric
sequence
= 1 ∙ −1
Excellent!
G. APPLICATION: (5 MINUTES ACTIVITY)
Differentiated Activities (Cooperative Learning)
General Instruction:
 Please form a circle within your group and answer the
assign task. Write it on the Cartolina.
 There are two task being posted in the screen
 Choose a leader from your group.
 A group will be graded by the following criteria:
CRITERIA
ACCURACY
TIMELINESS
COOPERATION AND PRESENTATION
CREATIVITY AND NEATNESS
TOTAL:
NUMBER OF POINTS
15
5
10
5
35
Task 1:
I. Determine whether the given sequence is geometric or not. If it is,
give the common ration.
a. 7, 10, 15, 22, 31,…
b. 1, -3, 5, -7,…
c. 80, 40, 20, 10,…
Answer:
TASK 1:
I.
a. Geometric r=2
b. Geometric r=2
c. Not
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II. In 25-40 words, Write the importance of geometric sequence
in real life?
II. In our own opinion the
importance of geometric sequence is
that it make and help us a lot in
making decision and to evaluate the
outcome of a situation or event.
Task 2: solve the following problems.
Answer:
Task 2:
1. Find the 9th term of the given geometric sequence 3,9,27,81,…
1.
= 1. −1
2. Find the 10th term of the series 2, -8, 32, -128,…
9
= 3(39−1)
= 3(38)
9
9
= 3(6,561)
9
= 19,683
2.
= 1. −1
1
= (−1−1)
1
1
= (−)
= ( − 𝟔, 1)
1
=− 𝟔,
(student answering)
How do you find the activity class?
Okay good job everyone.
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IV.
EVALUATION
To test your understanding in our discussion I prepared
individual activity.
Yes, Ma’am
Are you ready?
TEST I
TEST I.
Direction: Read each question carefully and Circle the letter of
the correct answer.
Answers:
1. What is the type of sequence in which each term is
obtained by multiplying the preceding term by a constant?
a. Arithmetic
b. geometric
c. harmonic
d. Fibonacci
2. What term is used for the constant r in the sequence?
a. common difference
b. common ratio
c. number of terms d. first term
3. Which of the following is a geometric sequence?
a. 5, 10, 15, 20, 25,...
c. 5, 10, 20, 40, 80,…
b. 5, 7, 9, 11, 15,…
d. 5, 10, 15, 25, 40,…
4. Which of the following is NOT a geometric sequence?
a. 3, 3, 3, 3, 3,…
c. 3, 6, 12, 24, 48,…
b. 3, 6, 9, 12, 15,…
d. 3, -3, 3, -3, 3,…
5. In the geometric sequence 6, 30, 150, 750, what is r?
a. 3 b. 4 c. 5 d. 6
6. If = 3(2−1), then what is 4?
a. 12
b. 24
c. 36
d. 48
7. In the geometric sequence 4, 16, 64, 256,…, what is the
8th term?
a. 65, 536
b. 65, 563
c. 56, 536
d. 56, 563
8. If 1 = 6 3 = 54, what is 8?
a. 11, 223
b. 12, 132 c. 12, 312
d. 13, 122
9. How many terms are there in the geometric sequence 15,
39, … 15360?
a. 8
b. 9
c. 10
d. 11
1. B 2. B 3. C 4. B 5. C 6. B
7. A 8. D 9. D
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TEST II
TEST II.
Direction: Solve and show your solution.
Answer:
10-15. Solve the 9th term of the geometric sequence 3, 15, 75, 375,
1875,…
(5 points).
Given: a1=3
r = 15/3=5
Solution:
= 1. −1
9
= 3(59−1)
9
9
9
= 3(58)
= 3(390,625)
= 1,171,875
TEST III.
Test III.
Direction: Write the importance of sequencing in real life
scenarios. (25-40 words) 5 points.
V.
Answer:
The
importance
of
sequencing in our lives is
that it serve this one as an
aid in predicting, evaluating
the
outcome
of
the
situation or an event and
help as a lot in decision
making.
ASSIGNMENT
For your assignment please do have an advance reading
about harmonic sequence.
Did you understand class?
Yes, ma’am
Let’s call it a day, Goodbye class.
Goodbye ma’am.
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