DETAILED LESSON PLAN

Mathematics 10

School Central Mindanao Laboratory High School Grade level Grade 10

Teacher Catherine Mae Colita Brandares Learning Area Classroom

Date & July 01, 2025 (1:00 PM – 2:00) Quarter 1st Quarter
Time

I. OBJECTIVES
A. Content Standards
The learners demonstrate understanding of key concepts of arithmetic sequence.
B. Performance Standards
The learner able to formulate an arithmetic sequence.
C. Learning Competency
The learner should be able illustrate an arithmetic sequence.(M10AL-Ib-1)
The learner should be able to determine arithmetic means and nth term of an
arithmetic sequence.( M10AL-Ib-c-1)

At the end of this lesson, at least 80% the students will be able to:

a. defined arithmetic sequence and arithmetic means;

b. solved the sum of the nth terms and its means of an arithmetic sequence; and
c. illustrated problems involving arithmetic sequences and arithmetic means.

II. SUBJECT MATTER

A. Topic: Patterns and Algebra: Arithmetic Sequence

B. References
i. Teacher’s Guide.
● Grade10 Math Teacher's Guide Pages14-25
ii. Grade 10 Mathematics Module. Learners Material. Pages 9-25
iii. Textbook pages
iv. Additional Materials for Learning Resources Portal
● Arithmeric Sequence Textbook

C. Materials needed: Bond Paper and illustration Board, Presentation Slides

D. Values integration: Focus, cooperation, participative and patience.
E. Teaching Strategies: Collaborative learning, interactive method, and
lecture method.
III. PROCEDURES
Teacher’s Activity Student’s Activity

Introduction G. Preliminary Activity

Greetings,
Prayer, and
Checking of Good morning
Attendance Ma’am Cath!
Good morning class!

Okay ma’am, let us

May I request everyone to put ourselves in the
please stand for our prayer? holy presence of
Julibee can you lead the God. Our Father,
prayer? who art in heaven,
hallowed be thy
name; thy kingdom
come thy will be
done; on earth as it
is in heaven. Give
us this day our daily
bread. And forgive
us our trespasses,
as we forgive those
who trespass
against us. And
lead us not into
temptation, but
deliver us from evil.
Amen.

(Students actively
picked papers and
arranged their
chairs as well.)
Amen.

Thank you Julibee for leading

our prayer.

Thank you, ma'am.

Okay class, before you take
your seats please pick up
some pieces of paper under
your chairs and please
arrange your chairs.
 Hooray!

You may now take your

seats.

Hephep!

Before starting our lesson

let’s have an energy check!
Hephep!

Hooray!

Yes ma'am.

Very good. It seems that

everyone is ready.

Is everyone present for

today's class?

Great.

Before starting our lesson let

me first introduce our
classroom rules.
A. Developmental Activity This should be practiced
during our class.
Rule no. 1 : Respect your
teacher and your classmates
Rule no. 2: Listen Attentively
Rule no. 3: Turn off your
phone when you don't need
it.

Alright I hope that you all

remembered all those rules,
because that will help us to
have an amazing discussion.

Are you ready to learn?

Okay, can someone share

with the class what our Yes Ma’am!
previous lesson was?
Aiah , you may stand up and
share your thoughts. Me ma’am.
 Our lesson was
about Generates
Patterns ma'am.

Excellent, Aiah what have

you learned about Patterns? Patterns can be
increasing or
decreasing. They
can also be finite
or infinite and
follow multiple
rules..

No ma’am.
Very good Aiah you may take
a seat.

Is there any question about

our past lesson?
B. Motivation

Seems that everyone

mastered and understood
our previous topic. Let’s
move forward to our next
topic,

But before that, we will have

an activity and I am sure that
everyone will enjoy it.
Yes ma'am!
Is everyone excited?

Okay! Our activity is entitled:

Complete the Missing

We get it, ma’am.

Okay, class, I will be showing
you an illustration and you
are going to guess what's Yes ma'am.
missing in the blank.

So, I will be asking numbers

1-40 and whatever number is
given I will see the Ahmmmm, 20
attendance for who's the ma'am.
corresponding number.

Ma'am I think it's

"+".
(Expected answer:
"+")

Did you get it class?

(1, 2, 3,)2x Wow!

Thank you, ma'am.

Alright, Are you ready?

7 ma'am.
Alright for the first one.
It's 6 ma'am.
(Expected answer:
1.++--++--_ "6")

You girl in red earing. Give

me a number. (5 claps)

Yes ma'am we are

Thank you! Ohhhh Alayza
more than ready!
you were chosen. Now can
you guess what is missing?
Everyone: Ma'am!

You get it Alayzaaa.. Let's

give a wow applause to miss
Alayzaa. A ma'am
(Expected answer:
B)

Now for the second round,

Everyone: Ma'am!
everyone be attentive.
Ma'am I think the
correct answer is B.
2. 1,2,3,4,5

Everyone:Ma'am!
Give me a number miss
Grazie. (Amazing clap)

Yes ma’am we’ve

enjoyed it so much!
Th, ohhhh it's Aira, Aira can
you please standup. Guess
what is the missing.
I think it has
 connections with
sequence.
Wow, amazing Aira it's
correct. 5 claps for Aira

For the last part. Who ever

wants to answer kindly raise
your hand.
Are you ready?

3.ABBABBAB_

Wow excellent it seems that

everyone wants to answer.

Okay, thank you Ignacio nice

try you're almost there but it
is wrong.

Yes? Aira again.

Correct Aira let's give 5 claps

to her.
And an amazing clap to
everyone. An arithmetic
sequence is a
sequence of
Did you enjoy our activity? numbers where
each successive
term is a sum of its
preceding term and
Okay fasten your seatbelts a fixed number.
and get ready for our next
adventure.

Now, our next topic is related

to the activity we did earlier
thus everyone has an idea of
our topic.
Yes, Arcely?
 Alright Thank you Arcely you
got it right our topic is all
C. Presentation of the
about arithmetic sequence.
lesson

So for our objectives;

I have observed
At the end of this lesson, at that there are
least 80% the students will patterns in getting
be able to: the next term of an
arithmetic
a. define arithmetic sequence.
sequence;
b. compute the sum of
the terms and its
means of an
arithmetic sequence;
and
c. solve problems
including arithmetic
sequence.
Ahmm 4 ma'am.
(Expected answer:
4)
Please take note of this
class, arithmetic sequence is
important in real life because
this enables us to understand I think ma'am it is 8.
things with the use of (Expected answer:
patterns. An arithmetic 8)
sequence is a great
foundation in describing
several things like time which
has a common difference or
other sequence that has a
pattern. Also, I want you all
to please listen because we
will be having an activity after
our discussion.

So, what is an arithmetic

sequence?
Justine, can you please
stand up, and answer my
question?

Ma'am, can we
have an example
for it?

Very good, Justine.

 So an arithmetic sequence is
An arithmetic sequence is a
sequence of numbers where
each successive term is a
sum of its preceding term
and a fixed number. This
fixed number is called a
common difference. So, in an
arithmetic sequence, the
differences between every
two consecutive terms are
the same or it has a pattern.

D. Discussion Let have some examples:

1. 1, 2, 3, _
2.2, 4, 6, _

What have you observed in

the examples?
Yes, Rovic? Yes ma'am, the
arithmetic
sequence is so
understandable.

None ma'am.

Wow! Amazing Rovic you are

an observant student of
mine.

So for the no. 1, What do

you think is the next number?
How about you Reniel?

Yes it is 4. Thank you ren.

How about no.2?

Ahmm Jeran can you please
stand?

Thank you Jeran, yes it is

correct.
So as you observed,
There are steps to find the
next term of an arithmetic
sequence that let us explore
and learn.

So the first step determines

the common difference
between terms in the given
sequence. Add the common
difference to the last term in
the given sequence to find
the next term in the
sequence. Repeat step 2,
adding the difference to the
most recently found term
until all desired terms are
found. Class.

Did you get it?

Sure!
Given the sequence below,
let’s find out what is the next
term.
1,3,6,10,15,21,...

By taking the difference

between two adjacent
numbers in the sequence, we Yes ma'am but can
can see that the common we have one more
difference increases by one example?
each time.
3−1=2
6−3=3
10−6=4
15−10=5
21−15=6
Since we can observe the
pattern we will let the next
term be x, then our next
term will fit the
equation x−21=7,
meaning that the next
term must be 28. Yes ma'am based
on the given our:

Did you get it? a=1

d=2
n = 30

(Expected answer:
Okay, very good class. a=1
d=2
Does anyone have n = 30)
clarification about this?

Okay let's have this one

finding the arithmetic means
and the sum of arithmetic
sequence. The arithmetic
mean is the simple average,
or sum of a series of
numbers divided by the count
of that series of numbers.
You know class there are
many ways in finding the
sum of it. So here are some.

The sum of arithmetic

sequence with first term 'a'
(or) a1 and common
difference 'd' is denoted by
Sn and can be calculated by
one of the two formulas:
None ma’am.
● Sn = n/2 [2a + (n -
1) d] (or)

Yes ma,’ am thank

you for the
● Sn = n/2 [a1 + an] additional example
we’ve learned a lot.

Sn/n this is the formula to get

the mean of the arithmetic

Sn = the sum of the first n

terms of the arithmetic
sequence,
a1 = the first term,
d = the common difference
n = the total number of terms
in the sequence and
an = the nth term of the
sequence.
Me ma’am? I'm
nervous.

Okay ma,’am.
Okay for example, (Reshiel wrote her
Find the sum of the first 40 answer at the
terms of the arithmetic board)
sequence 2, 5, 8, 11, …
First, find the 40th term
a40= a1 +(n-1)d
=2+39(3)
=119
Everyone:Yes
Then find the sum
ma’am.
Sn= n/2 (a1+an)
S40=40/2(2+119)
Because I've
= 2420 observed that there
Then find the arithmetic is an sequence of
the number of cans
mean
which is 11, 8, 5
2420/40= 60.5 and they have
common difference
which is 3.
First you have to do is to
evaluate the given and then
find the nth term ,solve for
the sum of the given
sequence using the formula
then get the arithmetic mean.

I have learned that

An arithmetic
Okay class, did you follow?
sequence is a
sequence where
every term after the
first is obtained by
adding a constant
and it has a
Sure! common difference
which is the
constant number
added to the
preceding term of
How about this one.Find the the arithmetic
sum of the first 30 terms of sequence. It can be
the sequence 1, 3, 5, 7, 9 calculated by
…… subtracting any two
consecutive terms
Okay class what is our a,d, in the arithmetic
and n? sequence.

Jaja can give what is a,d, Everyone shouted

and n? 55
(Expected answer:
55)

None ma’am.
Very good Jaja! That' correct!

So, here is our solution.

a=1
d=2
n = 30

Using the formula: S =

n/2 {2a + (n − 1)d}

We obtain,

S = 30/2 {2(1) + (30 −

1)2}

= 900

So 900 is the sum of the

sequence.

900/30=30

Now, do you have

questions?
Good bye ma’am!

Did you get it?

Okay it seems that everyone

understood our lesson and
for me to know that you really
understand our lesson try
this problem in a ¼ sheet of
paper and I will choose one
to answer in the board then
the rest pass your paper.

What is the 50th term, the

sum, and the mean of the
given arithmetic sequence?

Find the 50th term of the

sequence 293, 290, 287,
284, 281,…
Okay, Reshiel, can you write
your answer on the board?

You can do it!

Okay, correct! Very good

Reshiel.

A cashier in Roy Plaza was

tasked to stack 24 tanks of
gallons with 11 gallons at the
bottom of the stack 8 in the
middle and 5 on the top.

Now class based on the

problem does the number of
cans in each layer of the
stack?

Hmm, Arcely how do you say

that this is an arithmetic
sequence?

Amazing, Arcely!thank you,

you may now sit down.

We are almost done with our

lesson for today, Althea what
have you learned today? Can
you please stand and tell us?
 So if we have this sequence;
7, 19,31,43.. what is the next
term?

Alright class! You are already

mastered our lesson.

Do you have any questions?

To sum it up:

E. Application
Both arithmetic means and
sequence would help us in
identifying patterns of a
sequence specially in real life
settings. In getting the
arithmetic means the sum of
all observations in the given
data set divided by the total
number of observations in
the dataset.
So I think this will be all for
today's class. I hope that
you’ve learned a lot from our
discussion.

Kindly stand up, pick up

some pieces of papers, and
arrange your chairs.
Before we leave, please tell
your seatmate that you did
an amazing job today! And
you are more than what you
are capable of.

Goodbye class!
See you next meeting, have
a Good day!
F. Generalization
IV. EVALUATION

Instruction:

For our activity you will be doing this individual and I will give you 2 problems for you to
solve within 10 minutes. This will test your understanding and mastery of our lesson. Write your
answer in a 1 whole sheet of paper.
Calculate the 39th term of each sequence and solve for the sum of the sequence.
 1. 5,10,15,20,25…
2. 6,13,20,27…

Answer key for Evaluation:

Sum of the sequence: 39th term:

Sum of the sequence: 39th term:

V. ASSIGNMENT

For your assignment kindly get your notebook and copy this to be submitted next meeting.
Calculate the sum of the 55th term and the mean of the sequence and solve the sum of the
sequence. Write your answer in your notebook.

1, 4, 7, 10, …