The document provides a detailed lesson plan for teaching arithmetic sequences to a 10th grade mathematics class. The objectives are for students to illustrate, determine the nth term of, and appreciate arithmetic sequences. The lesson proper involves motivating students with a treasure box activity, defining and formulating the formula for an arithmetic sequence, working examples, and evaluating student understanding with an "Answer Me" game. Key points are the definition of an arithmetic sequence as having terms obtained by adding a constant difference, and the formula An=a1+(n-1)d to find the nth term.

1. A Detailed Lesson Plan
In Mathematics 10
(Grade 10)
Date of Submission:
Date of Execution:
Submittedby:
Stephanie JoyE.Lungub
Teacher Applicant

2. A Detailed Lesson Plan
In Mathematics 10
(Grade 10)
I. Objectives
At the endof a 60-minute discussion,the studentsare expectedto;
a. Illustrate an arithmeticsequence;
b. Determine the nthtermof a givenarithmeticsequence;
c. Show appreciationin arithmeticsequence.
II. SubjectMatter
A. Topic:ArithmeticSequence
B. References:Learner’sMaterial inMathematicsforGrade 10 by DepEdand Google
C. Materials:PrintedMaterials,PowerPointPresentation,Treasure box,chalkandboard
D. Strategies:InductiveMethod
E. Skillstobe Developed: defining,identifying,finding,determining
III. LessonProper
Teacher’s Activity Learners’ Activity
A. DailyRoutine
Good morning,class!
Let usstart ourclass withthe
guidance of our Lord.Who wantsto
leadus a prayer?Yes?
Before takingyourseats,see toit
that yourchair is properlyaligned
and pickup those piecesof paper
underthem.
You may nowtake your seats.
ClassSecretary, mayyoucheck the
attendance.Isthere anyone absent
for today?
Verygood.Keepupthe goodwork.
B. Motivation
Let me share you something,I
learnedall aboutalchemy.Yes,you
heardit right,I am an alchemist.I
have travelledall alongthe Sahara
: Good morning,ma’am!
: (Prayer)
: (The studentswill doastold.)
:None,ma’am.

3. Desertto findformy treasure and
finally,here itis.Iwantto share you
my treasure butwithone condition.
Helpme finishatask so that we can
able to openthe treasure box.Do
youwant to helpme,class?
Alright.We have here a table, help
me answerwhat isflash onthe
screento complete ourtable sothat
we can openour treasure box. Is
that alrightto you,class?
Now,let’sbegin.
C. Presentationof the Lesson
Since we alreadycomplete the table,
we can open nowour treasure box.
Anyrepresentative of the classmay
come at frontand openit.
Nowclass,what phrase hasrevealed
inour treasure box?
That’s right!Andthat will be our
focusfor today.
D. Developmentof the lesson
We have here the definitionof
ArithmeticSequence,whowantsto
readit? Yes?
Is the meaningof arithmetic
sequence cleartoyou,class?
For furtherunderstanding, let’stake
a lookto the resultof our activitya
while ago. What doyou observe on
the numberof matchsticks?
: Yes, ma’am!
: Yes,ma’am
: (The class will dothe task.)
: (Representativeof the class will openthe
treasure.)
: ArithmeticSequence
: An ArithmeticSequenceisasequence
where everytermafterthe firstisobtained
by addinga constantcalledthe common
difference.
: Yes,ma’am!
: The numberof matchsticksincreasesby3
as we add anothersquare.

4. Great Observation!
Suppose we wantto findthe
numberof matchsticksof 20
squares.Doyou thinka formula
wouldhelpusfindit,class?
Great! Now we needtoformulate a
formulasothat we can easilyfind
the numberof matchsticksof 20
squares.First, let’srewriteeach
termon howwe obtainthe second,
third,fourth, andfifthterms.What
isour firstterm,class?
That’s right!
Now,whatwe will addto the
secondterm?
Brilliant!
Whichis our secondtermwill be
4+3. How aboutour thirdterm, how
many3’s will we add?
Astonishing!
Whichis our thirdtermwill be
4+3+3, right?
Verygood!Now whowantsto
complete uptofifth term?Yes?
Excellent!
Now,we will studyeachtermsand
rewrite itinanotherform.Our 1st
termis 4+0(3), we multipliedinto
zerosince we don’thave 3 to add in
our firstterm,then,forour 2nd
term
is4+1(3) since we added3 once on
the firstterm.Am I right, class?
Nowwhowants to write for the 3rd
term?
Amazing!
How aboutthe 4th
term?5th
term?
Excellent!
Now,we can alreadydeterminethe
numberof matchsticksneededto
: Yes,ma’am.
: 4, ma’am
: 3, ma’am.
: We will addtwo3’s, ma’am.
: Yes,ma’am.
: a4= 4+3+3+3
a5= 4+3+3+3+3
: Yes,ma’am.
: 4+2(3)
: 4+3(3), 4+4(3)

5. formn square.Will youreadthe
formula,class?
Thank you!
Now,let’scheck fromour table.We
let4 as a1 whichisthe firstterm, n
whichisthe numberof termsand
subtractedby1 to get the 1 and we
let3 as d as the commondifference.
Didyou getit class?
Now,we can findalreadyof how
manynumbersof matchsticksin20
squares.We will now use the
formulaAn=a1+ (n-1) d to findit.
Who wantsto substitute ourgiven
inthe formula?Yes?
Commendable!
Who wantsto solve it?Yes?
Verygood!
We can nowconclude thatwe need
61 matchsticksto form20 squares.
Didyou getit, class?
For furtherunderstanding,let’s have
anotherexample.
Will youreadit? Yes?
Thank you!
Now,whatis the firsttermof our
sequence? Yes?
Verygood!
Who wantsto give me the common
difference?Yes?
Exactly!
Now,whowantsto substitute this
giveninthe formula?Yes?
Spectacular!
: An= a1+ (n-1) d
a1 isthe firstterm
d is the commondifference
n is the numberof terms
An is the nth term
: Yes,ma’am.
: A20= 4 + (20-1)3
: A20 =4+(19)3
=4+ 57
=61
: Yes,ma’am.
: What is the 10th
term of the arithmetic
sequence 5,12, 19, 26, … ?
: 5, ma’am.
: 7 ma’am.
: An= a1+ (n-1) d
A10=5 + (10-1) 7

6. Now,whowantsto solve onthe
board?Yes?
Precisely!
Andthe value of 10th
terminour
sequence is59. Didyoufollow,
class?
Seemslike youalreadyunderstand
on howto solve arithmeticsequence
E. Application
To testif youunderstandourtopic,
let’shave a game entitled“Answer
Me”. Who wantsto readthe
mechanics?Yes?
Is the instructioncleartoyou,class?
Ok,we may nowstart.
In the arithmeticsequence
3,7,11,15,19, . . .
What isthe firstterm?
What isthe commondifference?
What isthe 25th
termof the
sequence?
Is the sequence 15,17, 19, 21, . . .
consideranarithmeticsequence?
: A10= 5 +(9)7
= 5 + 54
= 59
:Yes,ma’am.
: Mechanics:
1. The classwill be dividedinto4
groups.
2. Representative of eachgroupwill
come at frontand gettheirmaterials
for the game.
3. The teacherwill give anarithmetic
sequence onscreenandanswer
whatis askedonit.
4. The firstgroup whoraise theirboard
firstand got the correct answerwill
geta point.
5. The group whowill getthe highest
pointswill be the winner.
(Note:The teacherwill deductpointson
a group whois noisywhile doingthe
activity.)
: Yes,ma’am.
: 3
: 4
: 99

7. Yes or No?
If a1=1 and d=5, whatisA4?
Is the sequence 1/2,1, 3/2, 2, 5/2,…
considerarithmeticsequence?Yes
or no?
What isthe commondifference?
Basedon the outcomesof your
work,it seemsyoulearnedaloton
our topic.
F. Valuing
We have here a figure,whatisyour
insightaboutit?Yes?
Sequence of Relationship
God –You –Family
Love Love
That’s true!
We have here the sequence of
relationshipwhichisGod,Youand
Familyandtheircommondifference
isLove.Why Love?Love is the
strongestforce,Godcreatedus
because he lovesusand we have a
familywhocaresus because they
love usso we needtolove them
back as theylove youwithall their
heart.
G. Generalization
To sum upwhat we have tackledfor
today,whowantsto give me the
definitionof ArithmeticSequence?
Yes?
Splendid!
Andwhowants to give me the
formulaof arithmeticsequence in
findingthe nthterm?
: Yes
: 16
: Yes
: ½
: Love is the one to complete inevery
relationship,withoutlove,there isnoany
kindof relationship.
: An ArithmeticSequenceisasequence
where everytermafterthe firstisobtained
by addinga constantcalledthe common
difference.
: An= a1+ (n-1) d

8. Excellent!
You didmasterour lessonfortoday.
IV. Evaluation
To testyour understandingonourtopicfortoday, bring out1 whole sheetof paperand
answerthe following.
1. Findthe 6th
termof the arithmeticsequence 1,0,-1,-2,-3,…
2. Usingthe formula,whichtermof the arithmeticsequence is -18,giventhata1=7 and
a2=2?
3. Findthe 9th
termof the arithmeticsequence witha1=10and d=-1/2
4. What isthe 15th
termof the arithmeticsequence2,4,6,8,…?
5. The third termof a sequence is16 and the fourthtermis 20, what isthe firstterm?
V. Assignment
For yourhome delight,bringoutyournotesandcopy whatis on the screentobe check
tomorrow.
1. Give the definitionof anarithmeticmean.
2. Findthe arithmeticmeansbetween5and25.
That’s fortoday.Goodbye,class! :Goodbye,ma’am.