Lesson Plan for Mathematics 10
I.
Objectives At the end end of the lesson, the the students students are expected expected to: to: identify and generate patterns; find the nth term of a sequence; find the general term of a sequence; and differentiate a finite sequence from an infinite sequence. • • • •
II.
Subject Matter Topic: Topic: SEQUE!E "eferences: E#$ath %& 'y (rlando A. (ronce and $arilyn (. $endo)a, pages *#*& +ntermediate Alge'ra Alge'ra ++ 'y ulieta -.erna'e, pages **/#**0 -lo'al $athematics %& 'y -eraldo 1-. anaag, pages *#2, 23 $aterials: !hal4 and 'oard, 5or4 sheets, slide presentation • •
•
III.
Procedure A. Priming/Activating Priming/Activat ing Prior Knowledge Action Song Song : “A Food Cheer” B. Presentation *Activity (Group Activity) The class 5ill 'e di6ided into four groups. Each group 5ill 'e gi6en a tas4 to do -roup %: 7Sequence -enerator8 -roup *: 7"adio Tuning8 -roup 9: 7$ultiplication Ta'le8 -roup : 7"outine o
• •
*Analysis Ans5er the the follo5ing guide questions questions %. =o5 do you fell fell a'out a'out the tas4 tas4 gi6en gi6en to to your your group> group> ?hy> ?hy> *. +n doing the acti6ity, acti6ity, 5hat mathematics mathematics concepts concepts or or principles did did your group group apply> apply> Explain ho5 you applied these mathematics concepts or principles> 9. =o5 5ould 5ould you you descr descri'e i'e the sequenc sequence> e>
*Abstraction Sequence is Sequence is a logical order or arrangement of 6alues defined 'y a general term or nth term. The general term of a sequence defines sequence defines the characteristic of the 5hole sequence. E6ery element in a sequence is called a term. term. Examples: %. *. 9. .
Set of of counting counting num'e num'ers: rs: %, *, *, 9, , 2, /, /, 3, 0, @, %&, %&, . . . $ultiple $ultiples s of 3: 3, 3, %, %, *%, *%, *0, 92, *, . . . o5ers o5ers of of *: *, , , 0, %/, %/, 9*, 9*, /, /, . . . $ultiples of of 2 'et5een 'et5een %% %% and and /&: %2, %2, *&, *2, *2, 9&, 92, 92, &, 2, 2, 2&, 22
Finite Sequence and Infinite Sequence A sequence ha6ing a finite num'er num'er of terms terms is called a finite sequence. sequence. A sequence that has has an infinite infinite num'er num'er of terms is called an infinite sequence. sequence.
Sequences may 'e o'tained 5ith the pro6ision of a general term. Example: Bind the first fi6e terms of the sequence, gi6en the general term
an
=2 ( n + 3 )
.
Solution:
a1 : for n=1 : 2 ( 1 + 3 )=2 ( 4 )=8 a2 : for n=2 : 2 ( 2+ 3 )=2 ( 5 )=1 0 a3 : for n=3 : 2 ( 3 + 3 )= 2 ( 6 )=1 2 a 4 : forn =4 : 2 ( 4 + 3 ) =2 ( 7 )=1 4 a5 : for n=5 : 2 ( 5 + 3 )=2 ( 8 )=16 ∴ The first fi6e terms of the sequence are 0, %&, %*, %, and %/ *Application 1irections: Sol6e the gi6en pro'lem assigned to your group. -roup %: essica 5anted to 'uy a monopod equipped 5ith shutter for her selfie ha'its that cost hp 9&& and started 'y sa6ing hp 2 on une %2, E6eryday from then on, she sa6ed hp 9 more than she did the preceding day. (n une *2, she chec4ed her sa6ings and found that she needed to sa6e more to 'uy the monopod. =o5 much does she still need to sa6e> -roup *: Alex is a 6ery athletic person. =e usually Coins fun runs and marathons. Unfortunately, he got inCured in one of his e6ents 5hen his an4le t5isted. =e 5as told to ta4e some rest and 5as ad6ised to return to his Cogging program slo5ly. +n the program, he needs to Cog for %2 minutes each day for the first 5ee4, then an increase of 3 minutes per day on the succeeding 5ee4s. =o5 many minutes does Alex ha6e to Cog on the %& th 5ee4 of the program> -roup 9: E6ery month, ose sa6es hp %%2 more than 5hat he sa6ed the preceding month in his 'an4 account. +f he initially put hp @*2 in his account, find a formula to find out ho5 much he sa6ed in his 'an4 account on the nth month. Dnote: neglect periodic interests -roup : A 'all is dropped from a height of * feet and al5ays 'ounces off to %F9 of the height from 5hich it falls. Express the height from 5hich the 'all falls as terms of a sequence. ?rite a formula for the nth term of the sequence.
IV.
Evaluation 1irections: "ead and analy)e the gi6en items carefully. ?rite on the spaces pro6ided 'efore each num'er the next t5o terms of each sequence. GGGG GGGG %. 9, 3, %%, %2, . . . GGGG GGGG *. 0, %%, %, %3, . . . GGGG GGGG 9. #2, #*, %, , . . . 1irections: "ead and analy)e the gi6en sequence carefully. !omplete the sequence 'y filling in the 'lan4s the missing termFs. 2. , 0, GGG, %/, *& /. %9, GGG, 99, GGG, 29 3. %./, GGG, *.*, GGG*.2, GGG
V.
Assignment $o6ie "e6ie5: 7ay it Bor5ard8 ?atch the mo6ie 7ay it Bor5ard8, starring e6in Spacey, =elen =unt, and =aley oel (sment. The mo6ie is a'out a middle school student, Tre6or $cinley, 5ho 5as caught 'et5een the extensi6e complexities of life 5hen he met his Social Studies teacher and pro6ided them 5ith an assignment: 7Thin4 of an idea to change our 5orld H and put it into A!T+(.8 See ho5 this student changes the li6es of a lot of people. "eali)e ho5 the concepts of sequences ha6e 'een used to illustrate the ain action of the mo6ie and ho5 you can do the same to help your community.
repared 'y:
JEMARJO E SALA!"A!A! alayaan !hristian School athematics
!hec4ed and E6aluated 'y:
!E!I#A A"AME 1r. uan A. astor $=S !rincipal ""
MARI#ES $O!IFA%IO Sta. $onica =S !rincipal "
JA%&'ELI!E ARIAS +tlugan =S #eacher """
ELI!O (AR%IA 1acanlao -. Agoncillo =S $ead #eacher "
Sequence Generator The -ree4 mathematician ythagoras 5ho li6ed during the sixth century ! 5as the founder of the ythagorean 'rotherhood. The group studied num'ers of geometric arrangements of points, such as triangular num%ers& s'uare num%ers& and pentagonal num%ers. The follo5ing illustrate the first fe5 of each of these types of num'ers. riangular !umbers % 9 / %&
%2
I
%/
*2
I
Pentagonal !umbers % 2 %* **
I
S"uare !umbers %
@
%. Use patterns to complete the ta'le 'elo5. Figurate !um)er
1st
*nd
#riangular S'uare !entagonal $exagonal $eptagonal 1ctagonal
, * 0
+rd
* . / ,
,th
+ * //
-th
.th
/th
, /,
*. Add t5o consecuti6e triangular num'ers. ?hat 4ind of figurate num'ers do you get>
1 + 3 = ? 9. $ultiply each triangular num'er 'y 0.then, add %. ?hat 4ind of figurate num'ers do you get>
#riangular !um)er 2
1
+
.
10
1-
2x 3 . Square any t5o consecuti6e triangular num'ers. Su'tract the smaller square num'er from the larger. ?hat 4ind of num'er do you get>
Radio Tuning The hilippines is tagged as home of great singers and stage performers. ?e al5ays li4e to hear good music 'eing played o6er the radio. +t has 'ecome part of our daily li6ing that 5e listen to music and sing 5ith it 5hene6er possi'le. (nce you turn on the radio, it is necessary that you 4no5 the station you are going to listen to. These stations, 'etter 4no5n as B$ Dfrequency modulation modulate or 6ary their frequencies to carry sound or information o6er an electromagnetic 5a6e.
?hat is your fa6ourite radio station> GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG 1o you 4no5 some atanguenyo radio station> !an you gi6e some> GGGGGGGGGGGGGGGGG =o5 do you identify these stations> GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG elo5 is a ta'le sho5ing the list of different existing B$ stations 5ith their corresponding frequency modulation. !omplete the ta'le 'y filling in the 'lan4 spaces the correct frequency assuming that the gi6en stations are arranged in increasing frequency.
Frequenc3
Station
Frequenc3
Station
00.9 B$ 0@.%B$ 0@.@ B$ @&.3 B$ @%.2 B$ @*.9 B$ @9.% B$ @9.@ B$ @.3 B$ @2.2 B$ @/.9 B$ @3.% B$ @3.@ B$
am 00.9 ?a6e 0@.% $agic 0@.@ @&.3 Ko6e "adio @%.2 ig "adio "adyo2 @*.9 e5s B$ $onster "adio "M @9.% @9.@ iB$ $ello5 @3 inas B$ @2.2 @/.9 Easy "oc4 arangay KS @3.% @3dot@ =ome "adio
@0.3 B$
@0.3 $asterJs Touch @@.2 "T " %&& %&%.% Les B$ Tam'ayan %&%.@ %&*.3 Star B$ %&9.2 ?o5 B$ %&.9 usiness "adio %&2.% !rosso6er "adio =igh %&2.@ %&/.3 Energy B$ %&3.2 ?in "adio
Routine Ko ‘To A schedule is an example of routine that creates a pattern4 !eople need patterns in their lives for t5o reasons: 6E7"A8"7"#9 and !6E"C#A8"7"#94 A person 5ho is 5himsical is often unrelia%le4
1iscuss among your group ho5 you are doing this tas4: coo4ing rice Examine each otherJs ans5er, and then chec4 if their ans5er is the same as yours. +llustrate the process of coo4ing rice 'ased from the procedures that your group had discussed.
Multiplication Table Lou are 6ery familiar 5ith the multiplication ta'le. The figures 'elo5 illustrate part of a multiplication ta'le.
M % * 9 2 /
%
*
9
2
/ , *
/ * 2 + /
* . / , 2
2 / * /+ /-
, + , /+ /, +
/ * / 2 /+ *
%an 3ou see an3 5attern in the multi5lication ta)le6 77777777777777777777777
8hat is the 5attern for the encircled num)ers in each ro9 in the ta)le )elo96 7777777777777777777777777777777777777777777777777777777777777777777
M % * 9 2 /
%
*
9
2
/ , *
/ * 2 + /
* . / , 2
2 / * /+ /-
, + , /+ /, +
/ * / 2 /+ *
8hat is the 5attern for the encircled num)ers along the diagonal in the ta)le )elo96 7777777777777777777777777777777777777777777777777777777777777777777
M % * 9 2 /
%
*
9
# / , *
/ $ * 2 + /
* % / , 2
2
/
, * 2 + / / , 2 #& /+ //+ '( + /- + )&
8hat is the 5attern for the num)ers grou5ed in in:erted ;L< in the ta)le )elo96 7777777777777777777777777777777777777777777777777777777777777777777
M % * 9 2 /
%
*
9
2
/ , *
/ * 2 + /
* . / , 2
2 / * /+ /-
, + , /+ /, +
/ * / 2 /+ *
