lesson plan, mathematics, matrix, cooperative learning
TRANSCRIPT
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LESSON PLAN
Matrix
(K13)
Compiled by:M. Helmy Firmansyah 12030174258
DEPARTMENT OF MATHEMATICS
FACULTY OF MATHEMATICS AND NATURAL SCIENCE
STATE UNIVERSITY OF SURABAYA
INTERNATIONAL PROGRAM OF MATHEMATICS EDUCATION
2015
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LESSON PLAN
SCHOOL UNIT : Senior High School
SUBJECT : MathematicsGRADE/SEMESTER : X / 1
TOPICS : Matrix Operations
TIME ALLOCATION : 2 x 45 minutes
A. Main Competence
K 1 Menghargai dan menghayati ajaran agama yang dianutnya.
Respect and appreciate the teachings of their religion.
K 2 Menghargai dan menghayati perilaku jujur, disiplin, tanggungjawab, peduli
(toleransi, gotong royong), santun, percaya diri, dalam berinteraksi secara
efektif dengan lingkungan sosial dan alam dalam jangkauan pergaulan dan
keberadaannya.
Respect and appreciate the honest behavior, discipline, responsibility, caring
(tolerance, mutual assistance), polite, confident, in interacting effectively with the
social environment and natural in a range of socially and presence.
K 3 Memahami pengetahuan (faktual, konseptual, dan prosedural) berdasarkan
rasa ingin tahunya tentang ilmu pengetahuan, teknologi, seni, budaya terkait
fenomena dan kejadian tampak mata.
Understanding knowledge (factual, conceptual, and procedural) based on his
curiosity about science, technology, arts, culture related phenomena and events
seem eye.
K 4 Mencoba, mengolah, dan menyaji dalam ranah konkret (menggunakan,
mengurai, merangkai, memodifikasi, dan membuat) dan ranah abstrak
(menulis, membaca, menghitung, menggambar, dan mengarang) sesuai
dengan yang dipelajari di sekolah dan sumber lain yang sama dalam sudut
pandang/teori.
Trying, processing, and presenting in the realm of concrete (using, parsing,
composing, modifying, and creating) and the realm of the abstract (writing, reading,
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counting, drawing, and fabricating) according to the learned in schools and other
sources in the same viewpoint / theory.
B. Basic Competence
1.1 Menghayati dan mengamalkan ajaran agama yang dianutnya.
Respect and apply the precepts of their religion.
2.1 Memiliki motivasi internal, kemampuan bekerjasama, konsisten, sikap disiplin, rasa
percaya diri, dan sikap toleransi dalam perbedaan strategi berpikir dalam memilih
dan menerapkan strategi menyelesaikan masalah.
Have internal motivation, cooperative skill, consistent, discipline, confident,
tolerance in thinking strategy different on choosing and applying strategy of solve
problem
3.5 Mendeskripsikan operasi sederhana matriks serta menerapkannya dalam pemecahan
masalah.
Able to describe simply matrix operation and apply it in problem solving
C. Indicators
1.1.1 Menunjukkan ketaatan kepada agama yang dianutnya.
Showed obedience to their religion.
2.1.1 Menunjukkan kemampuan bekerja sama dan toleransi dalam kelompok
Shows cooperative and tolerance in group
3.5.1 Menentukan hasil dari penjumlahan dan pengurangan matrix
Determine the results of matrix addition and matrix substraction
3.5.2 Menentukan hasil operasi perkalian matriks dengan skalar dan perkalian 2
matriks
Determine the results of matrix multiplication by scalar and 2-matrices
multiplication
D. Learning Objectives
1.1.1.1 Siswa dapat menunjukkan ketaatan kepada agama yang dianutnya dengan
berdoa sebelum pelajaran dimulai.
Students can show obedience to their religion to pray before the lesson begins.
2.3.1.1
Siswa dapat menunjukkan sikap bekerja sama dan toleransi dalam kelompok
Students can show cooperative and tolerance in group.
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3.5.1.1 Siswa dapat menentukan hasil dari penjumlahan matriks-matriks yang
diberikan.
Student can determine result of addition matrices that given before.
3.5.1.1 Siswa dapat menentukan nilai variable x, y, dan z yang terdapat pada matriks
dengan diketahui hasil dari pengurangan matriks
Student can determine variable value of x, y, and z that contained in the matrix
with known results from matrices substraction
3.5.2.1 Siswa dapat menentukan hasil operasi perkalian matriks dengan skalar
Student can determine results of matrix multiplication by scalar
3.5.2.2 Siswa dapat menentukan hasil perkalian 2 matriks
Student can determine results of 2-matrices multiplication
E. Learning Topic
Matrix
F. Learning Model and Learning Method
Learning Approach : Scientific Approach
The Model of Learning : Cooperative Learning
The Method of Learning : Asking-Questioning, discussion, and given task
G. Tool / Media / Learning Resources
1. Mathematics Book 10-Grade SMA/MAN Curriculum 2013
2. Worksheet
3.
Newspaper
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H. Instructional Activities
Activity Description of activitiesTime
Allocation
First-Activity
Phase 1: Giving Aim and Motivating Student
1. Students pray together
2. Teacher check student attendance
3. Motivation :
Look at cut of newspaper below.
How many columns in there?
How many row in there?
Is the column has same row?
Where word SMP Negeri 2? Show in row and
column?
Where word Paparan? Show in row and column?
4. To know what is connection that cut of newspaper that given
with the lesson lets try to solve worksheet.
( 10 minutes)
Main Activities
Phase II. Giving Experiment and The Steps
1. Teacher explains today activities :
a. Students will be divided into groups of 4-5 people
b. Students in group discuss problem where in worksheet
c. 1 student from each group will be selected at random to
present the results of his sub-group discussions in front
of the class.
( 70 minutes)
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Activity Description of ActivitiesTime
Allocation
Phase III. Organize students to the each learning group
2. Teacher divides the students into groups of 4-5 heterogen
students according lesson score previously
3. Teacher gives an explanation of the rules for discussion, such
as:
a. Use time wisely
b. Work with the group and do not interfere with other
groups.
c. Before ask the Teacher please ask to friend in 1 group
first.
d. Worksheet is used to study not only filled and collected
4. Teacher distribute worksheet on each group and ask for them
to divide the task in discussions.
Phase IV. Guiding Group to Work and Learn
6. Students observe and comprehend the problem in the
worksheet. (Comprehend)
7. Students cooperativelywith the friends friends in the group
about how to solve the proble.
8. Students remind and apply lesson previously like integer
operation and linear equation system to help solving the
problem. (Remind and Apply)
9. Students analyzetheir result to make conclusion. (Analyze)
10.During the discussion, Teacher supervise students with
guiding groups around the classroom and experiencing
difficulties.
11.
Teacher examine how the processes of each group ofstudents in solving problems.
12.Teacher provide guidance if there are groups that not true in
in solving problems.
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Activity Description of activitiesTime
Allocation
Final Activities
Phase 5. Evaluation (20 minutes)
8. 1 student from each group were randomly assigned to one of
the present the results while other students observe and
perceive actively during the presentation. And will be
continued other student with different problem. (Tolerance)
9. Teacher supervise students' presentation.
10.Teacher with students equate perception on problem solving.
11.Teacher gives an exercise and ask students working on an
individual basis within 10 minutes.
12.Discussing about the problems that considered difficult by
students.
13.Teacher asking what connection that motivation that given
before with lesson today.
Phase 6. Giving Reward (5 minutes)
14.Provide feedback that can be the form of praise and and
score/point to the students were able to ask good questions
and answer the questions correctly
15.Finish the presentation by giving applause to all the students
who have attended presentations
16.Teacher give awards to the groups based on the best group
today that are the most active on questioning, conducive, and
creative.
Closing
Activity
1. Teacher do reflection about learning activity today by asking
like:
a. What you have learnt today?
2.
Teacher gives homework in the BSE Book page 207, no 2 auntil 2 d
3. Teacher remind student to learn the next topic
(10 minutes)
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I. Assessment
1. Instruments Test :
a)
Quiz
b) Worksheet
2. Affective Scoring
Afective Observation Sheet
3. Cognitive Scoring
a. Cognitive Scoring Manual (Group)
b.
Cognitive Scoring Manual (Individual)
No. Assessment AspectAssessment
techniqueAssessment time
1. Attitude:
a. Cooperative in discussion
b. Tolerance when others present the resultObservation
During the
learning process
2. Knowledge:
Solving problem in daily life related to the
Matrix operation.Test
During solving
individual task
and group task
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AFECTIVE OBSERVATION SHEET
Competencies are assessed : Have internal motivation, cooperative skill, consistent,
discipline, confident, tolerance in thinking strategy
different on choosing and applying strategy of solve
problem. (KD 2.1)
Assessment Technique : Teacher-Observation
Class/Semester : X / Odd
Year : 2014 / 2015
Assessment Guidelines:
Give score in the column provided with the following conditions
No. Skills Criteria Score
1. CooperativeStudent always shows collaborate in group activities 4
Student shows the attitude of collaborate in the activities of
the group but has not been steady / consistent3
Student there have been effort to collaborate in group
activities2
Student didnt seek to collaborate in group activities 1
2. Tolerance Student didnt disturb other student when presenting their
results4
Student disturb other student when presenting their result
once3
Student disturb other student when presenting their result
twice2
Student disturb other student when presenting their result
more than twice1
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Recapitulation
No. NameAttitude
SumAttitude
ScorePredicate
Cooperative Tolerance
1. Aminatul2. Chorul
3. ....
4. ...
Note:
1. Maximal Score = Sum of Attitude Score x Number of Criteria.
In this case = 2 x 4 = 8
2. Attitude Score = (Gotten score : Maximal Score) x 100
Example score that gotten is 6 = 6/8 x 100 = 75
3.
Attitude Score can be qualified to be predicate as follows :
VG = Very Good = 80100 E = Enough = 60 - 69
G = Good = 7079 L = Less = < 60
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COGNITIVE SCORING MANUAL (GROUP)
No Alternative Solution Score
Kegiatan
1
Susunan peserta ujian ditinjau dari pola NIS
[
]
2
Matrix adalah susunan persegi panjang bilangan-bilangan atau obyek
matematika2
Jumlah kolom = 4
Jumlah baris = 5 4
Ordo matriks ditulis dengan jumlah baris x jumlah kolom
Ordo matriks tersebut yaiut 5 x 42
Kegiatan
2
Syarat matriks dapat dijumlahkan
1. Mempunyai jumlah baris yang sama
2. Mempunyai jumlah kolom yang sama
Atau bisa dibilang mempunyai ordo matriks yang sama4
Contoh 3 pasang matriks yang dapat dijumlahkan [1 3 4],[-2 4 10]
3
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Contoh 3 pasang matriks yang tidak dapat dijumlahkan
3Kegiatan
3 + =
= +
=
=
2
2
2
2
=
=
= =
Karena A + B = B + A maka penjumlahan matriks bersifat komutatif
2
2
2
2
2
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Agar matriks dapat dijumlahkan maka syarat matriks-matriksnya
1. Mempunyai jumlah baris yang sama
2. Mempunyai jumlah kolom yang sama
Atau bisa dibilang mempunyai ordo matriks yang sama. Selain itu
penjumlahan matriks bersifat komutatif karena matriks A + B = B + A
4
Kegiatan
4 - =
=
- = =
2
2
2
2
=
=
=
=
Oleh karena itu pengurangan matriks tidak bersifat komutatif
2
2
2
2
2
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Agar matriks dapat dikurangkan maka syarat matriks-matriksnya
1. Mempunyai jumlah baris yang sama
2. Mempunyai jumlah kolom yang sama
Atau bisa dibilang mempunyai ordo matriks yang sama. Selain itu
penjumlahan matriks tidak bersifat komutatif karena matriks A - B B - A4
Kegiatan
5 3 =
=
(-5) =
=
2
2
2
2
Jika P adalah bilangan real dan matriks H= maka PxH=
2
Kegiatan
6Rincian data tersebut dapat ditulis dalam bentuk matriks sebagai berikut
2
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Cabang 1
Total Biaya = (7 unit handphone x 2 juta) + (8 unit komputer x 5 juta) + (3
unit sepeda motor 15 juta)
= Rp 99.000.000,00
Cabang 2
Total Biaya = (5 unit handphone x 2 juta) + (6 unit komputer x 5 juta) + (2
unit sepeda motor 15 juta)
= Rp 70.000.000,00
Cabang 3
Total Biaya = (4 unit handphone x 2 juta) + (5 unit komputer x 5 juta) + (2
unit sepeda motor 15 juta)
= Rp 63.000.000,00
2
2
2
Total Biaya Pengadaan Peralatan tersebut dapat dituliskan dalam bentuk
matriks (dalam juta)
2rincian data pertama x rincian data kedua = total biaya pengadaan
peralatan dalam bentuk matriks
2Jika dicermati, perkalian matriks tersebut dapat dituliskan sebagai berikut:
() () () () () () () () ()
= (dalam satuan juta) 4Maximal Score 90
Note:
1.
Groupss Score= (Gotten Score : Maximal Score) x 1002.
Group Cognitive Score can be qualified as predicate as follows:
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VG = Very Good = 80100 E = Enough = 60 - 69
G = Good = 7079 L = Less = < 60
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COGNITIVE SCORING MANUAL (INDIVIDUAL)
No. Alternative Solution Score
1. Ordo masing-masing matriks tersebut adalah sebagai berikut
A1x3, B3x1, C2x3, D3x2, E1x3
2
Syarat matriks dapat dijumlahkan atau dikurangkan adalah
1. Mempunyai jumlah baris yang sama
2.
Mempunyai jumlah kolom yang sama
Atau bisa dibilang mempunyai ordo matriks yang sama.
Dari matriks-matriks tersebut, yang berordo sama adalah matriks A dan E
4
A + E = =
A - E = =
2
2
2. Ordo masing-masing matriks tersebut adalah sebagai berikut
H1x3, I3x3, K2x3, L3x1
2
Syarat matriks dapat dikalikan adalah jumlah baris matriks pertama sama
dengan jumlah kolom matriks kedua.
Dari matriks-matriks tersebut, matriks yang dapat dikalikan dengan matriks G
adalah matriks I dan matriks L 4
G x I = =
G x L = =
2
2
Maximal Score 20
Note:
1. Students Score= (Gotten Score : Maximal Score) x 100
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2. Individual Cognitive Score can be qualified to be predicate as follows :
VG = Very Good = 80100 E = Enough = 60 - 69
G = Good = 7079 L = Less = < 60
Mengetahui, Surabaya, .
Kepala Sekolah .. Guru Mata Pelajaran
Matematika
(___________________) (__________________)
NIP. . NIP.
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Day / Date :______________________________________________/______________
Group / Class : __________________________________ / _____________
MATRIX
Indicator :
3.5.1 Determine the results of matrix addition and matrix substraction
3.5.2 Determine the results of matrix multiplication by scalar and 2-matrices multiplication
Members Group : 1.______________________________________________
2.______________________________________________
3.______________________________________________
Hint :
1. Discuss and resolve the following issues with the members of your group
2.
Write down the answers on the answer sheet provided
3.
Write down the details of each step in solving problems started from what is given,what is asked until find the results
KEGIATAN 1:Masihkah kamu ingat posisi duduk sewaktu
kamu mengikuti Ujian Nasional SMP?
Maksimal siswa dalam satu ruang ujian
hanya 20 peserta, biasanya disusun dalam
lima baris, empat kolom, seperti yang
disajikan pada gambar disamping.
Untuk memudahkan pengaturan peserta ujian
dalam suatu ruangan, pihak sekolah menempatkan siswa dalam ruang ujian dengan pola
nomor ujian melalui Nomor Induk Siswa (NIS), yang ditempelkan di tempat duduk siswa.
Misalnya, nomor ujian peserta di ruang A adalah 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34,
41, 42, 43, 44, 51, 52, 53, 54.
orksheet
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Jika nomor peserta ujian adalah 12, itu berarti posisi peserta saat ujian berada pada baris ke-1
lajur ke-2, dan jika nomor ujian peserta adalah 34, artinya posisi peserta tersebut saat ujian
berada pada baris ke-3 kolom ke-4. Demikian pula, jika nomor peserta ujian adalah 51,
artinya posisi siswa saat ujian beradaa pada baris ke-5 kolom ke-1.
a) Tentukan susunan peserta ujian ditinjau dari pola Nomor Induk Siswa (NIS)!
[
]
b) Bentuk diatas merupakan bentuk matriks, maka apa yang dapat kalian definisikan tentang
matriks?
c) Dari susunan yang telah kalian buat, ada berapa kolom dan baris?
Meja Pengawas
Ujian
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d) Jika jumlah baris x jumlah kolom disebut ordo matriks, tuliskan ordo matriks dari
matriks yang kamu buat?
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KEGIATAN 2:Coba amati matriks-matriks berikut. Berikut adalah pasangan matrik yang dapat dijumlahkan
dan yang tidak dapat dijumlahkan.
Dapat dijumlahkan
, ,
,
, , ,
Tidak dapat dijumlahkan
, ,
, , ,
,
a) Setelah kalian mengamati, dapatkah menyebutkan syarat matriks dapat dijumlahkan?
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b) Sekarang coba buat 3 pasang matriks yang dapat dijumlahkan!
c) Buat pula 3 pasang matriks yang tidak dapat dijumlahkan!
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KEGIATAN 3:Amati contoh penjumlahan matriks berikut!
+
=
+ = +
=
+ = Dari contoh diatas, dapatkah kalian memprediksi hasil dari penjumlahan matrik berikut?
Coba hitung dengan mengoperasikan matriks kanan dijumlahkan matriks kiri. Apakah
penjumlahan matriks bersifat komutatif?
+ =
+ =
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Dari hasil penjabaran di atas, apa yang dapat kalian simpulkan?
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KEGIATAN 4:Amati contoh pengurangan matriks berikut!
-
=
- = -
=
- = Dari contoh diatas, dapatkah kalian memprediksi hasil dari pengurangan matrik berikut?
Coba hitung dengan mengoperasikan matriks kanan dikurangi matriks kiri. Apakah
pengurangan matriks bersifat komutatif?
- =
- =
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Dari hasil penjabaran di atas, dapatkah kalian menyimpulkan?
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KEGIATAN 5Amati contoh perkaliana bilangan real dengan matriks berikut!
2 = 2 = (-1) =
(-5) = Bilangan real: 2 , 2 , -1, -5 dalam matriks disebut dengan skalar
Dari contoh diatas, dapatkah kalian memprediksi hasil dari perkalian matrik dengan skalar
berikut?
Dari hasil penjabaran di atas, Tentukan hasil dari perkalian matrik dengan skalar berikut.
3 =
(-5) =
Jika P adalah bilangan real dan matriks H=
maka PxH=
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KEGIATAN 6
Suatu perusahaan yang bergerak pada bidang jasa akan membuka tiga cabang besar di
pulau Sumatera, yaitu cabang 1 di kota Palembang, cabang 2 di kota Padang, dan cabang 3
di kota Pekanbaru. Untuk itu, diperlukan beberapa perlatan untuk membantu kelancaran
usaha jasa tersebut, yaitu handphone, komputer dan sepeda motor. Di sisi lain, pihak
perusahaan mempertimbangkan harga per satuan peralatan tersebut. Lengkapnya, rincian
data tersebut disajikan sebagai berikut.
Handphone
(unit)
Komputer
(unit)
Sepeda
Motor
(unit)
Cabang 1 7 8 3
Cabang 2 5 6 2
Cabang 3 4 5 2
Berapakah total biaya pengadaan peralatan yang harus disediakan perusahaan di setiap
cabang?
a) Tuliskan rincian data tersebut kedalam matriks
b) Hitung total biaya pengadaan peralatan tersebut di setiap cabang
Harga
Handphone
(juta)
2
Harga
Komputer
(juta)
5
Harga
Sepeda
Morot (juta)
15
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c) Tuliskan hasil total biaya pengadaan tersebut kedalam matriks
d) Tuliskan pada bentuk matriks
rincian data pertama x rincian data kedua = total biaya pengadaan peralatan
e) Berdasarkan pengamatanmu bagaimana cara mengoperasikan dalam bentuk matriks
rincian data pertama x rincian data kedua sehingga menghasilkan total biaya
pengadaan peralatan(hubungkan dengan cara menyelesaikan kegiatan 4(b))?
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Quiz
Name : ________________________________________________
Class : ________________________________________________
Day / Date : ________________________________________________
Indicator:
3.5.1 Determine the results of matrix addition and matrix substraction
3.5.2 Determine the results of matrix multiplication by scalar and 2-matrices
multiplication
Do the following questions correctly and accurately!
1. Diketahui matriks-matriks
dan
Dari semua matriks di atas, pasangan matriks manakah yang dapat dijumlahkan dan
dikurangkan. Kemudian selesaikanlah!
2. Diketahui matriks Kemudian diberikan matriks-matriks berikut:
dan Matriks manakah yang dapat dikalikan dengan matriks G? Kemudian tentukan
hasilnya!