Tugas Akhir Modul 3 Matematika
May 6, 2019 | Author: oka adnyana | Category: N/A
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TUGAS AKHIR MODUL 3 MATEMATIKA
NAMA NO. PESERTA PROGRAM STUDI KELAS
OLEH : : I PUTU OKA ADNYANA, S.Pd : 19220302710004 : PGSD :E
PENDIDIKAN PROFESI GURU DALAM JABATAN ANGKATAN 1 2019
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BAGIAN A 1. Analisis kesalahan pemahaman pada gambar a. Pada soal tersebut terdapat kesalahan dalam menggambar dimana seharusnya gambar kedua lingkaran tersebut dibuat sama besar. Karena gambar lingkaran dibuat berbeda maka pemahaman anak menjadi. Maka dari itu agar tidak menimbulkan kesalahan pemahaman nilai pecahanmaka harus digambar sebagai berikut :
b. Pada konsep tersebut pengunaan gambar sudah benar, hanya saja pemahaman tersebut menjadi salah karena pembagian pada gambar yang salah, garis yang digunakan dalam membagi gambar tersebut berbeda yaitu horizontal dan vertikal. Penggunaan garis yang berbeda tersebut, mengakibatkan secara kasat mata kedua pembagian bangun tersebut berbeda, padahal sebenarnya memiliki nilai yang sama. Kesalahan tersebut mengakibatkan siswa salah dalam menggunakan tanda yang menyatakan perbandingan dua buah pecahan, dimana seharusnya ditulis
=
, bukan
≠
.
c. Pada gambar tersebut cara pembagian segitiga yang menyatakan nilai adalah salah. Dikatakan demikian karena dengan cara pembagian tersebut luas tiap bagian menjadi t idak sama, sehingga tidak bisa mewakili nilai . Gambar dengan pembagian yang benar adalah adala h sebagai berikut
2.
5 × 3
dapat di ilustrasikan sebagai berikut :
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Jadi dari gambar diatas dapat diperoleh hasil sebagai berikut :
5 × 3 15+ 15+ ++++ 1515+5+ 15+ 20 = = = = =
BAGIAN B 1. Pembuktian rumus luas segitiga sama sisi :
Menentukan tinggi segitiga dengan teorema Phytgoras (Sisi miring)2 = (Alas)2 + (Tinggi)2 Disesuaikan dengan gambar menjadi :
= + = − (12 ) = − = − = = × √ = 12 √3
Jadi, luas segitiga sama sisi adalah
= 12 ×× = 12 × × 12 √ 3 = 12 × 12 ××√3 = 14 × √3
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2. Pembuktian luas segi enam beraturan
Seperti dapay diamati pada gambar, segi enam beraturan tersusun atas 6 buah bangun segitiga sama sisi. Dari pernyataan tersebut maka dapat ditentukan sebagai berikut :
∆= 14 × √3 =6 .∆ 1 =66 × 4 × √3 = 43 × √3 = 2 × √3 = 3√ 32. Maka luas segi enam beraturan adalah:
BAGIAN C
52 55 58 60 61 62 63 67 68 68 70 70 70 70 71 71 71 72 72 72 73 74 75 75 75 76 77 77 78 78 79 79 79 80 80 80 81 81 82 82 82 82 83 83 83 83 83 83 84 84 84 85 85 85 85 86 86 86 86 86 87 87 87 87 88 88 88 88 89 89 89 90 90 91 92 93 95 96 97 99 Untuk memudahkan menganalisis data diatas, maka data tersebut akan dikelompokkan kedalam tabel distribusi frekuensi.
= −
Jangkauan
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=1+3, 3 log =1+3, 3 l o g80 =1+3, 3 1, 9 =7, 2 8 =7 = 47 ==6,77 =7
Banyak Kelas
(dibulatkan)
Panjang Kelas
(dibulatkan)
Tabel distribusi frekuensi Nilai
Turus
Frekuensi
52 – 58 58
c d eec eec eeeeeb eeea d
3
59 – 65 65 66 – 72 72 73 – 79 79 80 – 86 86 87 – 93 93 94 - 100
Mean Nilai
52 – 58 59 – 65 66 – 72 73 – 79 80 – 86 87 – 93 94 - 100
̅ = ∑∑ .
3 4 13 13 27 16 4
= 80
4 13 13 27 16 4
=80
55 62 69 76 83 90 97
. 165 248 897 988 2241 1440 388
. =6367
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Median Nilai
52 – 58 59 – 65 66 – 72 73 – 79 80 – 86 87 – 93 94 - 100
3 4 13 13 27 16 4
= 80
= 121 . == 402 . 80 : 80− 80 − 86 ℎ =80−0, 5 =79, 5 ℎ == 333+ 4 + 13+ 13 + 13 = = 7 =27 == 80 1 − 2 =+ 1 =79, 5 +72 80−33 27 =79, 5 +7(40−33 ) 27 727) =79, 5 +7( =79,5+1,81 Dari tabel diatas diketahui :
Maka median dapat ditentukan sebagai berikut :
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Modus Nilai
52 – 58 3 59 – 65 4 66 – 72 13 73 – 79 13 80 – 86 27 87 – 93 16 94 - 100 4 Dari tabel diatas dapat ditentukan : Modus terletak pada kelas 80 – 86 86
ℎ = = 81, 31 3 1 ℎ =80−0, 5 =79, 5 ==27−13 14 ==27−16 11 = 7 =+( + ) 14 ) =79, 5 +7(14+11 =79, 5 +7(142514) =79, 5 +7(9825) =79, 5 + 25 =79,5+3,92
Maka modus dapat ditentukan sebagai berikut:
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K = 1 × == 204 × 80 KBat as bawah b =66−0, 5 =65,5 K K K =+ 4 − =65, 5 +7(20−7 ) 13 1313) =65, 5 +7( =65, 5 +7 =72,5 = 2 × == 404 × 80 KBat taesrlbawah etetak pada padab kelke=80−0, las 8080 −586 =79,5
a. Kuartil Bawah ) Dari tabel tersebut dapat diketahui : Letak
terletak di kelas 66 – 72 72
Panjang kelas (p) = 7 Frekuensi kumulatif sebelum kelas Frekuensi kelas interval = 13
b. Kuartil Tengah Letak
= 7
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=81,31 = 3 × == 604 × 80 KBat taesrlbawah etbawah etak pada padab kelke=80−0, las 8080 −586 =79,5 K K K =+ 4 − =79, 5 +7(60−33 ) 27 2727) =79, 5 +7( =79, 5 +7 =86,5 [[~→ ]→ ~→ → ⋀⋁~⋁] ~⋁ → → →~] →~]⋀⋀ [ →~⋀~⋁ →]→ ~⋁ → → ⋀~⋁ ~⋁ → [ → ⋀~⋁] ~⋁]→→ →
c. Kuartil Atas Letak
Panjang kelas (p) = 7 Frekuensi kumulatif sebelum kelas Frekuensi kelas interval = 27
= 33
BAGIAN D 1. Pada materi utama , telah dibahas mengenai Tautology, kontradiksi, dam kontingensi. Buktikanlah: a. b. JAWABAN :
a. B
B
S
B
B
B
B
B
B
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[ ] ~ ~→ ⋁ →~ ⋀ ⋀ ~ ~ ~→ ~→ →~ →~ ~→ ~→⋁→~ →~ ~[~→ ~→⋁→~ →~] ~[~→ ~→⋁→~ →~]⋀⋀ b.
B B B B S S S S
B B S S B B S S
B S S B S B S S S S S B S B S S B S B B B B S S S S B B B B S S B B S B B B S S S B S S B B S S B B B B B B S S S B B S B B S S Karena pada kolom kesimpulan semua bernilai salah, maka pernyataan adalah Kontingensi 2. Carilah dan buktikan pola bilangan untuk permasalahan berikut ini: Pertandingan sepak bola yang diikuti sebanyak n kesebelasan dan menggunakan a. sistem kompetisi penuh b. sistem setengah kompetisi JAWABAN: a. Sistem Kompetisi Penuh
~[~→ ~→⋁ →
~] ~]⋀⋀
n = banyak kesebelasan 2 3 4 5 6 7 n
Banyak pertandingan pertandingan 2 (2 – 1) 1) = 1 3 (3 – 1) 1) = 6 4 (4 – 1) 1) = 12 5 (5 – 1) 1) = 20 6 (6 – 1) 1) = 30 7 (7 – 1) 1) = 42 n (n – 1) 1)
Dalam sistem kompetisi penuh setiap kesebelasan saling berhadapan sebanyak dua kali. Jadi dalam kompetisi penuh berlaku ketentuan sebagai berikut :
== − 1
b. sistem setengah kompetisi
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Jadi ada 6 pertadingan yang akan dilaksanakan atau n/2 (n-1) = 4/2 (4-1) = 2 x 3 = 6 3. Pada pelaksanaan PPG seluruh peserta diminta untuk membuat RPP untuk untuk eklas II, III dan IV. Dari 120 peserta PPG, 100 orang telah menyelesaikan RPP kelas II, kelas III, dan Kelas IV, 20 orang menyelesaikan RPP kelas II dan kelas III, 25 orang menyelesaikan RPP kelas III dan IV, 15 orang menyelesaikan RPP kelas II dan IV. Sementara itu, 65 orang membuat RPP kelas II, 45 orang membuat RPP kelas III, dan 42 orang membuat RPP Kelas IV. Dari permasalahan tersebut berapakah banyaknya peserta yang belum menyelesaikan satupun RPP yang harus dibuat? Ilustrasikan dengan menggambar diagram venn! JAWABAN : Banyak peserta = 120 orang 10 orang mengerjakan RPP Kelas II, III, IV 20 orang mengerjakan RPP Kelas II, III 25 orang mengerjakan RPP Kelas III, IV 15 orang mengerjakan RPP Kelas II, IV 65 orang mengerjakan RPP Kelas II 45 orang mengerjakan RPP Kelas III 42 orang mengerjakan RPP Kelas IV Peserta yang yang hanya mengerjakan RPP Kelas II, III Peserta yang hanya mengerjakan mengerjakan RPP Kelas III, IV Peserta yang yang hanya mengerjakan RPP Kelas II, IV Peserta yang hanya mengerjakan RPP Kelas II
= 20 – 10 10 = 10 Orang = 25 – 10 10 = 15 Orang = 15 – 10 10 = 5 Orang = 65 – (10 (10 + 10 + 5) = 65 – 25 25 = 40 Orang Peserta yang hanya mengerjakan RPP Kelas III = 45 – (10 (10 + 10 + 15) = 45 – 35 35 = 10 Orang Peserta yang hanya mengerjakan RPP Kelas IV = 42 – (10 (10 + 15 + 5) = 42 – 30 30 = 12 Orang Peserta yang tidak mengerjakan RPP = 120 – (10 (10 + 10 + 15 + 5 + 40 + 10 + 12) = 120 102
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120
II
40 10
5 10 12 IV
15
10 III
18
BAGIAN E Rancanglah sebuah RPP matematika pada materi perkalian dua bilangan pecahan JAWABAN: RENCANA PELAKSANAAN PEMBELAJARAN (RPP) MATEMATIKA Satuan Pendidikan : SD/MI Kelas / Semester : V/1 Tema : Pecahan Sub Tema : Perkalian Pecahan Pembelajaran ke:2 Alokasi waktu : 90 menit
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C. TUJUAN 1. Dengan penjelasan guru siswa mampu memahami perkalian pecahan. 2. Dengan berbagai latihan siswa mampu mengidentifikasi dan menyelesaikan masalah yang berkaitan dengan perkalian pecahan. D. MATERI 1. Perkalian Pecahan E. PENDEKATAN & METODE Pendekatan : Scientific Strategi : Cooperative Learning Teknik : Example : Example Non Example Example Metode : Pengamatan, Penugasan, Tanya Jawab, Diskusi dan Praktek F. KEGIATAN PEMBELAJARAN Kegiatan Kegiatan Pendahuluan
Deskripsi Kegiatan
1. Kelas dimulai dengan dibuka dengan salam, sal am, menanyakan kabar dan mengecek kehadiran siswa 2. Kelas dilanjutkan dengan do’a dipimpin oleh salah seorang siswa. Siswa yang diminta membaca do’a adalah siswa siswa yang hari ini datang paling awal. (Menghargai kedisiplikan siswa/PPK). 3. Siswa diingatkan untuk selalu mengutamakan sikap disiplin setiap saat dan menfaatnya bagi tercapainya sita-cita.
Alokasi Waktu 10 menit
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C. Menalar 1. Siswa berdiskusi dengan temannya tentang perkalian pecahan.
Jelaskan cara menghitung perkalian pecahan berikut:
14 × 12
2. Guru menunjuk beberapa siswa untuk maju dan menjelaskan hasil diskusi tentang perkalian pecahan dengan bimbingan guru. (Mengkomunikasikan) 3. Guru memberikan pembenaran dan masukan apabila terdapat kesalahan atau kekurangan pada siswa. 4. Guru menyatakan bahwa siswa telah paham tentang perkalian pecahan. D. Mencoba 1. Guru memberikan soal latihan perkalian pecahan kepada siswa. Coba kerjalan soal berikut :
× = ⋯
2. Guru meminta siswa untuk mengerjakan soal latihan tersebut secara individu 3. Guru menunjuk beberapa siswa untuk menuliskan hasil pekerjaanya didepan kelas secara bergantian
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2. BSE KTSP H. PENILAIAN Penilaian terhadap proses dan hasil pembelajaran dilakukan oleh guru untuk mengukur tingkat pencapaian kompetensi peserta didik. Hasil penilaian digunakan sebagai bahan penyusunan laporan kemajuan hasil belajar dan memperbaiki proses pembelajaran. Penilaian terhadap materi ini dapat dilakukan sesuai kebutuhan guru yaitu dari pengamatan sikap, tes pengetahuan dan praktek/unjuk kerja sesuai dengan rubrik penilaian penilaian sebagai berikut; 1. Penugasan Soal dan kunci jawaban terlampir 2. Diskusi Saat siswa melakukan diskusi, guru menilai mereka dengan menggunakan rubrik.
Centang (√) pada bagian yang memenuhi kriteria. kriteri a. Kriteria
Mendengarkan
Sangat Baik (4)
Baik (3)
Selalu Mendengarkan mendengarka teman yang n teman yang berbicara, sedang namun sesekali berbicara. masih perlu diingatkan.
Cukup (2)
Masih perlu diingatkan untuk mendengark an teman yang sedang berbicara.
Perlu Pendampingan (1) Sering diingatkan untuk mendengarkan teman yang sedang berbicara namun tidak mengindahkan.
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saat diskusi.
sesuai dengan topik.
3. Catatan Anekdot untuk mencatat sikap (Disiplin) (Disiplin) Contoh catatan pengamatan sikap dan keterampilan
Ayu menunjukkan rasa ingin tahunya tentang perkalian pecahan. Hal ini ditunjukan saat kegiatan mengamati permasalahan tentang perkalian pecahan. Dengan serius memperhatikan guru saat menjelaaskan dan menyajikan permasalahan di depan kelas. Ayu juga aktif bertanya tentang cara menyelesaikan permasalahan tentang perkalian pecahan. Saat Saat te
al
i
ulit ulit
dala dala
alia alia
ah
A
de
hati hati
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Lampiran Soal Penugasan
1. 2.
× = ⋯ × = ⋯
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