PUSAT PERBUKUAN
Departemen Pendidikan Nasional
i
Hak Cipta pada Departemen Pendidikan Nasional Dilindungi Undang-undang
Pintar
Bermatematika
Matematika untuk SD Kelas 4
Penulis
: Irwan Kusdinar Zikri
Penyunting
: Effendi
Penata Letak
: Sufyan
Desain Sampul : Irfansyah Ukuran Buku
372.7 IRW p
: 21 x 29,7 cm
IRWAN Kusdinar Pintar Matematika 4: Untuk SD/MI Kelas 4, penulis, Irwan Kusdinar, Zikri ; penyunting, Effendi -- Jakarta : Pusat Perbukuan, Departemen Pendidikan Nasional, 2009. viii, 210 hlm. : ilus. ; 30 cm. Bibliografi : hlm. 207-208 Indeks ISBN 978-979-068-567-3 (no. jilid lengkap) ISBN 978-979-068-571-0 1. Matematika-Studi dan Pengajaran 2. Matematika-Pendidikan Dasar I. Judul II. Irwan Kusdinar III. Effendi
Hak Cipta Buku ini dibeli oleh Departemen Pendidikan Nasional dari Penerbit Leuser Cita Pustaka, PT
Diterbitkan oleh Pusat Perbukuan Departemen Pendidikan Nasional Tahun 2009 Diperbanyak oleh ....
ii
Kata Sambutan
Puji syukur kami panjatkan ke hadirat Allah SWT, berkat rahmat dan karunia-Nya, Pemerintah, dalam hal ini, Departemen Pendidikan Nasional, pada tahun 2009, telah membeli hak cipta buku teks pelajaran ini dari penulis/penerbit untuk disebarluaskan kepada masyarakat melalui situs internet (website) Jaringan Pendidikan Nasional. Buku teks pelajaran ini telah dinilai oleh Badan Standar Nasional Pendidikan dan telah ditetapkan sebagai buku teks pelajaran yang memenuhi syarat kelayakan untuk digunakan dalam proses pembelajaran melalui Peraturan Menteri Pendidikan Nasional Nomor 9 Tahun 2009 tanggal 12 Februari 2009 Kami menyampaikan penghargaan yang setinggi-tingginya kepada para penulis/ penerbit yang telah berkenan mengalihkan hak cipta karyanya kepada Departemen Pendidikan Nasional untuk digunakan secara luas oleh para siswa dan guru di seluruh Indonesia. Buku-buku teks pelajaran yang telah dialihkan hak ciptanya kepada Departemen Pendidikan Nasional ini, dapat diunduh (down load), digandakan, dicetak, dialihmediakan, atau difotokopi oleh masyarakat. Namun, untuk penggandaan yang bersifat komersial harga penjualannya harus memenuhi ketentuan yang ditetapkan oleh Pemerintah. Diharapkan bahwa buku teks pelajaran ini akan lebih mudah diakses sehingga siswa dan guru di seluruh Indonesia maupun sekolah Indonesia yang berada di luar negeri dapat memanfaatkan sumber belajar ini. Kami berharap, semua pihak dapat mendukung kebijakan ini. Kepada para siswa kami ucapkan selamat belajar dan manfaatkanlah buku ini sebaik-baiknya. Kami menyadari bahwa buku ini masih perlu ditingkatkan mutunya. Oleh karena itu, saran dan kritik sangat kami harapkan.
Jakarta, Juni 2009 Kepala Pusat Perbukuan
iii
Kata Pengantar Matematika mempunyai peranan penting dalam berbagai Ilmu Pengetahuan dan memajukan daya pikir manusia. Untuk itu, mempelajari materi memberikan banyak manfaat untuk siswa, salah satunya siswa bisa berpikir logis dan sistematis. Setiap apa yang akan dilakukan siswa akan diperhitungkan terlebih dahulu. Sehingga siswa bisa lebih berhati-hati dalam mengambil suatu tindakan. Anugerah yang Tuhan berikan sungguh besar. Salah satunya memberikan kami kesehatan sehingga buku “Pintar Bermatematika” dapat diterbitkan. Buku ini disesuaikan dengan Standar Isi sehingga Standar Kompetensi dan Kompetensi Dasar yang harus dicapai siswa diuraikan secara terperinci. Buku “Pintar Bermatematika” menyajikan matematika yang nyata sehingga mudah dipahami siswa dan menjadikan siswa dekat dengan matematika. Pada buku ini terdapat Pendahuluan sebagai pengantar untuk siswa dalam mempelajari buku ini. Selain itu, Latihan dapat melatih siswa mempelajari subbab, siswa pun belajar untuk mengerjakan soal matematika dengan cara membuktikannya melalui Tugas. Siswa diharapkan dapat bersosialisasi dan melakukan kegiatan dalam Aktivitas Siswa. Buku ini diakhiri dengan Terapan Matematika yang merupakan penerapan materi dalam kehidupan sehari-hari, refleksi dari materi yang dipelajari dalam Refleksi. Tidak lupa ringkasan materi setiap bab dalam Rangkuman dan kumpulan soal-soal untuk mengulang pemahaman siswa dalam Mari Mengulang. Semoga buku “Pintar Bermatematika” ini bermanfaat bagi pembaca, khususnya siswa SD/MI kelas IV. Jakarta, Oktober 2008
iv
Bagaimana menggunakan buku ini?
Bab
1
Sifat Operasi Hitung Bilangan
Pendahuluan, merupakan pertanyaan pengantar anak untuk mempelajari bab tersebut dan tujuan pembelajarannya
Ilustrasi, mempermudah siswa dalam mempelajari materi
Di sebuah toko terdapat 30 dus mi. Tiap dus berisi 40 mi. Berapa bungkus mi yang ada di toko tersebut?
Latihan A. 1. 2. 3. 4. 5.
Isilah titik-titik di bawah ini. ... 8:9 = ... — ... 10 : 11 = — ... ... 12 : 15 = — ... ... 17 : 18 = — ... ... 19 : 20 = — ...
6. 7. 8. 9. 10.
... 21 : 13 = — ... ... =— ... ... 15 : 9 = — ... ... 16 : 7 = — ... ... 18 : 10 = — ... 12 : 7
B.
Kerjakanlah soal-soal berikut ini.
1.
Dina memiliki 7 kue berbentuk lingkaran. Ia ingin membagikan kepada 9 orang temannya dengan bagian sama besar. Berapa bagian kue yang diperoleh masing-masing temannya? Adi memiliki 2 pizza berbentuk lingkaran. Ia ingin membagikan kepada 7 orang temannya dengan bagian sama besar. Berapa bagian kue yang diperoleh masing-masing temannya? Rina memiliki 9 apel. Ia ingin membagikan kepada 7 orang teman sekelasnya dengan bagian yang sama besar. Berapa bagian apel yang diperoleh masingmasing teman Rina? Pak Darman memiliki 13 karung beras. Ia akan membagikan kepada 20 fakir miskin dengan bagian yang sama banyak. Berapa karung beras yang diperoleh fakir miskin? Yadi memiliki 15 potong roti yang sama panjang. Ia ingin memberi 10 orang teman bermainnya dengan bagian yang sama besar. Berapa bagian roti yang diperoleh masing-masing teman Yadi?
2.
3.
4.
5.
Melatih siswa setelah mempelajari subbab atau uraian yang disajikan terangkum dalam Latihan Siswa belajar sendiri untuk mengerjakan soal matematika dengan cara membuktikannya, lalu menyimpulkan di dalam Tugas
Tugas
1. 2. 3.
1.
Sebutkanlah sifat-sifat dari segitiga sama kaki. Sebutkanlah sifat-sifat dari segitiga siku-siku. Sebutkanlah sifat-sifat dari segitiga sama sisi.
Menemukan Keliling Segitiga Untuk menemukan rumus keliling segitiga, lakukan kegiatan berikut.
Aktivitas Matematika 1.
Sediakan selembar kertas karton, tali benang, dan jarum pentul. Kemudian, buatlah sebuah segitiga siku-siku pada kertas karton tersebut.
2.
Lilitkan benang mengelilingi sisi-sisi segitiga. Tahanlah benang pada satu pojokan menggunakan jarum pentul.
Siswa belajar untuk mengemukakan pendapat dalam berdiskusi sehingga persoalan matematika yang ada dapat terselesaikan dengan cara mempraktikkannya dalam Aktivitas Siswa
v
Terapan Matematika
Terapan Matematika, merupakan penerapan materi yang dipelajari dalam kehidupan sehari-hari agar siswa memahami kehidupannya tidak jauh dari matematika
Bangun jajargenjang dan segitiga dapat digunakan untuk membangun rangka bangunan. Contohnya, menara listrik tegangan tinggi (SUTET). Menara ini disusun oleh beberapa segitiga dan juga jajargenjang. Pernahkah kamu melihatnya?
Sumber: www.google.co.id
Sumber: www.google.co.id
Selain pada menara SUTET, bangun ini dapat digunakan juga untuk menopang jembatan besi. Di bawah jembatan, besi-besi disusun dalam bentuk segitiga dan jajargenjang.
Ringkasan materi yang telah dipelajari terangkum dalam Rangkuman
Rangkuman 1.
Jajargenjang memiliki keliling = (2 miring).
2. 3.
Luas jajargenjang = panjang alas tinggi Keliling segitiga = Jumlah panjang ketiga sisinya.
4.
Keliling segitiga sama sisi = 3
5.
1 Luas segitiga = — 2
alas
panjang alas + 2)
(panjang sisi
sisi
tinggi
Refleksi 1.
Temukanlah persamaan keliling dan luas jajargenjang berdasarkan caramu sendiri.
2.
Temukanlah persamaan keliling dan luas segitiga berdasarkan caramu sendiri.
3.
Sebutkan contoh lain yang merupakan penerapan segitiga dan jajargenjang dalam kehidupan sehari-hari.
Mari Mengulang, merupakan kumpulan soalsoal untuk mengulang pemahaman siswa pada bab yang telah dipelajari
Mari Mengulang Bab 2 A.
Isilah titik-titik pada soal berikut dengan singkat.
1.
Faktor dari 12 adalah 1, 2, …, …, …, 12.
2.
Kelipatan dari 8 adalah 8, 16, …, …, …, …, …, …, …, ….
3.
Terdapat dua kelipatan berikut: 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, … 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, … Kelipatan persekutuan dari 4 dan 5 adalah 20, …, ….
B. 1.
Berilah tanda (X) pada jawaban yang benar. Kelipatan persekutuan dari 2 dan 7 adalah …. a. 1, 2, … b. 1, 14, … c. 1, 21, …
2.
Faktor persekutuan terbesar dari 18 dan 14 adalah …. a. 2 b. 7 c. 14
3.
10, 20, 30, 40, …. Kelipatan di atas adalah kelipatan persekutuan dari .… a. 2 dan 5 b. 7 dan 9 c. 11 dan 14
70
vi
4.
KPK dari 20 dan 24 adalah …. a. 80 b. 120 c. 140
5.
FPB dari 12 dan 18 adalah …. a. 6 b. 8 c. 10
6.
FPB dan KPK dari 18 dan 48 adalah …. a. 6 dan 144 b. 8 dan 120
Refleksi, merupakan refleksi dari materi yang telah dipelajari pada bab tersebut
c.
10 dan 220
Pintar Bermatematika untuk SD/MI Kelas 4
Daftar Isi Kata Sambutan ........................................................................................... Kata Pengantar ........................................................................................... Bagaimana menggunakan buku ini? ............................................................ Daftar Isi ...................................................................................................... Bab 1
Bab 2
Bab 3
Bab 4
iii iv v vii
Sifat Operasi Hitung Bilangan A. Mengenal Sifat Operasi Hitung Bilangan ................................. B. Bilangan 1.000 sampai 50.000 ............................................... C. Perkalian Bilangan .................................................................. D. Pembagian Bilangan .............................................................. E. Operasi Hitung Campuran ....................................................... F. Penaksiran dan Pembulatan ................................................... G. Permasalahan yang Melibatkan Uang .....................................
2 16 25 31 36 39 45
Mari Mengulang Bab 1 ................................................................
51
Faktor dan Kelipatan A. Faktor dari Suatu Bilangan ...................................................... B. Kelipatan Suatu Bilangan ........................................................ C. Faktor Persekutuan Terbesar (FPB) ........................................ D. Kelipatan Persekutuan Terkecil (KPK) ..................................... E. Masalah yang Berkaitan dengan KPK dan FPB ......................
54 57 60 61 62
Mari Mengulang Bab 2 ................................................................
66
Pengukuran A. Sudut ...................................................................................... B. Waktu ..................................................................................... C. Panjang .................................................................................. D. Berat ....................................................................................... E. Permasalahan yang Berkaitan dengan Waktu, Panjang, dan Berat ................................................................................ F. Satuan Ukuran Kuantitas .........................................................
94 96
Mari Mengulang Bab 3 ................................................................
99
70 85 89 92
Jajargenjang dan Segitiga A. Keliling dan Luas Jajargenjang ................................................ 102 B. Keliling dan Luas Segitiga ...................................................... 107 C. Masalah yang Berkaitan dengan Keliling dan Luas Jajargenjang dan Segitiga .............................................. 114 Mari Mengulang Bab 4 ................................................................ 118 vii
Uji Kemampuan 1 ..................................................................................... 121 Bab 5
Operasi Hitung Bilangan Bulat A. B. C. D. E. F. G.
Mengenal Bilangan Bulat ......................................................... Membaca dan Menulis Lambang Bilangan Bulat ..................... Membandingkan Bilangan Bulat .............................................. Mengurutkan Bilangan Bulat .................................................... Penjumlahan Bilangan Bulat .................................................... Pengurangan Bilangan Bulat ................................................... Operasi Hitung Campuran Bilangan Bulat ...............................
124 125 127 128 129 135 139
Mari Mengulang Bab 5 ................................................................ 142 Bab 6
Bilangan Pecahan A. B. C. D. E.
Pengertian Pecahan dan Urutannya ........................................ Menyederhanakan Pecahan .................................................... Menjumlahkan Pecahan .......................................................... Mengurangkan Pecahan ......................................................... Menyelesaikan Masalah yang Berkaitan dengan Pecahan ......
146 156 160 163 166
Mari Mengulang Bab 6 ................................................................ 169 Bab 7
Bilangan Romawi A. Lambang Bilangan Romawi .................................................... 172 B. Mengubah Bilangan Cacah menjadi Bilangan Romawi atau Sebaliknya ...................................................................... 173 Mari Mengulang Bab 7 ................................................................ 176
Bab 8
Bangun Ruang Sederhana dan Hubungan Antarbangun Datar A. Bangun Ruang Sederhana ...................................................... 180 B. Jaring-Jaring Kubus dan Balok ............................................... 184 C. Benda dan Bangun Datar Simetris .......................................... 187 D. Pencerminan Bangun Datar .................................................... 193 Mari Mengulang Bab 8 ................................................................ 198
Uji Kemampuan 2 ..................................................................................... 201 Glosarium .................................................................................................. 203 Indeks ...................................................................................................... 205 Daftar Pustaka .......................................................................................... 207 Kunci Jawaban ......................................................................................... 209
viii
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ISBN 978-979-068-567-3 (no. jilid lengkap) ISBN 978-979-068-571-0
Harga Eceran Tertinggi (HET) Rp17.451,--