beberapa soal konteks kabupaten Pemalang

 ini saya bagi beberapa soal koteks yang berkaitan dengan number, statistika, dan geometry. semoga bermanfaat

   1.       Bu Ani sudah sepuluh tahun ini berjualan kamir khas kota pemalang. Bu Ani selalu mengemas kue kamir dalam kotak makanan. Tahun ini Bu Ani akan membuat terobosan dalam mengemas kue kamir. Kotak makanan yang biasanya terbuat dari kertas diganti dengan menggunakan bahan yang transparan sehingga kue-kue yang disusun di dalamnya terlihat dengan jelas.

Pak Bambang, guru kelas 5 SD N 02 Banjardawa, membeli sebuah kotak kue kamir ini dan memamerkannya di hadapan kelas. Pak Bambang meminta siswa untuk menebak banyaknya kue kamir yang ada dalam kotak tersebut tanpa mengeluarkan kue itu dari kotaknya. Pak Bambang hanya memperbolehkan siswa untuk mengamati kotak itu saja.

Nah, di bawah ini adalah gambar hasil pengamatan Dika, salah satu siswa yang diajar oleh Pak Bambang.

Tampak depan

tampak samping

tampak atas

Nah, dengan bantuan gambar Dika di atas, dapatkan kalian tebak berapa banyak kue kamir yang ada dalam kotak yang dibawa pak Guru.

   2.  Setiap hari selasa atau jum’at kliwon bulan muharram tiap tahunnya, di Pemalang diadakan sebuah festival sedekah laut atau yang lebih dikenal dengan nama ‘Baritan’. Dalam tiap tahunnya ada banyak kapal yang ikut serta dalam festival ini. Akan tetapi, tidak semua kapal ikut melaut untuk melarung persembahan ke laut. Berikut adalah data yang diperoleh dari dinas pariwisata kabupaten Pemalang berkaitan dengan jumlah kapal yang ikut memeriahkan Baritan.

Data Partisipasi Kapal dalam Baritan

Dinas Pariwisata Pemalang

(bukan data sebenarnya)

Tahun	Jumlah Kapal yang berpartisiapsi Baritan	Jumlah kapal yang melaut sewaktu baritan
2008	20	15
2009	25	22
2010	29	21
2011	28	20
2012	27	19

Berdasarkan data pada tabel di atas, tentukan

a.       Rata-rata jumlah kapal yang berpartisipasi pada tahun 2008-2012

b.      Rata-rata jumlah kapal yang melaut sewaktu baritan pada tahun 2008-2012

c.       Pada tahun berapakah, kapal berpartisipasi dalam baritan memiliki jumlah paling banyak

    3.   Untuk membuat sebuah kain lurik, pengrajin diharuskan untuk menenun benang dengan urutan tertentu agar bisa menghasilkan kreasi warna yang indah.

Perhatikan gambar kain lurik di samping

Gambar tersebut merupakan bagian dari sebuah kain lurik

Dari data urutan benang yang dimiliki tentukanlah benang warna apa yang digunakan perajin pada urutan benang ke:

a.       90

b.      253

 



untuk versi bahasa inggris dari soal ini akan saya upload di postingan yang lain.
Semoga bermanfaat..
^_^

bermain logika permainan matematika

Terkadang merasa jenuh dengan pembelajaran di kelas? atau bingung memberikan alternatif permainan pada anak yang tidak hanya menyenangkan tapi juga edukatif? ini saatnya, anda untuk mengenal lebih jauh permainan yang cukup membuat adiktif tapi tetap edukatif.

TAHUKAH ANDA?

Ada berbagai macam permainan lain yang bisa dipakai guru dalam melatih logika dan kemampuan siswa dalam menemukan jalan keluar. Permainan-permainan ini bisa dipakai guru sebagai proses ice breaking yang bisa mengalihkan sejenak kepenatan siswa setelah belajar dalam jangka waktu panjang. Guru juga bisa memodifikasi permainan sehingga bisa cocok dimainkan dalam kelas.

Berikut ada beberapa permainan yang bisa dipakai guru atau orang tua sebagai alternative permainan melatih logika untuk siswa-siswanya atau anak-anaknya. Namun, lebih dari itu permainan ini terbuka bagi siapa saja yang ingin menikmatinya.

dalam post ini saya akan membagi dua dari beberapa permainan logika yang tidak hanya menyenangkan tetapi juga melatih daya nalar siswa (anak). Let's see then..

1. Sudoku

Siapa yang tak kenal permainan yang satu ini?

 Permaian ini sudah cukup familiar di Indonesia, bahkan banyak surat kabar yang menyediakn permainan ini sebagai salah satu teka-teki di koran edisi akhir pekan. Fakta bahwa Sudoku cukup terkenal di Indonesia, terlihat ketika kita memasuki toko buku besar, di sana banyak dijual buku permainan mengasah otak ini 

Permainan yang berasal dari negeri sakura ini termasuk dalam permainan board yang menggunakan grid  layaknya buku kotak-kotak matematika. Tentu bukan sembarang ukuran yang dipakai, ukuran grid yang dipakai bervariasi menurut tingkat kesulitannya, tetapi umumnya menggunakan grid 9 x 9. Grid besar itu juga dibagi dalam kotak-kotak (grid) yang lebih kecil yang berukuran 3 x 3.  

Sebenarnya inti permaian Sudoku mudah, pemain hanya diminta untuk memasukkan bilangan 1 - 9 ke dalam kotak yang telah disediakan. Nah, tantangannya adalah aturan dalam memasukkan bilangan tersebut. Ketentuannya pemain tidak boleh menempatkan yang sama dalam baris (mendatar), kolom (menurun), dan kotak yang sama.

Sebenarnya ada banyak jenis Sudoku yang akan saya bahas di post yang lainnya. Untuk dapatkan beberapa soal Sudoku yang saya ambil dari math in English silahkan klik Sudoku Link

Untuk mendapatkan versi printable Sudoku ada banyak alamat yang bisa dikunjungi, antara lain Math in English, Daily Sudoku,

Sedangkan untuk tahu lebih jauh cara bermain Sudoku bisa dilihat tutorial youtube

2. Kakuro

Permainan ini cukup berbeda dengan Sudoku, persamaannya hanya karena kakuro memiliki grid juga dan memasukkan bilangan 1 – 9 dalam grid-grid itu tadi. Permainan kedua ini sangat cocok dimainkan di dalam ruang kelas, karena permainan ini melibatkan aritmatika yaitu penjumlahan dan perkalian. 

Permainan ini bisa dikatakan mirip dengan permainan teka-teki silang dengan menggunakan petunjuk untuk soal mendatar dan menurun. Setiap grid mendatar atau menurun bsisa berisi petunjuk ataupun kotak kosong yang harus diisi sesuai dengan petunjuk.

 Petunjuk yang ditulis di bawah garis diagonal dipergunakan untuk mengisi kolom di bawah bilangan itu, sedangkan petunjuk yang ditulis di atas garis diagonal dipergunakan untuk mengisi baris di samping bilangan itu. Pengerjaan petunjuk didasarkan pada jenis kakuronya, penjumlahan atau perkalian. Contoh, untuk kakuro penjumlahan, dalam petunjuk tertulis 4, maka jawaban bisa 1 dan 3 atau 3 dan 1.

Oh ya, setiap bilangan antara 1- 9 hanya bisa diisi sekali, jadi untuk petunjuk 4, tidak boleh diisi dengan 2 dan 2. 

Untuk mendapatkan beberapa contoh kakuro dari math in English dan crazy dave silahkan klik Kakuro Link

Untuk mendapatkan versi printable kakuro lain silahkan kunjungi Math in English, kakuro.com, krazydad.com

Untuk video pelatihan silahkan buka tutorial_Kakuro

Untuk Sementara dua permainan dulu ya yang dibahas, tunggu postingan berikutnya tentang permainan matematika ini. ^__^

 

pemecahan soal 1^2001+2^2001+3^2001+4^2001+ …+2001^2001

beberapa hari yang lalu seorang teman menanyakan soal ini kepada saya. berikut soalnya

kebetulan setelah mencari-cari ketemu juga jawaban soal ini. jawabannya sudah saya tulis dalam bentuk ppt (slide power point). berikut tautannya kunci jawaban.

Problem solving masalah 1^2001+2^2001+...+2001^2001 from hsenja

semoga postingan ini bermanfaat. ^__^

my first experience PMRI teaching

here i will give you one of my experiences in teaching PMRI. though this design may be not perfect, i hope it will help teachers to have alternative way in teaching factor and prime number.

Background

For some students mathematics becomes something that very frightening and frustrating. They thought mathematics not only was very hard to understand but also need to be memorized so that they can get a better mark.

Prime and factor of a number were one of materials that student could not grasp the real meaning behind it. Even months after they were taught this material, they easily forget about the prime numbers or the factor of a number. 

Characteristic of RME

There are 5 characteristics which have to be consulted when one design the instructional activities in teaching and learning. Those characteristic are:

    1.      The use of context in phenomenological exploration

As prime numbers and factors are hardly seen in daily life except for their application in cryptography, the concept of these materials should be brought to mathematics land. Of course the concept should be close and quite realistic for students. In this case, the concept of those two come from multiple, a material that students already know and I believe they know the meaning of that material.

   2.      The use of models for progressive mathematization

Models are used as a bridge from concrete level to a more formal level. In this case the students will be brought to understand the concept of the material by experienced the multiplying numbers. Then in the end of this process student will be able to understand the notion of prime numbers and factor of a number.

  3.      The use of students own construction and production

In the activity, the students are given the opportunity to solve some problems by themselves. They have the chance to solve the problem in their own strategies. In the end of this activity, there will be a class discussion to choose what the most efficient way to solve the problems is.

   4.      The interactivity in teaching process

The activities in the teaching process are designed so that students can take a part in solving a problems or finding the meaning of the materials. Teacher in the class will be a facilitator that will support and help the students to understand. 

    5.      The intertwining of various mathematics strands or units

The sequence of instructional activities not only emphasizes the meaning of factor and prime and strategy to solve the problems, but also stress the relation between factor and prime number and to multiple numbers.

 HLT

There will be a sequenced of activities that designed in a way to reach the aim of the lesson. The activities will be describe in table below

Activity	Goal	Description of activity	Conjecture
Working with multiple	-    Student can relate factor of a number and the multiplication -    Students understand the prime number is the number which have exactly two factors	-   Teacher provides a teaching aid (related to multiplication of a number) where the student will use that. -   Teacher provides a student worksheets to guide the students understand about the materials	-     Some student will easily find the multiplication using their memory of it -     Some student will count the boxes in teaching aid so that they can get the multiplication product -     Some student will use a paper and a pencil to count the multiplication
Working with prime number	-    Student can find a strategy to determine whether a given number is a prime number	-   teacher will provides a problem where students should solve related to determine a number whether it is prime or not -   two groups will present their solutions	-     Some students will try to find a multiplication to get the number. -     Some students will get the answer by divide the questioned number by numbers that they guess

Result and analysis

In this part of report, there will be a comparison between HLT and the actual teaching learning process.

Activity 1

In this first activity, the teacher presented a teaching aid that will help the students to grasp the meaning of factor and prime numbers.

The teacher let the students to stick the sticker in the board in terms they should stick it in the multiplication of the number in the sticker. Students do this activity until all of the stickers run out.

Every time students stuck a number, teacher reminded the students what is the multiplication of that number.

In this activity, most of students did not have any problems with multiplication of numbers under 11. Most of them can easily find which number is a multiplication of a particular number. However, some of students are still have a difficulty in multiplication fact. This quite became obstruction in the teaching learning process.

 

For numbers more than 12 most of students counted the number of the boxes in the teaching aid. However, some student tended to be incorrect when they counted the boxes, so there were some stickers which were misplaced.

After finishing the teaching aid, teacher asked the students to look at the stickers as those stickers have a particular name that is factors of number in the box. Then teacher asked the students what is the meaning of those. There are some idea came from students one of them even see that if the two of numbered sticker multiplied then the product will be the number in the box.

As for the prime numbers, teacher give hints to the students that the number which has only 2 stickers. And students have no difficulty to see which number is prime number and which one is not. And they could see that factor of prime numbers consist of 1 and other number.

It is believed that students can distinguish which number is prime and not. Even, the students understand that 1 is not prime and they also can mention numbers within 1-42 that are include in prime numbers.

Unfortunately, the second activity is not done yet. Because the time is ended before all the activities were done.

Conclusion

Most of the students can distinguish a number whether prime number and not. However, for the numbers higher than 42, it can be known yet. The evaluation should be assessing first so that the result could be assured.

for the pdf version (english-indonesia) could be found  here

new approach of angle areflection to a paper

Title: Developing a Local Instruction Theory for Learning the Concept of Angle through Visual Field Activities and Spatial Representations by Bustang

One of the materials which students tend to have misunderstanding is angle. Even when students could distinguish the name, some of them still have difficulty when come to draw the angle. This situation is happened to some of my students back then in my working place. They can name the angle, but they did not have the right concept of those angle. They cannot fathom the meaning behind those angles.

This paper will tell us about learning activities (HLT) which worth to try by teachers when teaching angle. However, because this design research creates only a local instructional theory, the HLT should be modified so that it would suitable for other classroom.

There were 4 main activities that Bustang developed, to make the students mastering angle. This reflection paper would only describe those activities in general. When one needs to find more information about those activities, one just has to look up in the actual paper.

The first activity proceed was a spatial representation task “Now you see it, now you don’t” where the student investigated the real situation represent vision line and blind spot. The second activity was constructing vision lines and blind spot while the third and fourth were coloring the blind spot and constructing angle of vision.

According to the researcher the notion of angle was emerge when students draw the vision lines resulted from some observations. However, the researcher also found that even when students can remember what they experienced in the field activities did not guarantee they would be able to construct the abstract concept of the materials. Students also still carry a misconception of the angle’s size which related to the length of the arms. In the end, the researcher suggest to adding an activity which will make students ease this misconceptions by focused in validating the results of angle’s measurements.

To sum up, what way teachers choose to make their students understand was simply an easy pick. There were lot of research where teachers welcome to modified, so that they did not need to think of the activities plan from the very beginning.

link to get the paper click here