The document summarizes an interview with a 5th grade student about percentage problems. It discusses 3 problems given to the student of varying difficulty: 1) Finding 30% of bikes that are broken. The student correctly solved this as a fraction and percentage. 2) Finding the percentage of students in a class that are in a sports club. The student used a rectangle model to represent fractions and solve that 75% are in the club. 3) Finding a discount percentage on a bike priced at Rp600,000. The student struggled at first but eventually used a rectangle model to correctly solve that a 15% discount is Rp90,000.

1. The Way of Student’s Thinking
about Percentage Problems
By: Sari Saraswati
International Master Program on Mathematics Education (IMPoME) 2013
Sriwijaya University
Email: Sarisaraswati7@gmail.com

2. Introduction
The interview was conducted to know the
students’ thinking related with percentage.
The interview conducted in SD IBA
Palembang. The subject of this observation
is M. Dzar Alghifari who is one of students
grade 5 SD IBA Palembang. The problems
consist of three levels which are easy,
intermediate, hard.

3. Problem 1

4. Student’s Answer
3
10
30
100
=
= 30%
Jadi, persen
sepeda yang rusak
adalah 30%

5. Analyze Problem 1

Based on the student’s answer, it have been gotten that bikes
3
turned out represented by the fraction which is .
10

The student know that percentage is hundredth. Therefore, it
3
is , so that the student only changed the fraction become
10
percentage such that have been gotten

30
100
.
From the concept that had been gotten by the student, so
30
that the student presented that
equal to 30%.
100
So, the perncentage is 30%.

6. Problem 2

7. Student’s Answer

8. Analyze Problem 2

From the student’s answer, known that the student sum all of students in class such that had
been gotten 20 child in class.

The student used the rectangle to represent the fraction of the number in class.
Satu persegi panjang yang diarsir sebanding dengan 20 anak
¾ bagian persegi panjang yang diarsir sebanding dengan 15 anak
½ bagian persegi panjang yang diarsir sebanding dengan 10 anak
¼ bagian persegi panjang yang diarsir sebanding dengan 5 anak
1/20 bagian persegi panjang yang diarsir sebanding dengan 1 anak

9.  The
student explained that 20 child represent
100%.
 because a half of 20 is 10, so that the
percentage is 50% which is a half of 100%.
 Then, a half of 10 is 5, so that a half of 50% is
25%.
 Then, 5 child divide by 5 is 1, so a child
represent 5%.
 So, percentage of the children in class 5 a
member of a sports club is 75%.

10. Dialog the observer and student

Observer: Dua puluh itu apanya?

Alghi

Observer: He’em..terus?

Alghi
: Kalau semuanya dua puluh anak ikut, ada seratus persen. Tapi Kalau
hanya lima belas yang ikut.. tujuh puluh lima persen.

Observer: He’em

Alghi

Obserever

Alghi

Observer: Iya..terus?

Alghi
: Kalau sepuluh anak setengahnya. Kalau lima anak se per empatnya.
Kalau satu anak....sama dengan lima persennya.

Observer: iya..berarti kesimpulannya.. berapa persen yang termasuk dalam
kelompok yang suka sepak bola?

Alghi
: Dua puluh jumlah semua siswa.
: Karena dua puluh sama dengan....(siswa menulis)
: He’em
: lima belas...tiga per empatnya.
: Ada tujuh puluh lima persen.

11. Problem 3

12. Student’s Answer

13. Analyze Problem 3
The student explained that Rp. 600.000 represent 100%
 Then, he found a half of 100% is 50% so that a half of
Rp.600.000 is Rp. 300.000 which have to be paid.
 Then, a half of 50% is 25% such that a half of
Rp.300.000 is Rp. 150.000, so the number of money
which have to be paid is Rp.450.000 (Rp.300.000 +
Rp.150.000)
 Then, a half of 25% is 12.5 % such that a half of
Rp.150.000 is Rp75.000 so that the number of money
which have to be paid is Rp.525.000 (Rp.450.000 +
Rp.75.000)
 But, to find 15% of Rp.600.000, the student was
difficult.


14. 
The student used the rectangle to find 15% of Rp.600.000.

15. The dialogue between observer and student

Alghi
: Kalau seratus persen, berarti enam ratus ribu, jadi satu full. Setengahnya
tiga ratus ribu...seperempatnya...seratus li...

Observer : Tiga piluh ribu daa..dari?...tiga ratus ribu darimana?

Alghi

Observer : Dibagi..dibagi?

Alghi

Observer : Iya...terus kalau yang ini?

Alghi

Observer : Dari? siapa yang dibagi empat? Berapa yang dibagi empat?

Alghi

Observer : He’em..

Alghi

Observer : He’em..

Alghi

Observer : he’em..

Alghi
: Dibagi setengah..
: Dibagi dua.
: Dibagi empat..
: Satu dibagi empat. Enam ratus ribu dibagi empat.
: Jadi seratus lima puluh ribu.
: Sedangkan lima persen ini sama dengan satu per dua puluh.
: Satu per dua puluh.

16. 
Using the particular of rectangle, the student found that 5% of Rp.600.000 is
Rp.30.000.

Then, he multiplied 5% by 3 such that had been gotten Rp.90.000.

Therefore, the price of bike is Rp.600.000, while the discount is Rp.90.000, so the
total money that have been paid is (Rp. 600.000 – Rp. 90.000 equal to Rp. 510.000,-.

17. Thank You