Education aims to foster a variety of potential which exists in human, including the potential to solve any problems, involving solving mathematical problems. This study aimed to describe students’ problem-solving skills during mathematics learning about social arithmetic through Problem-Based Learning (PBL) model. The subjects of this research were 32 Year 7 students in Banda Aceh. This study used a qualitative descriptive approach. Data collection was conducted by problem-solving skills test and interview. The interview data were analysed descriptively, while the data of the test results were analysed based on the assessment guideline of students’ problem-solving skills. It was found that students’ mathematical problem-solving skills through PBL model were already classified as good. High-achieving students of problem-solving skills solved the problem by understanding the problem, planning the solution, doing the solution and rechecking it. Middle-achieving students of problem-solving skills solved the problem by understanding the problem, planning the solution and doing the solution without rechecking it so they get incorrect results. Low-achieving students of problem-solving skills solved the problem by understanding the problem and planning the solution, yet they presented the incorrect solution and did not recheck it. PBL model can be used to improve students’ problem-solving abilities.

Fraction is one of the important topics in learning mathematics. However, it is still challenging for students. Lack of students’ mastery of the prerequisite topics might be one of the potential causes. For this reason, this study aims to: 1) Investigate whether students’ mastery of fractions and prerequisite topics in the 7th grade of a junior high school in Banda Aceh, Indonesia has reached the minimum learning mastery standard and 2) Investigate the relationship between students’ mastery of fractions and their abilities to understand the prerequisite topics in the 7th grade of a junior high school in Banda Aceh, Indonesia. This study used a quantitative approach. Data were collected from 50 students selected randomly from all of the 7th grade students in the junior high school. The results showed that the students’ mastery of fractions and their abilities to understand the prerequisites has achieved the minimum learning mastery standard. Also, there is a significant relationship between students’ fractions mastery and their abilities in the prerequisites. Finally, the lack of students’ mastery of the prerequisites resulted in students’ beliefs that the concept of fractions is difficult.