Fraction magnitude addresses an important concepts and skills to study fractions. Understanding concepts of fraction magnitude is necessary and inevitable steps of mastering fractions. Some difficulties in comprehending fractions may affect students’ beliefs to learn mathematics in advanced level. Indeed, it is important for students to have understanding of fractions magnitude correctly. One way is through magnitude estimation. Every student has different strategies for solving the mathematics problem. Those strategies may indicate how comprehend students understanding, for instance, in estimating fractions.

This study examined students’ strategies in estimating fractions based on fraction magnitude knowledge. The sample was the students of VII^B class of the Unesa’s Labschool, consisted of 20 boys and 8 girls. All students had to complete a diagnostic’s test which was the fraction estimation test. There were 9 students with the high ability in estimating fractions, 8 students with medium ability in estimating fraction, and 11 students with low ability in estimating fraction. Three volunteer students with high ability in estimating fraction who had different and interesting strategies were chosen as our respondents. The semi-structured interview was utilized to investigate the process and students’ conceptual of fraction magnitudes.

The strategy used by the high ability subject was firstly changing the fraction into equivalence fraction and converting a fraction into decimal. He was able to check and estimate the magnitude of fraction. He applied correctly and fluently procedures. For example, in estimating 110/321, he divided 1000 by 321 to find the equivalent fraction with 1000 basis. He had chosen 1000 basis because 321 was between 100 and 1000. After obtaining the equivalent fraction, it was converted into decimal to know the magnitude of fraction in the line number. Moreover, he also explained the used procedure correctly. It showed that he understood a fraction as a number.

The strategy implemented by the medium ability subject was by dividing a whole into parts, and apportioning into smaller parts to estimate fractions. For instance, he started to estimate 1/6 by dividing 1 by 2 and obtained ½, then divided ½ by 2 and resulted  ¼. He employed that strategy until he found the magnitude of 1/6 in the number line. Although he was able to check the fraction magnitude, but he was to estimate fraction magnitude incorrectly. He stated that his strategy was based on the concept of fraction, which is whole-part. He faced still some difficulties in procedural knowledge. Moreover, he was fluent in estimating unit fraction.

The low ability subjects began by converting fraction into decimal form. He had estimated 84/216 by divided 84 with 216 and obtained a decimal number. He was able to check and estimate the fraction magnitude. He just applied the procedure without understanding the used procedure. He had low understanding of fraction conceptual knowledge.

This study emphasized that the strategy which used by the high and low ability subjects referred to the concept of equivalence fraction and converting fraction into decimal number. Moreover, the strategy used by the medium ability subject was by applying the concept of whole-part, but he was fluent in estimating unit fraction only. For further study, there is need to categorize the logical stage of students’ strategy in estimating fractions.