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The purpose of this study was to determine whether there is any difference between students' mathematical representation ability who were taught by using the learning model of Project Based Learning with students who were taught by Guided Discovery Learning; there is any difference in the students' mathematical representation ability based on high, medium, or low learning motivation categories, and there is an interaction between the learning model and the learning motivation toward mathematical representation ability. A quasi experiment was used with 2x3 factorial designs. Instrument used to collect data was mathematics test and learning motivation questionnaire. The hypothesis testing used two way analysis of variance with unequal cell. Based on the results of hypothesis testing, it can be concluded that there is a difference in the students' mathematics ability that was taught by using Project Based Learning model with students who were taught by sing Guided Discovery Learning model; there is a difference in the students'mathematical representation ability based on high, medium, or low learning motivation; and there is an interaction between the learning model and the learning motivation on the mathematics ability. [ABSTRACT FROM AUTHOR]