Purpose of this research is to discribe the proses of learning alternative through discovery learning model to improve the activity and results of learning mathematics subjests.This research is class action research (PTK). Subjects in this research were the fourth grade students of SD Muhammadiyah Sambisari Yogyakarta academik year 2016/2017 which amountes 28 students. While the object of this research is the activity and results of learning mathematics obtained from the aplication of discovery learning model. The result of this research showed that the activeness and the results of learning mathematic using discovery learning model has increased. This is shown based on the results of data analysis on pre cycle student's activity in classical is 27%. In the cycle I increased to 53%. In the cycle II the student's activity increased to 79,6%. Students learning results show an increase from pre cycle,cycle I, and cycle II. In the pre cycle 36% of students reach KKM. In the cycle I has increased to 57% of students reach KKM. In the cycle II has increased to 78,57% of students reach KKM. Based on the above research results can be concluded that the aplication discovery kearning model can improve the activity and students learning results of fourth grades students of SD Muhammadiyah Sambisari Yogyakarta.