This study aims to determine to determine the effectiveness of discovery learning and inquiry learning learning models on students’ on critical thinking skills in the fifth grade mathematics subject in elementary school. This research is a quasi-experimental research using a research design that is The Static-Group Comparison. Population used by tifth grade elementary school students in the Pattimura. cluster. Sampling with non-probability sampling technique which is purposive sampling type. The sample used were the fifth grade students of SD Negeri Wonorejo 01 as the experimental class 1 which amounted to 36 people and the tifth grade students of SD Negeri Wonorejo 04 as the experimental class 2 whitch amounted to 36 people. So the number of all samples used is 72 students. This research method uses observation and tests. The two elementary schools used as research were experimental group1 and experimental group 2. Eksperimental group 1 uses the treatment with discovery learning model while the experimental group 2 uses inuiry learning model. Based on the results of this study indicate that the average value of critical thinking skills in the experimental class 1 is 66,41 while the experimental class 2 is 58,55. T test result t count of 2,889 and sig. (2-tailed) 0,005 with sig. (1-tailed) 0,0025 and a df of 70. Value on probability < 0,05 then Ho is rejected and Ha is accepted. So it concluded that the application of the discovery learning, learning model is significantly more effective than the inquiry learning model on critical thinking skills of fifth grade subject in elementary school students. Keywords : Discovery Learning, Inquiry Learning, Critical thinking skills, Mathematics