Student Worksheets (LKS) are an interactive bridge between teachers and students, this is also related to measuring student learning outcomes. The use of worksheets affects the level of effectiveness in working on test questions. Stimulating students' cognitive critical thinking can be obtained, including from learning mathematics with the right approach method. One of the students' learning goals is to be innovative and creative in solving problems with solutions. The aim of this research is to develop a LKPD (Learner Worksheet) model of discovery learning assisted by a live worksheet to make it more effective and efficient and have the potential impact of growing students' cognitive level of critical thinking. The research method used is a design research model which is divided into two parts, namely preliminary (preliminary study and LKPD-Liveworksheet design) and formative evaluation including self-evaluation, prototyping (expert review, one-to-one, and small groups) research field tests as well revision. Research data was analyzed quantitatively and qualitatively. The research results show students' critical thinking abilities for Liveworksheet LKPD teaching materials with exponents and logarithms in the "Legal" and "Easy" categories according to experts and practitioners. The results of the research show that the LKPD developed is feasible, effective and influences students' critical thinking skills using the discovery learning model. The activities in this research have resulted in a product being developed in the form of a critical thinking worksheet using a discovery learning model assisted by a live worksheet which creates productive learning.