The purpose of this study is to describe the steps for planning a project-based learning (PjBL) model in teaching Mathematics in grade X in the global context of Globalization and Sustainability and describe how students' mathematical reasoning abilities are after experiencing learning using the PjBL model. The type of research used in this research is design research. In this study, researchers designed a hypothetical learning trajectory (HLT) to teach Mathematics using the PjBL model in the context of planning to build a house. The stages of the research carried out were making the initial design, conducting design trials, and conducting retrospective analysis. The research subjects were six grade X students of private high schools in Yogyakarta who used the IB (International Baccalaureate) curriculum. The data collection instruments used by the researcher were field note sheets, written test sheets in the form of worksheets containing project questions, and structured interview sheets. From this study, the results obtained were that five students were able to use mathematical reasoning to complete the construction planning project of a house. Four students have been able to check the correctness of the solution and make conclusions.