To help with the improvement of the high school math curriculum, a theoretical framework named DNR (Duality-Necessity-Repeated Reasoning) was employed in order to identify activities and appropriate methods for teaching certain concepts in high school math. These activities and methods were initially used experimentally by the first author in real high school math classes, and then during the final stage of the experiment, the concepts of Cartesian coordinate system and the display of lines within this system were presented to three classes of 9th graders while their regular teacher was observing and giving critical feedback. The collected data revealed that the designed activities and methods facilitated learning the presented math concepts to a greater depth and fill many gaps impeding learning within the current curriculum.