There are various synonyms for the phrase "draw a map," depending on the context and purpose of creating the map. One synonym is "cartograph," which refers to the practice of creating maps that are used in scientific research and exploration. Another synonym is "chart," which is often used in the context of nautical navigation. Additionally, the phrase "plot a course" can be used when creating a map that is intended to guide travelers or hikers. "Sketch out" may also be used when creating a quick and informal map. Ultimately, the synonym used for "draw a map" depends on the intended purpose and the level of detail required.