Innovative models of teaching through research have broken the long-held paradigm that core chemistry competencies must be taught with predictable, scripted experiments. We describe here five fundamentally different, course-based undergraduate research experiences that integrate faculty research projects, accomplish ACS accreditation objectives, provide the benefits of an early research experience to students, and have resulted in publishable findings. The model detailed is the Freshman Research Initiative (FRI) at The University of Texas at Austin. While there are currently 30+ active FRI research groups, or "streams", we focus this report on five different chemistry streams in these four areas (organic, inorganic, analytical, and biochemistry) to demonstrate how general chemistry laboratory skills are taught in the context of these varied research disciplines. To illustrate the flexibility of the FRI model for teaching first-year chemistry, we show how each stream teaches students three different skills within the context of their research: making (synthesis), measuring (UV-vis spectroscopy), and characterization. As a unifying example, all five chemistry streams describe using UV-vis spectroscopy to characterize new synthetic molecules, complexes, and compounds, followed by extensive quantitative collection, processing, and analysis of experimental data sets. The FRI model allows full integration of training in mandatory and accredited general chemistry skill sets with open-ended research experiences with unexpected outcomes in undergraduate science curricula. In turn, this model enables undergraduates to be productive contributors to new knowledge and scientific discovery at the earliest levels of the undergraduate experience.