Raman spectroscopy, a powerful vibrational spectroscopic technique widely used in chemistry, materials science, and environmental analysis, provides critical molecular insights through spectral fingerprints. However, undergraduate students often lack proficiency in optimizing experimental parameters, interpreting vibrational modes, and applying chemometric tools to real-world samples. To address this gap, we designed a problem-based learning (PBL) laboratory course for chemical engineering students in a Polymeric Materials curriculum. Participants analyzed microplastics--an emerging environmental contaminant--using Raman spectroscopy to identify polymer types, assign functional groups, and correlate spectral features with material properties. Students employed principal component analysis (PCA) to classify polymer spectra and visualize results through score plots, integrating hands-on instrumentation with computational data analysis. This inquiry-driven experiment achieved educational outcomes including enhanced technical skills in Raman parameter optimization and spectral interpretation, proficiency in chemometrics for material classification, and heightened critical thinking through authentic environmental problem-solving. This practical framework bridges fundamental spectroscopy, materials science, and data analytics, preparing undergraduates for interdisciplinary research.