Math modeling for high school students is a nice pathway to build up analysis and problem solving skills. For instance, the COMAP High School Math Modeling Competition allows small teams of students two weeks to try and develop a viable, reasonable solution to an open-ended, complex, real-world problem. This is unlike typical math problem solving in school, and allows students to break free with a wonderful challenge that requires their creativity and skills in numerous STEM areas. They also have the experience of doing some technical writing. So many of the skills students can develop and grow with these experiences only enhance and help with science research. Encourage students to try this. Another opportunity is the MathWorks Math Modeling Challenge.
