Partnerships for Progress and Prosperity Act or the P3 Act This bill requires the Department of Education (ED) to award grants to local educational agencies (LEAs) and institutions of higher education to improve students' education in science, technology, engineering, and mathematics (STEM). Each grantee shall partner with an employer in a STEM field to assist students in obtaining internships or apprenticeships, develop STEM coursework curricula and metrics, carry out dual-credit courses, provide tutoring and mentoring, enable students and teachers to attend STEM events outside of the classroom, provide after-school and summer STEM programs, and purchase educational materials or equipment to facilitate STEM instruction. In awarding grants under the program, ED shall give special consideration to applicants that promote in-classroom engagement between STEM professionals and students; use technology-based instructional materials and content; pair mentors and tutors with students struggling to meet curriculum benchmarks; in the case of LEA applicants, serve schools in which most students are eligible for free or reduced-price lunch; and propose to use grant funds to target interventions for populations that are traditionally underrepresented in STEM fields, including women, minorities, and low-income students. Each grantee shall provide matching funds equal to 50% of the grant amount.