American Regions Mathematics League (ARML), https://www.arml.com
MathWorks Math Modeling Challenge, https://m3challenge.siam.org
Art of Problem Solving, http://www.artofproblemsolving.com
Purple Comet Math Meet, https://purplecomet.org
Crux Mathematicorum, the problem-solving journal of the Canadian Mathematical Society, is online for free: https://cms.math.ca/publications/crux/.
Competitions
The American Mathematics Competition
The High School Mathematical Contest in Modeling
The Siemens Westinghouse Competition in Math, Science & Technology
Summer Programs
Link to the careers in mathematics page of the AMS
We need many more opportunities for students to participate in meaningful mathematics activities. Please send suggestions to David Stephens.