There is an international competition for high school students each July called the International Mathematical Olympiad. The competition rotates to a different country each year. The United States won the competition in 2016 when it took place in Hong Kong This year the competition is in Romania. It will Travel to the United Kingdom in 2019 and the Russian Federation in 2020, before coming to the United State in 2021.
For two-year college students the American Mathematical Association of Two-Year Colleges (AMATYC) puts on an annual competition through its AMATYC Student Math League.There are both school and individual winners recognized. West Valley College has won five of the past six competitions.
The Mathematics Association of America also hosts an annual team competitions for middle and high schoolers called the American Mathematics Competition (AMC)
There are dozens of such competitions nationally and internationally. Here’s a sampling:
There are also ways opportunities to include Olympic sports in math lessons. These could be used your Math for Elementary Teachers course or adapted for developmental math students.