Participating in athletic activities is a great way to stay fit and to socialize. Staying fit and socializing are good for your health. Reducing the needs healthcare by exercising is an important part of living sustainably. Sports even have an important role in achieving global sustainability. So, participate in activities that limit your risk of injury.
The biggest issue with participation in athletic activities is the impacts of travel to and from activities and events. If you are driving your hybrid car a few miles to get to a bike trail because the roads aren't bike friendly, you should keep doing what you are doing. If you are making a 50 mile roundtrip in a large truck to take a 3 mile run, you could find a better balance between your activities and sustainability. Also, consider that there are a lot of great aspects of youth athletics, but, you should balance what you have your kids do with how much travel is required to do it.
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