1. Be careful when you retweet a story on Twitter or post something to Facebook because there's a real chance it's just a rumor or not even true. We saw this during Hurricane Sandy where people were quick to spread photos that they thought were of storm battered New York City but were actually intricate Photoshop jobs or of a different catastrophe.
2. Don't go immediately splashing links to the social media accounts of people that are named in the event until reputable news outlets have confirmed their identities. There are millions of people on Facebook with the same name so wait until somebody confirms that the guy wearing dark clothes in his profile picture is the same guy that shot up a school.
3. When the event is politically charged, like this one, be mindful of whether you want to engage in that discussion with friends and family in a public forum. If you go posting "Ban all handguns" as your status update it's all but guaranteed one of your Facebook friends will disagree. This can lead to uncomfortable fights with friends that you may not want to have. People sometimes forget that Facebook and Twitter can be read by everyone, too.
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