Is there anything natural that I can use to melt ice besides rock salt?

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My husband bought a bag of rock salt at wal-mart. We had a piece of rock on our sidewalk about 4 ft x 4 ft that was solid ice. Instead of sprinkling a little bit on it at a time he dumped the whole 25 pound bag on the ice. Everyone has been tracking it in on the rugs and carpet. Its horrible. I vacummed 7 times yesterday and already 3 times today. I'm tired of cleaning it up. I have two children one who is crawling around and puts everything in his mouth so that is why I am making sure to clean up every drop of salt that gets tracked in. I dont think it would be good for him to ingest any. Is there any alternative to using rock salt that you can think of? I know that if you have dogs and they get rock salt on their paws and lick the residue off after they step on it then they can become really ill so I guess it is toxic.