In chapter ten of To Kill a Mockingbird, what does Atticus do that makes him a hero to his children?

Atticus's children are impressed when he shoots a rabid dog with one shot.

Atticus’s children do not find him very impressive. To them, he is “nearly fifty” and feeble. He does not play tackle football with Jem. They find themselves wishing for a younger father, or at least a more interesting one.

Besides that, he wore glasses. He was nearly blind in his left eye, and said left eyes were the tribal curse of the Finches....

Atticus's children are impressed when he shoots a rabid dog with one shot.

Atticus’s children do not find him very impressive. To them, he is “nearly fifty” and feeble. He does not play tackle football with Jem. They find themselves wishing for a younger father, or at least a more interesting one.

Besides that, he wore glasses. He was nearly blind in his left eye, and said left eyes were the tribal curse of the Finches. Whenever he wanted to see something well, he turned his head and looked from his right eye. (Ch. 10)

It takes a major event for the children to realize that Atticus is not worthless after all. When he gets them guns for Christmas, he tells them to only shoot cans and not mockingbirds. He also tells them never to aim their guns at people when he catches them aiming at Miss Maudie. He is not very excited about the guns, but is only bowing to the inevitable. Every Southern child learns to shoot!  

However, Atticus can shoot a gun remarkably well himself when he has to. One day a rabid dog named Tim Johnson threatens the town of Maycomb. Heck Tate, the sheriff, gives the gun to Atticus because Atticus is a better shot, and the dog needs to come down with one shot.

Atticus shook his head vehemently: “Don’t just stand there, Heck! He won’t wait all day for you—”

“For God’s sake, Mr. Finch, look where he is! Miss and you’ll go straight into the Radley house! I can’t shoot that well and you know it!” (Ch. 10)

Atticus first objects that he has not shot a gun in thirty years, but he is still One-Shot Finch. He shoots the dog in one shot and ends the danger to the town. His children have an enormous newfound respect for him. Their father is not boring after all!

The dog is symbolic. Atticus is the only one that can shoot it, just as he is the only one who can take Tom Robinson’s case. While Atticus does not win the case, he does make people stop and think. In doing so, Atticus makes some headway against killing what really threatens Maycomb—racial prejudice.