In Lyddie, what is one example of symbolism in Chapters 1 through 10?

An obvious symbol throughout the book Lyddie is the bear that Lyddie stares down in chapter 1 and which she remembers often. Lyddie's encounter with the bear represents her ability to deal successfully with challenges and danger.

Another interesting symbol occurs in chapter 4. When Lyddie starts working at the tavern, she gets to know Tryphena, the cook. As Lyddie churns butter one day, Tryphena tells her the story of two frogs who fell into...

An obvious symbol throughout the book Lyddie is the bear that Lyddie stares down in chapter 1 and which she remembers often. Lyddie's encounter with the bear represents her ability to deal successfully with challenges and danger.

Another interesting symbol occurs in chapter 4. When Lyddie starts working at the tavern, she gets to know Tryphena, the cook. As Lyddie churns butter one day, Tryphena tells her the story of two frogs who fell into the pail of milk. One drowned immediately, but the other one kept kicking and kicking until it formed a pat of butter on which it could float. Tryphena explains the symbolism of the story: "Some folks are natural born kickers. They can always find a way to turn disaster into butter." The first frog could represent Lyddie's mother, who gives up on life after her husband leaves the family. The second frog represents Lyddie, who doesn't give up and works with all her might to save her family's farm and to try to make a better life for herself and her siblings. 

The frog story brings to Lyddie's mind the private joke between Lyddie and Charlie: "We can still hop." Their mother had written to them with her incorrect spelling, meaning to say, "We can still hope," but instead writing, "We can still hop." Lyddie's mother's approach, to hope vainly without "kicking," results in her drowning in her grief. But Lyddie, like the frog, can still hop. She kicks and takes action, and that keeps her afloat until her life improves. 

When Charlie comes to visit Lyddie, she finds little to talk about. After he leaves, she wishes she had told him about the frogs. Connecting Charlie with the frog story symbolizes that he, too, will survive because, like Lyddie, he can still hop.