What happens in chapters 1-6 in The Devil's Arithmetic?

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The story begins in the present on the first day of Passover in America. Hannah, a twelve year old girl, is complaining to her mother about having to attend the Seder dinner at the home of her grandparents. Hannah is embarrassed and annoyed by the way that her grandparents insist on remembering the past. Even though Hannah's mother reminds Hannah that both of her grandparents lost family during the Holocaust, Hannah is unmoved.

When they arrive at her grandparents, Hannah talks with her favourite aunt, Aunt Eva. Eva lives with her brother who is Hannah's grandfather, and she also helped raise Hannah's father. We are told that Hannah was named after a dead friend of Eva's.

Later on, Hannah is told to open the front door to the prophet Elijah and symbolically welcome him in as part of the ritual of celebrating Passover. However, when Hannah does this, she finds herself in a different time and place. She is in an old-fashioned kitchen and she is addressed by a woman in old-fashioned clothes as "Chaya" in Yiddish, which Hannah is surprised to discover that she understands perfectly.

Hannah is understandably confused and scared but thinks this must be a dream or game, and so plays along with it. A man enters saying he is Hannah's uncle Shmuel, and we learn that the woman in the kitchen is Gitl, his sister. Shmuel is going to marry a woman from another village called Fayge the next day. The three eat and Hannah goes to sleep.

Hannah wakes up and finds herself still in the same place. She tries to tell her truth, but Gitl and Shmuel treat it as a joke. Gitl tells Hannah that she arrived two days before from Dublin to recover from the same disease that killed her parents. The three soon leave for Shemuel's wedding and Hannah befriends some of the girls from the village.