One example of Lizabeth acting childish is during the beginning of the story. Lizabeth, her brother, and a couple of friends decide to go and taunt Miss Lottie, an old lady nearby who plants marigolds in her yard. Going and being mean to the elderly is a very childlike action, so this shows the beginning stages of Lizabeth´s growth.
An example of Lizabeth´s transition is at the end of the story. Her parents start to have an intense conversation, which leads to her father crying. When her father starts to cry, she gets confused and angry. In her anger, Lizabeth goes over to Miss Lottie´s marigold garden and starts ruining the beautiful flowers. She then realizes what she has done, and comes to know that she needed to grow up at that moment.
The last example shows how Lizabeth has grown. After her angry outburst on Miss Lottie and her flowers, Lizabeth decided it was time for her to grow up. She also realizes how Miss Lottie is just an old broken lady, trying to bring happiness into the dark world they were in using marigolds. Miss Lottie passes later on, so Lizabeth decides to plant marigolds in honor of her. That action is a very grown up thing to do.