“Those tiny wings can lead to whipping winds, churning season, and a mighty STORM […] Or a perfectly sunny day. You never know! Small changes. Big unpredictable effects!”

Ralph explains the butterfly effect to Bree, demonstrating how one small action can have a significant impact. Bree doesn’t know that she will join the swim team at the beginning of the novel. However, she is surprised to find the huge impact it has on her life, bringing her closer to her friends at school, her neighbor Etta, and even her father at the end.

“Remember, an education is one thing no one can take away from you.”

Ralph sees education as a way forward, which is why he moves his family to Florida so that he can complete a training program. He emphasizes, likewise, that Bree’s studies should come before friendships. By the end of the novel, however, he sees how important friends are to Bree and reminds her that friendship is pivotal, too.

“In fact, your true talent isn’t math. It’s that you—You never give up. Not on a hard math problem or a difficult puzzle.”

Bree does not recognize her strengths as extending beyond solving puzzles. However, she comes to recognize that the skills she uses when doing math apply more broadly to her life, which is evident when she pursues swimming and helps to reunite Etta with her swim sisters.