Tuesday Teacher Tips: Two of Everything
Welcome to the Tuesday Teacher Tips series! Each week we’ll highlight teaching and learning resources, ideas to use in the classroom, as well as things to ponder as you go about your teaching day.
About the Book
I was recently introduced to the book Two of Everything: A Chinese Folktale (1993) retold by Lily Toy Hong. One day while Mr. Haktak was digging in his tiny garden he comes upon an ancient pot. He soon learns that the pot is magical and doubles everything that is placed inside of it.
Mr. Haktak and his wife experience some difficulty with the magical pot. My favorite line comes after Mrs. Haktak falls in the pot and a second Mrs. Haktak appears. As the couple tries to figure out what to do with the new Mrs. Haktak, Mr. Haktak yells, “…If I put her back we will not have two women but THREE. One wife is enough for me!” (My husband would most likely agree with this sentiment!)
Using it in the Classroom
This book works well in introducing upper elementary students to input-output tables and expressing function rules algebraically. In the article, “Two of Everything,” from the October 2010 issue of Teaching Children Mathematics (available as a free download to NCTM members or $7.00 to nonmembers), Julie C. McNamara wrote of how she used the book in the classroom.
After reading the story, McNamara created an input-output chart with picture representations of what happened in the story. Columns were labeled, “What goes IN the pot” and “What comes OUT of the pot.” Next, she drew another T-chart with only number representations. With the new T-chart the student were asked to describe in words what the chart represented. Students responded that numbers that were put in doubled, were multiplied by two, or “got a match.” McNamara furthered her students thinking by asking them to write the rule algebraically. For example, 2n or n x 2 or n + n.
Later, she introduced students to another pot that yielded different results. For this new pot, when one item was put in, three items came out. After student predicted the rule, she continued by putting a new number of items in the pot. When three items were put in, five items appeared. She emphasized that a rule can’t be determined for sure after studying only one input-output pair.
Students then created their own magic pot with an original rule and a corresponding T-table. The pots were used in an interactive bulletin board; students had to figure out the rule for each other’s pots.
I think this would be a great lesson to start the year. It’s hands-on and concrete enough to pull your struggling learners into the lesson, but still challenging to your advanced learners, especially when students are asked to describe the rule algebraically. After this lesson, the “magic pot” could serve as a starter to the day. When students entered the classroom in the morning, there could be a picture of the magic pot with a corresponding input-output chart. Students could be asked to figure out the rule, describe the rule algebraically, and continue the chart with five additional input-output pairs.
Have you used this book in your classroom? Tell us about it, we’d love to hear about other ways you used the book to teach math concepts.
Another book that could be used to partner with this book would be One Grain of Rice: A Mathematical Folktale, which was highlighted on an earlier post.
In addition, check out an article in Teaching Children Mathematics (November 2007), “Developing ‘Algebra-‘Rithmetic’ in the Elementary Grades” that also uses Two of Everything in the classroom.
Demi. One Grain of Rice: A Mathematical Folktale. New York: Scholastic Press, 1997.
Hong, Lily Toy. Two of Everything: A Chinese Folktale. Morton Grove, IL: Albert Whitman and Company, 1993.
McNamara, Julie C. “Two of Everything.” Teaching Children Mathematics (October 2010): 132-136.
Suh, Jennifer M. “Developing ‘Algebra-‘Rithmetic’ in the Elementary Grades.” Teaching Children Mathematics (November 2007): 246-253.