Happy (almost) Halloween! It seems like the number of trick-or-treating opportunities doubles each year along with the size of the candy bars.  Although children enjoy this candy growth pattern, this week’s math picture book shows us that doubling can get a bit out of control.

The Book

Two of Everything was written and illustrated by Lily Toy Hong and published in 1993 by Albert Whitman & Company.

Hong re-tells this Chinese folktale with clarity and humor. In the tale, Mr. Haktak digs up an ancient brass pot and brings it home to his wife. While the Haktak’s can’t find any practical uses for the pot, they discover it has magical ones. Whatever they place in pot, ends up doubling.  The problem is the magical pot doubles EVERYTHING. In the end, the  Haktaks find a way wield the magical pot’s powers.

Hong’s charming illustrations in beautiful blues and greens are a lovely companion to this delightful tale.  This story will amuse children in kindergarten through middle school.

The Math

This book can be used to practice double addition facts. For example, when Mr. Haktak accidentally drops his coin purse containing 5 coins in the pot, the 5 coins are transformed into 10 coins. (Doubles fact: 5+5=10 or using multiplication 2×5=10).

This book is also a great way to talk about growing patterns with children. The lesson presented here from Marilyn Burn’s website Math Solutions leverages the story’s engaging context and provides a “beginning experience with examining a growth pattern, recording and extending data on a T- chart, and representing the pattern algebraically with an equation. The experience is then extended by changing the doubling rule of the pot to other rules for the children to figure out.” [From Math Solutions website, Lessons for Algebraic Thinking, Grades 3–5, a lovely resource for supporting algebraic thinking in early grades]

Growth patterns are examples of a mathematical function. The function y=2x represents the growing pattern of the magical pot in the story where x represents the number of the objects placed in the pot and y represents the number of objects that are taken out of the pot. One metaphor used to teach functions is a function machine. When you input something into the function machine, you get a unique output.

The pot in Two of Everything is similar to the machine metaphor with a bit of magic thrown in. If you input five coins in the magic pot, you will get 10 coins, which is the unique output for 5 coins. [Note: Functions do not always change inputs as in the case of the magic pot. For example, the identity function will map any input to itself.]

The Magic

The magic pot gave me a useful context to talk about growth patterns with my children. Here are an example of some questions we talked about on the short ride to school the other day.

If you drop 3 pieces of candy into the magic pot, how many pieces come out?

If you drop 1 1/2 cookies into the pot, how many cookies come out?

What if 10 snakes came out of the pot, how many snakes were put in?

The magical pot put the fun in function for our family. Go to your local library and check out Two of Everything if you haven’t already. This folktale does double duty with a great story plus a magical pot in-out function metaphor.

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Thanks and see you next Monday! #mathbookmagic