Recently I shared the image below in my son’s 3rd grade class. Between bites of sandwich and sips of juice, students shared their counts (12, 6, 1, 12 trillion, ∞) and challenged each other to find their unit of measure (grapefruit halves, whole grapefruits, measuring cup, juicer). Even their outlandish, silly “counts”  of 12 trillion and infinity prompted side conversations about large numbers.

Prompts like those in How Many? A Counting Book  support multiple ways of thinking and encourage students to consider situations where one isn’t always one. When students choose a half-grapefruit as 1, they get a count of 12. When they choose a grapefruit as 1, they arrive at a count of 6.

In this post, we share two more magical books that ask this same question:  Is one always one?

The Book (s)

The 1st book, More than One, was written by Miriam Schlein and illustrated by Donald Crews. Schlein has authored more than 100 books for children over 5 decades. Crews has written and illustrated many books for children including the classic counting Book Ten Black Dots and Caldecott honor awards books Freight Train and Truck. More than One was published in 1996 by Greenwillow.

This book begins with the line: One sun in the sky. One whale in the water. Can One be more than 1?

The text continues with different situations (e.g., One pair of shoes is 2 shoes) and questions that encourage students to consider when one is more than one.   Crews’s  bright and bold illustrations making this an excellent book for counting along with as well.

The 2nd book about one is Only One written by Marc Harshman and illustrated Barbara Garrison. It was published in 1993 by Cobblehill Books.

Only One also explores the idea of something being both many and one at the same time.  Garrison uses a warm fall palette to bring to life her curious images  accompanying each of Harshman’s ONE situations. Here are a few examples from the book. [I especially like how the 100 patch quilt isn’t 10 by 10 array, making counting patches slightly more interesting.]

Harshman and Garrison combined talents for a second book titled One Neighborhood which is similar in spirit to Only One.  

The Math

Miriam Schlein is an “author of big ideas for small readers.” (Saxon, NYT article, 2004) The mathematical idea central in Schlein and Crew’s  More than One and Harshman and Garrison’s Only One is the idea of units or what counts as one. In his Teacher’s Guide to How many? Danielson argues that the “what counts as one?”  is one of the most important questions in elementary mathematics.

This idea of what counts of one is a very big idea indeed.  Children will revisit it over and over as the engage in processes of counting, grouping, partitioning and explore ideas such as place value, fractions, decimals, percents, probability, and measurement.

Magic

We began with More than One. As I read the first page pictured above with the whale, my daughter immediately answered the question, Can One be more than 1? aloud:  No!

Seeing the image on the next page, she quickly realized the game being played. She remarked before reading the page, “Oh, one pair of shoes is two whole shoes. Oh, one PAIR of shoes. Is two WHOLE shoes.”

Siena happily continued engaging with this book through counting and responding to the question prompts throughout the book. She confirmed that this book was “Math Book Magic” at the end of our reading.

After we read More Than One, we read Only One. At the end of this book, I asked her if this was math book magic too, to which she agreed. When I pressed her for why, she said because they are the books “are the same, but they are different. They are both about one and many, but they are different because this one (Only One) is backwards.”

As I glanced back to the two books I realized what she noticed. In More than One, each situation presented is ONE of something and then explores the MORE of that one  (1 pair of shoes → 2 shoes, 1 dozen eggs →12 eggs) whereas in Only One the situations are reversed (100 patches →1 quilt, 10 cents→dime). What a lovely noticing of structure that resulted from reading both of these books together.

We heartedly recommend both More than One and Only one to explore with children ages 4-8 the idea that one thing can be more than one of a second thing.

And with that we leave you with a favorite quote about one that I was reminded as Siena  shared her observations about the connection between these two magical books.

“To the world you may be one person; but to one person you may be the world.” Dr. Suess.

 

 

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Thanks and see you next month!  Touch #mathbookmagic, pass it on.