Introduction

Part I:  Some Books for Mathematizing

General Children’s Books

         Good Night Gorilla written and illustrated by Peggy Rathmann

Goodnight Moon written by Margaret Wise Brown and illustrated by Clement Hurd

Just a Little Bit written by Ann Tompert and illustrated by Lynn Munsinger

“More More More,” said the Baby: 3 Love Stories written and illustrated by Vera B. Williams

The Carrot Seed written by Ruth Krauss and illustrated by Crockett Johnson

         Whistle for Willie written and illustrated by Ezra Jack Keats

Books That Highlight Math

         Is It Larger? Is It Smaller? written and illustrated by Tana Hoban

The Very Hungry Caterpillar written and illustrated by Eric Carle

Part II:  Highlighting Number and Operations

Anno’s Counting Book written and illustrated by Mitsumasa Anno

         Feast for 10 written and illustrated by Cathryn Falwell

         Over in the Meadow written and illustrated by Paul Galdone

         Quack and Count written and illustrated by Keith Baker

         Ten Black Dots written and illustrated by Donald Crews

         Ten, Nine, Eight written and illustrated by Molly Bang

Part III:  Highlighting Geometry and Spatial Sense – in development

Part IV:  Highlighting Patterns – in development

Part V:  Highlighting Measurement – in development

Glossary

Bibliography


Sharing books with children is a way for staff to learn more about what children know and understand about math and to expand children’s understanding of math. This guide provides information on how to use books to highlight math learning. Staff may also want to share this information with the families of the children in their classroom.

Children often reveal what they know about math as they interact with books. For example, children will often spontaneously count objects in a book or make comments about the size or position of characters in a book (“That dog is so big!”). Children’s questions and
their responses to adults’ comments let us know (1) what they know and (2) what they are thinking.


Staff can use books, with individual children or small groups, to assess children’s mathematical understanding and help them to solidify and expand their knowledge and their vocabulary.

Many children’s books are rich in math and math-related content. Some children’s books focus specifically on math concepts. These range from simple counting books to books that embed math concepts or problem solving in the story or pictures.

Others, including many favorites, are not specifically mathematical but include situations in their text or illustrations that invite “mathematizing.” Such books allow staff to intentionally expand children’s understandings and their vocabularies.

For example, Good Night Gorilla is a story about a zookeeper saying good night to each of the animals in the zoo. While this is not specifically a number book, staff can encourage children to count the animals, to talk about the sequence of events in the story (“Who did the gorilla let out last?”), and to learn ordinal number words (first, second, third).

How can staff “mathematize” book reading? It is helpful for staff to read the book to themselves before reading it to children. This enables them to identify vocabulary words and concepts that they want to focus on to expand children’s knowledge.

Staff can enhance the book-reading experience in these ways:

This section offers a small sample of children’s books that are appropriate for supporting a wide variety of math concepts. Most are general children’s books that aren’t necessarily thought of as books for math, for example The Carrot Seed. However, these books are rich in math and math-related content, and contain multiple opportunities for mathematizing. 

Several of the books in this section focus specifically on one or more math concepts. For example, Is It Larger? Is It Smaller? focuses on measurement. However, this book is also full of opportunities for teaching number concepts and skills.

For each book, there is a brief summary of the book and suggestions for how to support math learning. This includes ideas for sharing the book with families. There are also multiple examples of the mathematical ideas that each book contains. You and the children may find many more.

Good Night Gorilla by Peggy Rathmann
Spanish edition: Buenas Noches, Gorila


About the book . . .
This book relates a story with pictures and very few words. As the zookeeper says “Good night” to the animals one by one, the gorilla unlocks their cages one by one, and all the animals follow the zookeeper home.
Appropriate for toddlers and preschoolers
        

Using this book . . .

 


 

Good Night Gorilla by Peggy Rathman
Spanish edition: Buenas Noches, Gorila
Mathematical ideas . . .
Number—counting, cardinal numbers, ordinal numbers

Measurement—size comparisons

Spatial sense—position

Patterns—repeating patterns

 

Goodnight Moon by Margaret Wise Brown
Illustrated by Clement Hurd
Spanish edition: Buenas Noches, Luna


About the book . . .
This lyrical book with its warm, detailed illustrations is a favorite for generations of children. At bedtime, the bunny takes us on a tour of the “great green room” by naming the special things in it. Then he says goodnight to each one—and to a few things he hasn’t named before—and then he falls asleep.
Appropriate for infants and toddlers, and very young preschoolers

Using this book . . .

 

Goodnight Moon by Margaret Wise Brown
Spanish edition: Buenas Noches, Luna
Mathematical ideas . . .
Number—very small number words (one, two, three), identifying “how many,” counting, comparing

Spatial sense—position, spatial vocabulary

Pattern—repeating pattern


Just a Little Bit by Ann Tompert
Illustrated by Lynn Munsinger


About the book . . .

An elephant and mouse are at the park and want to play on the seesaw together. Their animal friends come to help them out when they encounter the obvious problem. 

Appropriate for preschoolers


Using this book . . .

This book could be used along with classroom activities related to weight and balance, introducing words such as heavier, lighter, and same weight as.
Share with family members that this book about friends cooperating is also about solving a problem involving weight. Family members and children can talk about the problem that the mouse and elephant face, using words such as lighter and heavier. Questions such as “What should the animals do         now?” encourage children to think about the problem and suggest solutions.

Just a Little Bit by Ann Tompert
Mathematical ideas . . .

Measurement—weight and size comparisons and vocabulary
Compare the sizes and weights of the various animals (heavy, light, big, small; heavier, lighter, bigger, smaller). “Which animal looks bigger—the bear or the monkey?” “Which animal do you think is lighter—the lion or the ostrich?”
Compare the collective weight of the animals on the mouse’s side of the seesaw to the weight of the elephant. “How can you tell if the elephant weighs more than the mouse, giraffe, and zebra all put together?” 
Problem solving involving concepts of weight, size, and balance
Ask the children to predict what will happen as each friend joins the mouse on his side of the seesaw. “What do you think will happen when the bear gets on?” 
Ask the children to give explanations for why it's not working when different animals get on the seesaw. “Why didn’t the seesaw go down? What should the animals do now?”

“More More More,” Said the Baby:
3 Love Stories
by Vera B. Williams
Spanish edition: “Más Más Más,” Dijo el Bebé: 3 Historias de Amor


About the book . . .
This book consists of three short stories about adults interacting with babies they love. Each of the beautifully illustrated stories depicts a similar sequence of catching the running baby, picking the baby up, holding the baby close, and kissing and playing with the baby until the baby laughs, “More More More.”
Appropriate for toddlers

Using this book . . .

“More More More,” Said the Baby: 3 Love Stories by Vera B. Williams
Spanish edition: “Más Más Más,” Dijo el Bebé: 3 Historias de Amor
Mathematical ideas . . .
Pattern—repeating pattern

Number, spatial sense

The Carrot Seed by Ruth Krauss                              
Illustrated by Crockett Johnson
Spanish edition: La Semilla de Zanahoria


About the book . . .
This classic favorite tells the story of a little boy who plants a carrot seed. No one but the boy believes the carrot will come up. He pulls the weeds and waters it carefully day after day and, finally, a very big carrot grows!

Appropriate for preschoolers

Using this book . . .



 

The Carrot Seed by Ruth Krauss
Spanish edition: La Semilla de Zanahoria
Mathematical ideas . . .
Time—passage of time, ordering of events in time, time-related vocabulary

Measurement—size comparisons, ordering by size


 

Whistle for Willie by Ezra Jack Keats
Spanish edition: Sílbale a Willie                               
About the book . . .
Peter wants so much to be able to whistle for his dog, Willie, to come to him. The book follows Peter’s adventures as he practices and practices his whistling around the neighborhood and at home. The book is full of very rich language describing Peter’s actions. These actions come to life in the simple but vivid illustrations.

Appropriate for preschoolers

Using this book . . .

using position/location words such as in, on, and in front of. 

Whistle for Willie by Ezra Jack Keats
Spanish edition: Sílbale a Willie
Mathematical ideas . . .
Spatial sense and vocabulary

Geometry—shapes

Number—counting

Patterns


Is It Larger? Is It Smaller? by Tana Hoban
                         
About the book . . .
In this wordless book, beautiful photographs show a wide variety of objects, and sometimes people, of various sizes—some large, some small, and some middle-size. The objects in the photographs also vary in shape, color, number, and other qualities.

Appropriate for toddlers and preschoolers

Using this book . . .

 

Is It Larger? Is It Smaller? by Tana Hoban
Mathematical ideas . . .
Measurement—size comparisons, measurement vocabulary (big, little, small, middle-sized, short, long; larger, smaller, shorter, longer; largest, smallest)

Number—counting, comparing

The Very Hungry Caterpillar by Eric Carle  
Spanish edition: La Oruga Muy Hambrienta
                 

About the book . . .
This classic children’s book tells the story of a caterpillar and what he eats in the one week before he builds a cocoon and, two weeks later, turns into a butterfly! On Monday he eats through one apple. Each day after, he eats one more fruit than the day before—up to five oranges on Friday. On Saturday, he eats 10 things and grows very big!
Appropriate for toddlers and preschoolers

Using this book . . .


 

The Very Hungry Caterpillar by Eric Carle
Spanish edition: La Oruga Muy Hambrienta
Mathematical ideas . . .
Number—counting, comparing

Number operations, number patterns


Many children’s books help young children learn about number and operations. They provide opportunities for staff to help children explore number (counting, quantity, comparing quantity, ordering numbers, and numeral recognition) as well as operations (adding—joining to, taking away—separating, multiplying, and dividing—sharing). There are excellent books written to support counting and other number skills and concepts. Many of the number concepts are found in the illustrations. These books also contain other math concepts that you can point out and discuss with children. Six books are described. For each book, the story line is described and suggestions are made for ways that staff can use the books with young children. Specific ideas are included on how to read each book to highlight the mathematical content. The glossary defines mathematical terms that are used."


Infants and toddlers enjoy hearing simple, rhyming language and looking at the pictures in counting books even before they understand the mathematical content.

 



What infants and toddlers can learn from counting books:

 

How staff can use counting books with infants and toddlers:


 

Preschool children love to count and explore number concepts in all their activities, including book reading.


What preschoolers can learn from counting books:

How staff can use counting books with preschoolers:


Anno’s Counting Book by Mitsumasa Anno

      
About the book . . .
This wordless book represents the numbers 1through 12 in scenes of a growing village across the 12 months of the year. The first page has a snowy landscape with a river running through it. On the next page, the village begins to appear with one house, one child, one adult, one pine tree, and so forth. Objects are added as the village grows. The seasons and activities change. The scenes become more and more complex as the numbers of objects increase.
Appropriate for preschoolers


Using this book . . .


 


 

Anno’s Counting Book by Mitsumasa Anno
Number and Operations ideas . . . 
Counting up to 12 objects, cardinal numbers, comparing quantity

Number composition (composing and decomposing), addition (joining to)


Feast for 10 by Cathryn Falwell
Spanish edition: Fiesta para 10

About the book . . . In this counting book, a mother and children go shopping for food and then cook and serve a “feast” to their family. As the family shops for food, the numbers 1 through 10 are represented by one shopping cart and the items they put into it (two pumpkins, three chickens, and so forth). The sequence (1 to 10) is repeated at home when the family prepares and serves the meal. The book uses numbers in a real-life activity that children may relate to their own experiences. Appropriate for preschoolers"


Using this book . . .


Feast for 10 by Cathryn Falwell
Number and Operations ideas . . .
Counting up to 10 objects, cardinal numbers, comparing, numeral recognition

Number composition (composing and decomposing), addition and subtraction, problem solving


Over in the Meadow by Paul Galdone

About the book . . . This book is an adaptation of the old nursery counting rhyme – counting baby animals from 1 to 10. Each rhyming verse has two parts. First, we see a group of baby animals in their habitat (by the barn door, in their nest of sticks). Second, the mother tells the babies to do something, for example squeak or caw. The repeating pattern of the rhyme makes this an especially nice book for helping children learn the number sequence 1 to 10. Appropriate for toddlers and preschoolers"

Using this book . . .


In addition to learning the rhyme, preschoolers will enjoy counting the animals and recognizing numerals.


 Over in the Meadow by Paul Galdone
Number and Operations ideas . . .
Counting to 10, repeating and growing patterns

Counting to 10, cardinal numbers, number representation, numeral recognition, comparing number

Adding one more, counting on

Quack and Count by Keith Baker

About the book . . . This counting and adding book follows seven ducklings as they slip and slide through the forest, swim and splash in the water, and finally fly away. Even very young children will enjoy the ducklings’ antics and the simple rhyming verse. Preschoolers will enjoy exploring the number concepts and practicing their counting, number composition, and adding skills. Appropriate for preschoolers"

Using this book . . .

 


Quack and Count by Keith Baker
Number and Operations ideas . . .
Concept of seven, counting

Number composition (composing and decomposing), addition and subtraction, math vocabulary (“plus” to signify addition)


Ten Black Dots by Donald Crews      
Spanish edition: Diez Puntos Negros


About the book . . . In this book, large black dots (1 through 10 of them) become the eyes of a fox, spots on a snake, wheels on a train, and more. For example, five dots appear in a straight vertical row as buttons on a coat and then as the portholes of a boat, two at deck level and three below. This book helps children begin to understand that changing the arrangement of objects doesn’t change their number. Appropriate for toddlers and preschoolers"



Using this book . . .




Ten Black Dots by Donald Crews
Number and Operations ideas . . .
Counting up to 10 objects, recognizing number in different configurations, comparing quantity, math vocabulary (number words, same number)

 


Ten, Nine, Eight by Molly Bang
Spanish edition: Diez, Nueve, Ocho  

About the book . . . In this counting book and bedtime story told in rhyme, a father and his little girl count down to bedtime. Beginning with “10 small toes” and ending with “1 big girl all ready for bed,” the book counts backward in scenes of bedtime routines in the child’s room. Even hugs and kisses are counted (“3”). The warm illustrations and simple lullaby-like quality of the language make this book appealing to even the youngest children. Appropriate for infants, toddlers, and preschoolers"

 Using this book . . .

When reading this book to infants and toddlers, relate the number concepts to the child’s own experience—for example, their own “two strong arms.” 
  
With preschoolers, encourage children to count and compare pictured objects, recognize the numerals that tell how many objects, and learn to count backward from 10. 
Have children practice counting backward by using 
songs or short chants during large group activity time. For example, chant "Five, four, three, two, one" gradually moving from standing to a crouched position and then jump up saying "Blast off!”
 
Share with family members that while reading this story, they can relate the number concepts to their child’s own experiences.  For example, count the baby’s ten toes, then count their child’s toes and talk about the same number.

Ten, Nine, Eight by Molly Bang
Number and Operations ideas . . .
Counting up to 10, counting objects, number correspondence

Numeral recognition, counting backward

Comparing number, correspondence, addition and subtraction


Cardinal number:  the last object that has been counted also represents the total number of objects in a group; answers the question “how many?”

Composing and decomposing number:  discovering the many ways that one number can be taken apart and put together—for example, “five” is 2 fingers plus 3 fingers or 4 fingers plus 1 finger

Geometry: the area of mathematics that studies shape, size, space, position, direction, and movement

Mathematize: highlight mathematical concepts in everyday activities

Number: quantity

Number word:  spoken word to represent a quantity—for example, “one,” “two,” or “three”

Numeral: written symbol that represents a number—for example, 1, 2, or 3

Operations: addition, subtraction, multiplication, and division of numbers

Ordinal number:  number word that describes the order of
objects—for example, “first,” “second,” or “last”
Represent number: show a number with concrete objects such as blocks, dice, fingers; spoken number word such as “four”; or written symbols such as a numeral (4) or tally marks (/ / / /)
Spatial sense: knowing about the position of people and objects in space

 

Anno, Mitsumasa. Anno’s Counting Book. New York: HarperTrophy, 1986.

Baker, Keith. Quack and Count. San Diego, CA: Harcourt, 1999.

Bang, Molly. Ten, Nine, Eight (Diez, Nueve, Ocho). New York: HarperTrophy, 2003.

Carle, Eric. The Very Hungry Caterpillar (La Oruga Muy Hambrienta). New York: Philomel, 1981.

Crews, Donald. Ten Black Dots (Diez Puntos Negros). New York: HarperTrophy, 1995.

Falwell, Cathryn. Feast for 10 (Fiesta para 10). Boston: Clarion, 1993.

Galdone, Paul. Over in the Meadow. New York: Aladdin, 1989.

Hoban, Tana. Is It Larger? Is It Smaller? New York: HarperTrophy, 1997.

Keats, Ezra Jack. Whistle for Willie (SÍlbale a Willie). New York: Viking Juvenile, 1964.

Krauss, Ruth. The Carrot Seed (La Semilla de Zanahoria). Illustrated by Crockett Johnson. New York: HarperTrophy, 2004.

Rathmann, Peggy. Good Night Gorilla (Buenas Noches Gorila). New York: Putnam Juvenile, 1994.

Tompert, Ann. Just a Little Bit. Illustrated by Lynn M. Munsinger. New York: Scholastic, 2000.

Williams, Vera B. “More More More,” Said the Baby: 3 Love Stories (“Más Más Más,” Dijo el Bebé: 3 Historias de Amor). New York: HarperCollins, 1990.

Wise Brown, Margaret.  Goodnight Moon (Buenas Noches, Luna).  Illustrated by Clement Hurd.  New York: HarperCollins, 1991.