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:
- Use a variety of mathematical vocabulary to describe pictures or events in the book. For example, use math language to talk about the scenes in Goodnight Moon – “The two little kittens are in the middle of the rug.”
- Draw children’s attention to mathematical relationships, such as same, more than, less than.
- Encourage children to solve problems posed in the story line.
- Pose natural mathematical questions that follow from the text or illustrations of the book. For example, books like Is It Larger? Is It Smaller? picture many objects that children will enjoy counting. Ask “How many hats are hanging on the wall?”
- Use children’s natural interests to introduce new math concepts. For example, use a child’s interest in animals to talk about the number of animals on each page.
- Carry the mathematical concepts and language from a book-reading experience to daily experiences. For example, after reading The Carrot Seed, plant seeds and keep a record of how long it takes for the seeds to come up.
- Consider the cultural and linguistic characteristics of individual families when selecting books. People enjoy and are comfortable with different things. Choose a variety of books, including books that reflect the cultural heritage and languages of families in your program. Give lots of options!
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
- This is a nice book to share with family members who may have a wide range of reading abilities. The story line is easily picked up from the illustrations, and family members can be encouraged to talk about what’s happening in their own words.
- Talk with toddlers about what’s happening in the pictures—for example, “The gorilla opened the cage door. The giraffe is coming out.” and “Where is the little mouse now? He’s sleeping in the drawer.”
- Encourage preschoolers to notice the story’s repeating pattern, to count the animals, and to identify which animal gets out of the cage first, second, and so on.
Good Night Gorilla by Peggy Rathman
Spanish edition: Buenas Noches, Gorila
Mathematical ideas . . .
Number—counting, cardinal numbers, ordinal numbers
- Count the animals with the children to find out how many there are altogether. “Let’s count the animals on this page . . . one, two, three. That’s right, there are three!” Encourage preschoolers to count by asking questions like “How many animals are following the zookeeper?” (cardinal numbers)
- Ask preschoolers to identify which animal is first, second, third in line. “The gorilla is walking behind the zookeeper. He’s the first animal in line. Which animal is second? Which animal is third?” (ordinal numbers)
Measurement—size comparisons
- Compare the animals by size. “Which animal is tallest? Which animal is fattest? Which animal has the longest tail?”
Spatial sense—position
- Describe or ask the children where the animals are sleeping. “The mouse is sleeping in the drawer.” “Where are the elephant and the lion?” “Yes, the elephant and lion are on the floor.” “Who is sleeping in the bed?” “The gorilla is beside the zookeeper’s wife in the bed.”
Patterns—repeating patterns
- Encourage the children to notice the predictable, repeating sequence—the zookeeper says good night, the gorilla unlocks the cage, and each animal follows one by one. “The zookeeper says good night to the animal. Next the gorilla unlocks the door. And then the animal gets in line and follows the zookeeper and the other animals. The line of animals keeps getting longer.” Encourage children to predict what will happen next. “What will the gorilla do now?”
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
- As the bunny bids goodnight to all the things in his room as well as the moon and other things he sees out the window, notice that his words form a simple repeating pattern of “goodnights.”
- Infants enjoy hearing the words and looking at the pictures. Point to the objects as you name them. Stress the number words when pointing to multiples, such as two kittens and two mittens.
- This is an excellent book for supporting toddlers and young preschoolers’ number sense, spatial sense, and vocabulary.
- Family members will be pleased to hear that this popular book can help very young children to begin to learn math concepts. Share some ideas for supporting children’s learning about two and three.
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
- As you read the book, stress the numbers of things that are named and/or pictured. “There are three bears in the picture.” “I see two kittens and four mittens.”
- Many things in the “great green room” come in groups of two (socks, clocks, slippers). Ask “Where are…?” questions that emphasize number. “Where are the two kittens?”
- With older toddlers, ask “How many?” questions. “How many clocks are there?” “How many windows do you see?”
- Compare numbers of things (same number, more than, less/fewer than). “There are more mittens than slippers.”
Spatial sense—position, spatial vocabulary
- Describe the cow jumping “over the moon” and the bears “sitting on chairs.” Use these words as a starting point to talk about position. “The kittens are on the rug.” “The bowl, comb, and brush are on the table.” “The little bunny is in bed.”
- Ask “Where’s the mouse?” Even very young children enjoy finding the mouse that moves from place to place on different pages and pointing to it. Use spatial position terms to describe where the mouse is. “The mouse is on the floor.” “Oh—now the mouse is in front of the fire.” “The mouse is on the window sill looking out.”
Pattern—repeating pattern
- Young children learn to anticipate that each “goodnight” is followed by the name of whatever is pictured on that page. They may begin to participate in the reading by saying “goodnight” and/or naming what is pictured.
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
- Encourage children to talk about their own experiences with seesaws. “What happened when you sat on the seesaw by yourself?” “What happened when your friend got on the other side?” Share with families that asking these kinds of questions can help children relate their own experiences with weight and balance to what happens in the story.
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
- The overall sequence of events in each story forms a sort of simple repeating pattern: We meet the baby; the adult picks up the baby, plays with and talks to the baby; and so on. This repetition helps the very young child follow the story and begin to anticipate what will happen next.
- Share with family members that while reading this book, they may want to playfully do the same actions as those described in the book and encourage use of the word “more.”
“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
- The sequence of events in each story forms a simple repeating pattern. After hearing the book a few times, toddlers may repeat some of the words and phrases as you come to them in the book. Toward the end of a story, ask “And, then, what did the baby say?”
Number, spatial sense
- The dynamic illustrations bring to life concepts such as speed (running fast), motion (swinging all around), and position in space (lifting up high), all in relation to the baby’s own experience and body. “Little Guy is running fast. Let’s see if his daddy can catch him.”
- Other concepts include number and quantity (two eyes, ten toes; more) and location (middle, side, end). “Grandma is tasting Little Pumpkin’s ten toes. Let’s count your ten little toes.” “Here’s your belly button. It’s right in the middle of your tummy.”
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 . . .
- Along with many other important concepts, the story illustrates the passage of time in a way that is understandable and interesting to young children.
- Extend these time concepts to other activities. For example, plant seeds and keep track of how long it takes for them to come up.
- Share with family members that this story about growing a carrot can encourage children to think about and begin to understand time concepts and words related to time. They can point out the passage of time and the order of events by asking questions such as “What happened first? Next? Every day?”
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
- Encourage children to think about and retell the order of events in the story. “What did the little boy do first?” “What did the boy do every day to make the carrot come up?”
- Try to figure out how long it took to grow the carrot. “How many days do you think it took for the carrot to come up?”
Measurement—size comparisons, ordering by size
- The carrot that the boy grows is very, very big. Ask children to compare the size of the carrot the boy grew to the size of the little boy. “Which is bigger—the carrot or the boy?”
- Compare the size of the carrot in the story to the size of real carrots. “Are the real carrots that we eat this big?” “How big are they?”
- Have carrots for snack and compare their sizes. Help the children to put the carrots in order by size. Talk about same size, longer, shorter, and middle-sized. “These carrots look like they’re the same size.” “Which carrot is longer—your carrot or my carrot?” Then take the carrots to the kitchen so that the cook can clean them and cut them up for future snack, soup, or stew. Talk about the carrots and their new shape, size, and taste when the children are eating the cooked carrots.
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
- Read the book outside with the children. Then give them chalk and encourage them to draw their own paths on the playground. Talk with them about where their chalk lines go using different spatial vocabulary.
- Share with family members that they can use this book to help their children develop spatial concepts and language. Suggest that they talk with their children about the various places that Willie practiced whistling
using position/location words such as in, on, and in front of.
- After reading the book, ask the children to imitate some of the things Willie did—turning around and around, walking on a crack or line, jumping, hiding in a box. Ask them to tell you what they’re doing, and model using spatial words. For example, “You’re walking on the chalk line you drew.” “Rashad and Emily went under that big box.”
Whistle for Willie by Ezra Jack Keats
Spanish edition: Sílbale a Willie
Mathematical ideas . . .
Spatial sense and vocabulary
- As Peter practices his whistling, he whirls around and around, he hides in a carton, he draws a long line, and so forth. Ask “Where did Peter practice his whistling?” Help children to use spatial vocabulary when they reply: on the sidewalk, in the carton, in front of the mirror, and other places.
- Follow the path of the long line that Peter draws, and talk with the children about where the line goes. “Where did Peter’s line go?” Again encourage the children to use different spatial words as they describe where the line goes: out of the box, around the corner, along the sidewalk, in a circle around the girls jumping rope, in another circle around the barber pole, and right up to Peter’s door.
Geometry—shapes
- Find other circles in the pictures. “Where else do you see a circle?” Encourage the children to find other shapes (lots of rectangular shapes). “What shapes do you see on the building?”
Number—counting
- Count the locations in the book where Peter tried to whistle. “How many different places did Peter practice his whistling?” Together, you and the children can find and count all the places that Peter practiced whistling. “Let’s find where Peter first tried to whistle. Where did he go next?”
Patterns
- Encourage children to notice the visual patterns in the colorful illustrations. For example, point out the repeating zigzag pattern on Peter’s shirt “See the pattern – up, down, up, down.” or the two different color patterns on the barber pole (white, red, white, red and white, blue, white, red).
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 . . .
- This book provides many opportunities to “mathematize.” Draw children’s attention to size relationships in the photographs by using words such as bigger/smaller and longer/shorter. There are lots of things to compare on every page. The more you look, the more you find to compare.
- When reading this book with toddlers, focus on identifying big and little objects and counting small numbers of objects.
- When reading this book with preschoolers, compare the sizes of objects using a variety of comparison terms.
- Share with family members ways to use comparison terms when looking at the pictures. Family members and children may also enjoy making real life comparisons – for example, comparing the size of parent’s hand with child’s hand when looking at the photograph of the hands.
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)
- With toddlers, you may want to simply identify, and eventually have the child identify, the objects by size using words like big and little. “Here’s the big fish, and there’s the little fish.”
- With preschoolers, use comparison terms to order objects by size (larger, smaller, longest, shortest). “Which leaf is the biggest?” “Which leaf is the smallest?” “Which one is middle-sized?” “The blue pitcher with the pink flowers is larger than the white pitcher with the yellow flowers.”
Number—counting, comparing
- Count the objects in the photographs. Ask “How many?” questions. “How many hats are hanging on the wall? Let’s count them—one, two, three, four.”
- Count and compare numbers of objects by type, size, or other properties such as color or shape. “How many big hats are there?” “How many little hats?” “I see one big pig. Let’s count the little pigs.” “There are two white shoes and two black shoes.”
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
- For toddlers and younger preschoolers who are learning to count, provide plastic fruit that they can use to practice counting.
- Older preschoolers may enjoy acting out the story or retelling the story with a felt or flannel board.
- Share with family members that they can use this book to help their children learn to count. Together with their children they can notice the pattern of one more fruit each day and count the number of fruits the caterpillar eats each day.
The Very Hungry Caterpillar by Eric Carle
Spanish edition: La Oruga Muy Hambrienta
Mathematical ideas . . .
Number—counting, comparing
- Count the items the caterpillar eats each day. “On Wednesday the caterpillar ate plums. How many plums did he eat?” “How many things did he eat on Saturday?”
- Compare the amounts the caterpillar eats each day. “Did the caterpillar eat more plums or more strawberries?” “Did he eat more on Friday or more on Saturday?”
- For very small numbers (one, two, three), children may just want to say the number without counting. Encourage children who are learning counting to count two or three items.
- Ask older preschoolers to show how many items the caterpillar ate by holding up the same number of fingers.
Number operations, number patterns
- Point out the pattern in the story. “For the first five days, the caterpillar eats one more fruit each day.”
- Ask children to make predictions. “The caterpillar ate three on Wednesday. Each day he eats one more fruit. How many will he eat the next day?” Ask older preschoolers “How many will he eat on Thursday?”
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:
- Begin to understand that number words are about amounts of things
- Begin to learn math words
How staff can use counting books with infants and toddlers:
- Point to the pictures that the number words refer to
- Model counting small numbers of objects
- Relate the words and pictures to the child’s own experience
Preschool children love to count and explore number concepts in all their activities, including book reading.
What preschoolers can learn from counting books:
- Develop their counting skills
- Explore number relationships and concepts in the book’s text or illustrations.
- Practice using mathematical operations to solve real-life problems
- Make connections between numerals, number words, and the number of objects they represent
How staff can use counting books with preschoolers:
- Count objects with the children.
- Encourage children to count to find out how many and to solve simple problems.
- Ask questions that guide children to explore number relations and concepts in the book’s text or illustrations.
- Encourage older preschoolers to recognize and name some written numerals and notice that each numeral and number word stands for a particular number of objects.
- Plan activities that extend the mathematical ideas in books.
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
- Some objects in the pictures are much easier to count because they are large or are in a line. Others are scattered about on the page, and you have to look for them. Count the easier ones first. Try the harder ones as children’s skills develop.
- Read this book again and again over time as the children and you find new things to think about and more concepts to explore.
- Older preschool children can create their own counting books with scenes of their community, using numbers one to five (or more or fewer, as appropriate).
- This is a nice book to share with families who may have a wide range of reading abilities. Encourage family members to talk about the scenes in the book and count the objects with their children. Explain that children who are starting to count have an easier time counting large objects that are arranged in a line. Suggest that they and their children can make a game out of finding and counting the children, animals, flowers, or other objects that are scattered on the page.
Anno’s Counting Book by Mitsumasa Anno
Number and Operations ideas . . .
Counting up to 12 objects, cardinal numbers, comparing quantity
- Count the buildings, trees, adults, children, animals, and other objects with the children. Depending on children’s counting knowledge and skills, you may want to count the objects for them, ask them to count with you, or encourage them to count on their own. “Let’s count the ducks walking in a row—one, two, three, four, five, six. Six ducks!”
- Ask questions about the numbers of objects. “How many pigs is the lady feeding?” “How many of the same kind of flowers (or trees) do you see?”
- Ask questions to encourage children to compare numbers of items in the pictures. “Do you think there are the same number of dragonflies and horses? Let’s count to find out.”
Number composition (composing and decomposing), addition (joining to)
- Ask questions to guide the children in exploring the math concepts and relations. “Two children are holding the rope. How many are running? How many children are there altogether?”
- Encourage children to describe and tell stories about what is happening in the scenes using number words and other math-related vocabulary. “See the children playing at the river? How many are in the water? What are the other children doing?”
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"
- Objects in this book are pictured as they might appear in real-life activities – shopping, cooking, and serving food. Children can practice counting objects that are not organized in lines or rows for easy counting. Help them, as needed, to find and count the objects.
- Have the children retell the story using props and math language from the book.
- Staff can set up a grocery store for children to pretend to go shopping and practice their number skills.
- Share some ideas for math learning with family members. They can encourage children to tell their own story about going shopping or helping with cooking at home using the numbers 1 though 10. Children can also count to find out the answer to “How many?” on each page.
Feast for 10 by Cathryn Falwell
Number and Operations ideas . . .
Counting up to 10 objects, cardinal numbers, comparing, numeral recognition
- Count the pictured items with the children. “Let’s count the pickles in this jar.” “Help me count how many children are helping with the shopping.”
- As you read the number words, point out the numeral on the page. Once children have learned to recognize and read some of the numerals, instead of saying the number word, point to the numeral and let the children say it.
- Ask “How many?” questions that encourage children to compare numbers. “How many pumpkins for pie? How many chickens to fry? Are there more pumpkins or more chickens?” “How many ripe tomatoes? How many plump potatoes? Are there fewer (or less) tomatoes or potatoes?”
Number composition (composing and decomposing), addition and subtraction, problem solving
- Ask mathematical problems suggested by the text and pictures. “How many pans are on the stove? How many are in the oven? How many pans altogether?”
- After reading “Ten hungry folks to share the meal,” ask “How many chairs are at the table?” If necessary, go back to the page before to see that there are nine. Ask “How many people don’t have a chair? Are there more people or chairs? What should they do?”
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 . . .
- Read the book enough times to familiarize children with the repeating, rhyming pattern so that they can participate in the reading by saying the number, naming the animals, or making the animals’ sounds.
- Toddlers will enjoy the rhyming and repetition and may want to join in with number words or animal sounds. They may want to try counting some of the animals.
In addition to learning the rhyme, preschoolers will enjoy counting the animals and recognizing numerals.
- Share with family members that they can enjoy the repeating, rhyming pattern of the story as they read the book to their children. They can also count the animals together and look at the corresponding numeral to build children’s understanding of numerals.
- There are many book versions of this counting rhyme. Use the one you have or prefer.
Over in the Meadow by Paul Galdone
Number and Operations ideas . . .
Counting to 10, repeating and growing patterns
- Read the book to familiarize children with the repeating, rhyming pattern. Once they are familiar with the verses and the regular predictable pattern, children can anticipate the number words. Children will enjoy participating in the reading by saying the number of baby animals. For example, after reading “. . . in a nest built of sticks, lived a noisy mother crow and her little crows,” stop and let the children say the number of crows.
- Encourage children to notice the growing pattern – each verse includes one more baby animal (from one to ten). Older preschool children can help you represent the pattern by creating a drawing or graph with symbols or pictures. Arrange the symbols or pictures to show the growing pattern.
Counting to 10, cardinal numbers, number representation, numeral recognition, comparing number
- Count the baby animals with the children; stress the last number counted. “One, two, three, FOUR. There are four mice.”
- Encourage older preschoolers to use their fingers to show how many.
- If the version of the book you are using includes written numerals, point to the numeral when children say the number word to build their knowledge of written numerals.
- Ask questions that encourage children to compare numbers of things, for example “Count the flowers and the bees. Are there more flowers than bees?” or “Are there fewer (or less) ducks or fewer crows? Let’s count them to find out.”
Adding one more, counting on
- Add one more by including the mother animal when counting. “There are four baby mice, and the mother mouse makes one more. How many mice altogether?” The children may need to count all the animals (the four babies and the mother) to get the answer. Encourage older preschoolers to count on from four to get the answer. “Four, five. Five mice altogether!”
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"
- The illustrations and rhyming text show all possible number combinations for seven, for example “7 ducklings, 6 plus 1” and, on the next page, “7 ducklings, 5 plus 2.” Encourage children to notice all the different combinations of numbers that make seven. Talk about all the ways to show seven.
- Children can draw pictures or use duck stickers to make their own pictures of seven ducks (or a different number of ducks or other animals or items) in different groupings. For example, children might make pictures that show some ducks in the pond and some playing in the grass.
- Older children may write, or have staff write, the corresponding numeral on each page of their books. Organize and display the children’s pictures to show the possible number combinations for seven.
- Share with family members that they can encourage their children to notice all of the different ways to show the number seven as they are counting the ducklings.
Quack and Count by Keith Baker
Number and Operations ideas . . .
Concept of seven, counting
- Count the ducklings with the children. Emphasize the meaning of the number words by pointing to the groups of ducklings as you read the numbers. “7 ducklings, 5 plus 2.”
- Count the ducks for toddlers, and encourage them to help you count. Have them help you “find” the ducks who are playing peekaboo.
- Encourage preschoolers to count the groups of ducks, such as 5 and 2, then to count all seven.
Number composition (composing and decomposing), addition and subtraction, math vocabulary (“plus” to signify addition)
- Older children can explore the addition “problems” in the book.
After reading “4 plus 3,” say “Four ducklings over here and three ducklings over here. How many ducklings altogether?” Count with the children to check.
- The word plus may be an unfamiliar term to children. Explain that “4 plus 3” means the same thing as “4 and 3.”
- As you read, encourage children to represent the numbers in the groupings with their fingers and to notice that they always add up to seven.
- Practice adding by counting on instead of counting all the objects. For example say “Five ducklings here.” Then point to the sixth and seventh duckling as the children count “six, seven.” Ask “How many ducklings altogether?”
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"
- When reading to toddlers, point to the groups of dots when you read the numbers. Count the dots and talk about how many there are. Because the dots are large and easy to count, toddlers may want to try counting them, too!
- When reading to preschoolers, ask them to compare the numbers of dots in the pictures. This will help them discover that rearranging objects does not change their number.
- This book can be used with other preschool activities that are based on various configurations of dots, such as card games, dice games, and dominos.
- Share with family members that as they read this book, they can encourage their children to compare the number of dots to find the same number.
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)
- Seeing the same numbers of dots in different arrangements helps children learn to recognize the patterns that particular numbers of objects form.
- Draw toddlers’ attention to the pictures with the same small numbers of dots. “See, there are two dots here – the fox’s eyes – and two dots here – the holes in the keys.”
- Preschoolers can count and compare the numbers of dots in different arrangements. “How many dots make the spots on the snake? How many dots are stones to rake? Let’s count to make sure there are the same number of dots here (spots) and here (stones).”
- Compare the number of objects by asking “How many foxes? How many keys? Are there more foxes or keys? Let’s count to find out.”
- As preschool children look at the different pictures and count the dots, encourage them to notice that the dots are the same number no matter how they are arranged. For example – “Here are the five dots in a straight line on the coat. Here the five dots are in two rows on the boat. How can we check to make sure the pictures have the same number of dots – five here and five here?”
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"
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
- Call the young child’s attention to the relation between what is pictured on the book’s pages, the book’s words, and her own world. “See the baby’s 10 toes. Here are your 10 toes. You have the same number of toes as the baby.”
Numeral recognition, counting backward
- Preschool children can also use this book to learn to recognize and read written numerals and to practice counting backward. Ask “What number comes next?”
Comparing number, correspondence, addition and subtraction
- Older toddlers and preschoolers can also begin to notice the numerical relationships in the pictures. “There are 8 square windowpanes. See—there are 4 in each window, 4 here and 4 here. They are the same number.” “Where are the 4 sleepy eyes? Whose eyes are they?”
- The page with “7” shows pairs of shoes. Ask “What is missing? How many shoes should there be?” “How many shoes make a pair?”
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.