When older children and adults perform chores such as doing laundry or putting away dishes, they may not even realize they are making decisions about how to classify objects into categories—washing the white clothes together and putting the plates together on a shelf.  Young children can begin to see how objects can be sorted into categories with the help of several children’s literature books.

Young children naturally sort objects by color.  Have a variety of books available that introduce colors and show objects of a particular color so children can make associations with the object and the color.  A fun book that can be used to explore colors is The Color Box (Dodds, 1992), in which a monkey named Alexander crawls into a box to discover a world where everything is black, then another where everything is white, then yellow, and so on until he ends up back in his world where there are objects of every different color.  Then provide groups of objects that can only be sorted by color such as Unifix cubes or square tiles.  Once children have sorted these objects by color, they can count the number of cubes or tiles in each group and compare them—which group has the most?  Are there more red cubes or more orange cubes? Then make several types of objects available for children to sort by color such as beads, tiles, cubes and blocks.

After children have had several experiences sorting objects by color, they can begin to explore other attributes.  In the book, The Button Box (Reid, 1990), a boy visits his grandma and finds a box with hundreds of buttons inside.  He sorts them into categories such as buttons covered with cloth, sparkly buttons, metal buttons and buttons from uniforms.  He also lines them up based on size and color.  At the end of the story, the boy and his grandma close their eyes and each choose a button from the box.  Then they look at them and talk about all of the ways the two buttons are alike and the ways they are different.  Follow up the story with a game similar to the one in the story, by comparing two buttons or other toys that have similar attributes such as two dolls or two cars.

Another book that can be used for classification of objects is How Many Snails? A Counting Book (Giganti, 1988).  On each page there are illustrations of one type of object but they vary by size, color or design.  On the first page there are eight clouds for children to count.  Then there are more questions to answer, “How many clouds were big and fluffy?  How many clouds were big and fluffy and gray?”  Children can use their toys to count, sort and answer questions such as, “How many frogs?  How many frogs are yellow?  How many frogs are yellow with a green stripe?”  Incorporate science by introducing various types of insects and asking children to tell you how they can sort them—by putting all of the insects that are the same color together or by putting the insects with wings in a group. 

When children sort and classify objects into groups, they are building a foundation for graphing and data collection.  They can create unique ways of sorting objects into groups and once they know how to put objects into categories, they can help with all of those chores!

Young children naturally begin to create patterns with objects such as Unifix cubes or colored tiles, even if they do not realize what they’ve created is called a pattern. A child’s early knowledge of color or shape patterns can lead to later recognition of more complex patterns in large numbers and within the four operations.

A book that can be used to introduce young children to patterns in the environment is the book Math Counts: Pattern (Pluckrose, 1995).  The book contains photographs of patterns found in nature such as on leaves, flowers and insects.  The book also shows patterns found in familiar objects such as on a car tire, the sole of a shoe and wallpaper.  Encourage children to draw or photograph their own pattern discoveries such as on clothing, jewelry or furniture

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Another book that can be used to introduce patterns is Rooster’s Off to See the World (Carle, 1972).  In the story, one rooster decides to travel and meets two cats, three frogs, four turtles and lastly, five fish.  As he meets each set of animals, pictures of the animals are displayed in the upper corner of the right page.  Children can see the growing pattern of animals from one rooster up through five fish.  Eventually, all of the animals disappear, starting with the five fish.  The pictures of the animals appear in the upper corner of the left page and gradually disappear until only a picture of one rooster is there.  Children can see another pattern as the number of animals decreases from five down to one again.

Set up activities following this book such as displaying familiar object to create an AB pattern (using only two different elements in the pattern) for a child to continue.  Start with color patterns and say the colors aloud as you display each one, “Red, blue, red, blue.…”  After several examples of color patterns, use toys and say the name of the objects as you display each one, “plate, spoon, plate, spoon….”

Once children have practiced recognizing and repeating patterns with cubes, blocks, toys and familiar objects, they can begin to listen for patterns in songs, stories and nursery rhymes.  A book that can be used as an example of a pattern set within a story structure is The Napping House (Wood, 1984).  It’s a rainy day and everyone is napping in the house, including a snoring granny.  But then the granny is joined by a dreaming child, followed by a dozing dog, then a snoozing cat, a slumbering mouse, and a wakeful flea.  Each of these nappers pile on the bed with granny one by one, and are introduced on each page, one by one, adding to the words from the previous page:  “And on that granny there is a child…and on that child there is a dog…and on that dog there is a cat….”

Encourage young children to listen for patterns when you read stories or to look for patterns in photographs and illustrations in books, on posters and other media.  Recognizing patterns sets the foundation for algebraic thinking—analyzing patterns, relationships and change throughout the study of mathematics.

As young children are formally introduced to the names of shapes, they begin to notice these shapes in their surroundings.  They see their plate as a circle and their napkin as a square when they eat dinner.  They look at the windows and doors in a room and recognize them as rectangles.  Tana Hoban’s book Shapes, Shapes, Shapes (1986) uses photographs of familiar objects such as pots and pans, and scenes such as construction sites, to present various shapes. Children will find more shapes on each page as they look at the photos again and again, and as they learn to name more shapes such as trapezoids and ovals.

An activity that can follow the introduction of this book can be allowing children along with family members to take photos of shapes in their home, their neighborhood or school.  They can display and compare the photos and name the shapes in each other’s photo.

In addition to two-dimensional, flat shapes, young children should be introduced to three-dimensional, fat shapes.  Reading the book, Changes, Changes (Hutchins, 1987), can open a child’s mind to the endless possibilities of how to arrange 3D blocks to build structures.  In this wordless picture book, a wooden couple builds a house but it catches on fire, so they must build a fire engine, then a boat to deal with all of the water, and so on.  Encourage children to find 3D objects in their environment such as food containers that represent cubes, cylinders, and rectangular prisms.  They can build their own structure with these containers and name them as they build.

Once children are familiar with the names of shapes, they can expand their vocabulary to include attributes of shapes.  The book, If You Were a Triangle (Aboff, 2010), includes illustrations of triangles that are slices of watermelon, Yield signs, faces of pyramids, designs on wallpaper, and more.  The text repeats the phrase, “If you were a triangle…” and lists attributes such as “three sides,” or “three corners” and introduces the terms polygon and angle.  At the end of the book, specific triangles are shown—equilateral, right and isosceles—along with examples of these triangles put together to form a new, composite, shape such as a rectangle or rhombus.  Children can look for triangles in their environment as well as practice putting the triangle Pattern Blocks together to form new shapes.

Another concept children learn in early geometry is relative position.  Young children are gradually exposed to words used to describe the position of an object or person relative to other objects or people such as above, below, beside, in front of, behind, and next to.  Young children are also starting to distinguish between their right and left and are learning to move, and count, forward and backward.  A book that is fun for children to use to learn these concepts is Bug Dance (Murphy, 2002).  The bugs in this book go to school together and in gym class they learn a dance that teaches them to take steps to the right and to the left, then hop forward and backward.  Young children can perform the dance as the book is being read over and over.

After children have practiced their dance moves they can practice the terms in the book, as well as other position words, to describe the position of Pattern Blocks.  For example, children might say: the square is below the hexagon; the triangle is on the right of the square; the trapezoid is on the left of the square; the triangle is next to the square. 

There are many children’s books that are written to introduce shapes, however many use the word “diamond” instead of rhombus.  I try to avoid these books or let children know a diamond shape is called a rhombus when we are learning math.

Young children love it when an adult sits down and reads a book to them, carefully studying the illustrations before the adult can turn the page.  Why not seize these opportunities as a way to introduce or reinforce mathematical concepts?  There are four reasons why I like to use children’s literature as a mathematical resource:

1. Literature can offer examples of real-life problem solving.

When I read The 3 Little Pigs to a child, we discuss how many pigs there are and how each one has a way to solve the problem of how to prevent the wolf from blowing down their house.  Even though pigs can’t really talk or build a house, the young child begins to understand the idea of a problem and solution as well as the lesson that sometimes we have to go back and try a new solution.

2. Children can discuss and demonstrate how characters use math.

In the book, Pete the Cat and His Four Groovy Buttons (Litwin, 2012), Pete the Cat sings a song about his four buttons.  But as he loses one button at a time, he alters his song to include three buttons, then two, then one.  Young children can see, and hear, how Pete the Cat uses math in his everyday life by counting the remaining buttons each time he loses one.

3. The text can provide common language and context for problem solving situations.

When I would read the book, The Doorbell Rang (Hutchins, 1986), to my primary students, we used little chocolate chip “cookies” cut out of brown tagboard and small paper plates to act out the story.  On the first page, Mom makes 12 cookies for Victoria and Sam to share.  This provides an opportunity for children to talk about how to distribute the 12 cookies on the two plates and then how to make sure the same number of cookies is on each plate.  Throughout the story, more children come to the house to share the 12 cookies, which are continuously distributed evenly among the growing number of children.

4. Children can apply mathematical concepts with literature.

In the 12 years I have been teaching math methods for the pre-service teachers at Elmhurst College, the teacher candidates are always amazed at the number of children’s literature books used to teach mathematical concepts, from PreK through eighth grade.  I have also conducted workshops for preschool and kindergarten teachers, as well as for families of young children, who are also surprised at how easy it is to use literature to teach and reinforce mathematical concepts including counting, patterns, geometry and sorting.

Using Children’s Literature for Counting and Cardinality

Young children learn to count to ten with meaning—they should not only be able to rote count from 1 to 10 but be able to count up to ten objects.  Adults and older children can become role models for counting and demonstrate the concept of cardinality, the awareness that the last number said is the total amount. When first introducing the concept of counting, use a book with the same objects on each page such as Ten Black Dots (Crews, 1986).  As you read each page and model how to count the number of black dots on each page, the child only has to pay attention to quantity since each object is the same size, color and shape.  Then practice counting up to ten circle counters so the child is only paying attention to the quantity.

Once children are able to count objects that are the same size, color and shape, read a book such as Math Fables (Tang, 2004), in which animals are shown in different configurations along with a rhyming fable, from one spider up to ten beavers.  This book can be read to children again when they are ready to break down numbers and group them into more manageable and familiar amounts.

An activity that can follow this book can be counting familiar objects such as toys or food.  Allow the child to touch each object while counting, whether counting illustrations in the book or toys on a table.  The child should also be able to repeat the total number of objects.  For example, “One, two, three.  Three frogs.”

Once children can count up to ten objects, they can begin to learn the complements of ten (one and nine, two and eight, etc.) with the book Ten Flashing Fireflies (Sturges, 1995).  In this book, two children are outside collecting fireflies in a jar.  First there is one firefly in their jar and nine fireflies in the night sky.  Then they catch another firefly and two can be seen in the jar and eight in the night sky.  After repeated readings of this book, try playing a game in which some “fireflies” are in the jar and some are in the sky.  Show the number of fireflies in the sky and have children figure out how many are in the jar.  They can have ten counters of their own to help them figure out the math problem.

I hope you have as much fun as I do, reading children’s literature and creating related math activities to introduce and reinforce these counting and cardinality concepts.