Owen giggles with glee as he pokes his eighteen-month-old fingers through the caterpillar holes; Ashley, age five, and Ryan, six, diligently work to stuff as many lima beans as possible into a child’s mitten;

Matthew and Haley carefully measure the perimeter of their fifth-grade classroom while their classmates are online researching the sizes of various farm animals. All three scenarios have one thing in common: they are the result of good picture books doing double duty as really good mathematical motivators.

Some picture books are aimed at specific math concepts that are clear from the books’ titles: The Greedy Triangle, Anno’s Counting Book, Math Curse, How Big Is a Foot?, and A Remainder of One are a few examples. The Brainy Day Books series presents math concepts in story form: Spaghetti and Meatballs for All! deals with division, for example, while Amanda Bean’s Amazing Dream is all about multiplication. A takeoff on Chinese folklore, Grandfather Tang’s Story explores geometric shapes using tangrams.

However, many picture books that are not specifically math-focused can be used quite successfully in connection to math standards at any level. The following are good examples of classic picture books that can be enjoyed as works of literature and also to painlessly introduce math concepts to children.

The Very Hungry Caterpillar As the caterpillar eats its way toward becoming a butterfly, young children can begin to use addition to tally the foods being consumed. The very basics of subtraction can also be introduced through the die-cut holes; the missing areas of food aptly illustrate “taking away.” Those round holes — perfect for little fingers — also help little ones explore the geometry of circles, and increasing-in-size pages can illustrate fractions. Calendar math can be taught through the days-of-the-week munching, leading up to the Sunday leaf double-page spread. The now-fat caterpillar takes up an entire page mirrored by the cocoon of the same size; these pages are perfect for measuring, estimation, scale, and even comparisons to actual caterpillars.

To extend beyond the text, students in grades four and above love to revisit this caterpillar friend and can investigate and calculate the number of calories consumed throughout the week by eating fruit, cheese, salami, pickles, cake, and other people-food. Comparing the caloric input of the actual science-based diet of caterpillars to the fictional one would encourage student research. A visual treat, The Very Hungry Caterpillar is sure to enliven math classes.

Make Way for Ducklings This Caldecott Medal winner about Mrs. Mallard’s relocation of her eight little ducklings to Boston’s Public Garden (with the assistance of Policeman Michael) offers many math possibilities. The obvious one is counting: Mrs. Mallard counts those eggs every day! As the ducklings hatch, they can be counted, and ordinals of “first” through “eighth” can also be taught. Because the duck family loves peanuts, figuring out how many peanuts are needed if each duckling wants two will introduce the basics of doing repeated addition and the connection to multiplication.

Other mathematical concepts include: sorting; size and weight (comparing adult ducks to newborns, for example, or the Boston Public Garden’s well-known statues of the ducklings to actual ducks); measuring; distance; and even inflation. Older students can research prices and salaries from the 1940s in comparison to today.

Map math is another useful concept that is possible to glean from Make Way for Ducklings. Readers trace the ducks’ flyover journey above Beacon Hill and the State House, over Louisburg Square to the Public Garden, and finally to the Charles River to nest. Students can use programs like Google Earth to compute distances, then compute the mileage the newly hatched ducklings and their mother cover as they march down Mount Vernon and Charles streets to meet Mr. Mallard at the Public Garden. Discovering alternate routes — or even duckling-type routes in their own towns — can make for rich mathematical discussions. Readers do not have to be Bostonians to recognize the practical applications of math in Make Way for Ducklings.

The Mitten This Ukrainian folktale, beautifully illustrated, describes a young child who loses his white mitten in the snow, where it quickly becomes “home” to a variety of woodland creatures. Mathematical concepts for this book include: capacity and volume (i.e., although the capacity of the mitten changes, the volume of each creature remains constant); counting (the number of creatures that discover the mitten as a potential home); measuring and estimation (as each creature enters, students can be invited to compare the expanded mitten to the original).

Older students can research the actual average sizes of the woodland creatures and rank them accordingly. An enterprising adult could even provide pairs of knitted mittens to see how much stretching is actually possible. Students predict the capacity of each mitten by guessing how many marbles or beans will be needed to fill each one. A variety of mittens brought in by students could also be used for introducing relative size.

Jan Brett’s website offers pictures of the animals to print out and mount on flannel boards or use as masks for classroom reenactments. Comparing these cutouts to the pictures in the book can also help introduce students to ratio, proportion, and scale. Using The Mitten to explore mathematical concepts can motivate both teacher and students on gray, wintry days.

Strega Nona This is another story that reinforces capacity and volume. As Strega Nona’s magic pasta pot endlessly overflows, the illustrations help students realize that the capacity of this pot — unlike Brett’s mitten! — is a constant. Calories, recipes, sorting of pasta shapes, and creating pasta patterns are mathematic concepts that could be launched from reading Strega Nona. Measuring various macaroni shapes before and after cooking can lead to mathematical predictions. Recipes for pasta dishes lead to measuring and fractions. This book is a delicious read-aloud (and busy parents and math teachers may just wish they owned that magical pot!).

It Could Always Be Worse This Jewish folktale describes the dilemma of a household that is crowded by too many family members. Desperate for relief, the father seeks advice from the wise rabbi — who gives him the surprising advice to bring the barnyard animals inside (leading to the lesson: “It could always be worse”).

Counting and capacity immediately come to mind with this book; the excellent watercolor illustrations invite counting of legs, arms, bodies, etc. The exploration of area and perimeter is also a natural choice when dealing with real estate, and the book could be used as a springboard for researching square footage, starting in the abstract with the book’s one-room hut and moving to the concrete with the students’ classroom, their school, etc. Older students can research square-footage capacity safety recommendations for classrooms, auditoriums, and even elevators. Real estate ads or the television show House Hunters can add to the study.

A similar story is It Couldn’t Be Worse. In this version of the folktale, the mother of the crowded house visits a wise fishmonger for advice. The illustrator uses bright colors and unusual angles in the cluttered illustrations to exemplify the chaotic household.

Math students of all ages would have a grand time acting out the events in a designated space (i.e., area and perimeter), along with researching animal sizes, area and perimeter relationships, and drawing to scale. An introduction to architectural blueprints and models — creating floor plans and locations for all the animals — could interest budding architects.

Parents and other adults who encourage discovery of math-related concepts with little ones at the earliest preschool ages will be providing children with a distinct advantage when those children enter school. Approaching math through the pages of picture books can help eliminate math anxiety for parent and child. As parents embrace and model the mathematical fun of these works, they are providing children with positive attitudes about the fun of math.

Reading strategies are evident in all books, but astute readers must often search for the math. To do so and share this discovery with children creates a fondness for — and link between — math and literature.

Good Math Storybooks

Anno’s Counting Book (Crowell, 1977) by Mitsumasa Anno

The Mitten: A Ukrainian Folktale (Putnam, 1989) adapted and illus. by Jan Brett

The Greedy Triangle [Brainy Day Books] (Scholastic, 1994) by Marilyn Burns, illus. by Gordon Silveria

Spaghetti and Meatballs for All!: A Mathematical Story [Brainy Day Books] (Scholastic, 1997) by Marilyn Burns; illus. by Debbie Tilley

The Very Hungry Caterpillar (World Publishing Company, 1969) by Eric Carle

Strega Nona: An Old Tale (Prentice-Hall, 1975) by Tomie dePaola

Make Way for Ducklings (Viking, 1941) by Robert McCloskey

How Big Is a Foot? (Atheneum, 1962) by Rolf Myller

Amanda Bean’s Amazing Dream: A Mathematical Story [Brainy Day Books] (Scholastic, 1998) by Cindy Neuschwander; illus. by Liza Woodruff

A Remainder of One (Houghton, 1995) by Elinor J. Pinczes; illus. by Bonnie MacKain

Math Curse (Viking, 1995) by Jon Scieszka; illus. by Lane Smith

Grandfather Tang’s Story (Crown, 1990) by Ann Tompert; illus. by Robert Andrew Parker

It Couldn’t Be Worse (Annick, 2003) by Vlasta van Kampen

It Could Always Be Worse: A Yiddish Folk Tale (Farrar, 1976) retold and illustrated by Margot Zemach

From the January/February 2015 issue of The Horn Book Magazine. For more recommended math-centric picture books, see "From The Guide: Math Picture Books" in the same issue.