Reprinted from Connect
Vol.17 No.4, March/April, 2004
Focus on: Integrating Math and Science
Grade Level: 3-5
Grade Level: K-2

Integrating Science and Mathematics

through Children's Books

by Phyllis & David Whitin

Well-written children’s books can open worlds of meaningful exploration for young scientists and mathematicians. Science and mathematics both involve strategies such as using tools, solving problems, making models, describing attributes, and classifying. The National Council of Teachers of Mathematics (2000) emphasizes that children learn mathematics with understanding when mathematical ideas are applied in real-life contexts. Conversely, the National Science Education Standards (1996) note that all dimensions of scientific inquiry incorporate mathematics. It’s time to put the two together. It makes sense for children; it’s pragmatic for teachers. Let’s turn to some primary grade classrooms, and see how children engaged in some key mathematical experiences in response to hearing one particularly valuable book, If You Hopped Like a Frog (Schwartz, 1999). (Note: The book is a good choice for older children as well.)

What’s the potential?

In the introduction to the book, David Schwartz describes a boyhood wish. While his peers desired to be famous sports figures, he secretly wanted to be a frog. He marveled at the frog’s ability to leap long distances, and later his wonder led him to do some calculations. He found that a frog leaps twenty times its body length. Using an average child’s height of four and a half feet, he calculated that, as a frog, he could jump from home plate to first base (ninety feet) “in one mighty leap.”

On the following pages, Schwartz describes an attribute of various animals and an application to humans. The different attributes provide many contexts for the concept of ratio, e.g. length (a chameleon’s tongue), density (cones on an eagle’s retina), and weight (an ant’s strength). The book concludes with endnotes that give specific mathematical information and invite readers to try some further calculations. Children find the invitation hard to resist. As the following examples show, this book involves children in exploring the concept of ratio while they practice estimating, measuring, and computing. At the same time, they better appreciate the scientific principles of specialization and adaptation.

Extensions inspired by the book

In one first grade classroom some students were fascinated with the fact that a chameleon’s tongue is half the length of its body. Their teacher invited them to cut a piece of adding tape as tall as they were, and then fold it in half to find half their body length (Schwartz, 2001). The children then lay that half-length on the floor, stepped on one end, and looked ahead to see how far their tongue could reach. (Older children might move the tape in various directions around themselves to make a circle, and then calculate how much area they could cover with their tongue).

In a second grade classroom the students connected the book to a concept they had been studying in science: how do animals survive. The children interpreted the unique feature of each animal in the book as an attribute that helped it survive. For instance, they hypothesized that the long neck of a crane must help it reach food; the expert vision of the eagle helps it spot food from a great distance; and the jaws of a snake detach so that it can swallow large prey in its quest to survive. By putting the story in the context of survival, the children could discuss this book in a more meaningful way. The teacher then invited the children to test out this ability of the snake: if you could swallow things twice as large as your head, what do you think you could eat that you see in the classroom? After the children offered some predictions the teacher asked, “How could we be sure if you could really swallow these things?”

The children said they needed to know how wide their heads were. They then measured their heads, doubled that length, and found things in the room that were equal to, or less than, that length. They found books, chalk, erasers, and even their teacher’s head! This investigation gave them experience in using a ratio (2:1 of open mouth : head), determining equivalent lengths, and measuring with a ruler.

In a third grade class the children were most interested in being able to hop like a frog. Their teacher invited them to measure each other, and then challenged them to find what twenty of those lengths would be. Since the children had not yet been introduced to two-digit by two-digit multiplication, their teacher was interested in how they would solve this problem. When she asked the children what strategies they might use to find the total, Kristina remarked, “You could write down your height 20 times on the paper, and then just add it up.”

However, as the teacher observed the children working she noticed that some were becoming frustrated in having to add such a long column of numbers. When she came to Elizabeth she saw her using a different strategy. She was adding fifty twenty times even though she was only forty-nine inches tall. The teacher asked her to explain her thinking: “Well, since forty-nine was too hard to add twenty times, I decided to add fifty twenty times. When I am done I know I have to subtract one from each fifty, which means I have to subtract twenty from my answer” (i.e,. 50 x 20 = 1,000 – 20 = 980 inches). Several other students listened to this conversation and decided to use easier numbers to help them in their calculations.

For instance, Tiara did not want to add fifty-two twenty times “because I know I would get confused.” She added twenty fifties, then twenty twos, and added the two sums together, i.e. 52 x 20 = (50 + 2) x 20 = (50 x 20) + (2 x 20) = 1,000 + 40 = 1,040 inches (Figure 1). Each “5” on her paper represented a fifty; she crossed off two fifties at a time and then wrote “100” next to these “5’s” to show how she grouped two fifties to make each 100. Her strategy is a clear example of the distributive property in multiplication.

These third graders demonstrated a flexible use of strategies as well as good number sense by using “friendly numbers” to complete their calculations.

Providing a context

Literature provides a meaningful context for understanding scientific concepts, applying mathematical strategies, and inspiring further questions to research. We invite you to investigate this potential further by exploring some of the books below.

National Science Education Standards. (1996). Washington, DC: National Academy Press.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Schwartz, D. M. (2001, March). “We disagree with what you wrote: Challenging the author and other delights”. Paper presented at the Association of Mathematics

Teachers of Connecticut Annual Conference, Cromwell, CT.

Whitin, D.J., & Whitin, P. (2004), New Visions for Linking Literature and Mathematics. Urbana, IL: National Council of Teachers of English, and Reston, VA: National Council of Teachers of Mathematics.

Brown, Ruth. (2001). Ten Seeds. New York: Alfred A. Knopf. (life cycle of plants, subtraction)
Facklam, Margery. (1994). The Big Bug Book. Boston: Little Brown. (insects, measurement)
Feldman, Judy. (1991). Shapes in Nature. Chicago: Children’s Press. (nature, basic geometric shapes)
Hulme, Joy. (1991). Sea Squares. New York: Hyperion. (sea creatures, square numbers, multiplication) Jenkins, Steve. (1996). Big and Little. Boston: Houghton Mifflin. (animals, comparisons)
Jenkins, Steve. (1995). Biggest, Strongest, Fastest. New York: Tichnor and Fields. (animals, comparisons)
Lasky, Kathryn. (1997). The Most Beautiful Roof in the World: Exploring the Rainforest Canopy. New York, Harcourt Brace. (ecosystems, measurement, data collection)
Lesser, Carolyn. (1999). Spots: Counting Creatures from Sky to Sea. San Diego, CA: Harcourt Brace. (biomes, patterns, counting)
Marshall, Janet. (1995). Look Once, Look Twice. New York: Tichnor and Fields. (nature, shape, pattern)
Nagda, Ann Whitehead, and Cindy Bickel. (2002). Chimp Math: Learning About Time from a Baby Chimpanzee. New York: Holt. (health, time)
Nagda, Ann Whitehead, and Cindy Bickel. (2000). Tiger Math: Learning to Graph from a Baby Tiger. New York: Holt. (health, graphing)
Rau, Dana. A Star in My Orange. (2002). Brookfield, CT: Millbrook Press. (nature, basic geometric shapes)
Rice, David L. Lifetimes. (1997). Nevada City, CA: Dawn Publications. (plant and animal life spans, statistics, large numbers)
Schwartz, David M. (1999). If You Hopped like a Frog. New York: Scholastic. (animal attributes, adaptation, ratio)
Wahl, John, and Stacey Wahl. (1976). I Can Count the Petals of a Flower. Reston, VA: National Council of Teachers of Mathematics. (botany, prime and composite numbers, multiplication)
Wells, Robert. (1997). What’s Faster than a Speeding Cheetah? Morton Grove, IL: Albert Whitman. (animals, speed) Wells, Robert. (1993). Is a Blue Whale the Biggest Thing There Is? Morton Grove, IL:Albert Whitman. (animals, earth and space, large numbers)

©Synergy Learning International, Inc., 2004, All Rights Reserved.

Phyllis & David Whitin - Phyllis and David Whitin are both faculty members at Wayne State University in Detroit, Michigan. Phyllis teaches courses in children's literature and language arts. David teaches mathematics education and general curriculum courses. Their collaborative work focuses on inquiry learning and math-related children's literature. The ideas in this article are described further in their newly released book, New Visions for Linking literature and Mathematics, published by National Council of Teachers of English and National Council of Teachers of Mathematics (2004).
List all articles by Phyllis & David Whitin