Math Rules in the Animal Kingdom
Henry, Kerridwen Eliot, Hammond, Brenda, Teaching Children Mathematics
Teachers who continually assess their students' understanding, develop their knowledge of content and curriculum, and take time to reflect are able to guide their students to amazing success. If You Hopped Like a Frog (Schwartz 1999) has proven to be an extremely valuable resource for me as I go through this process of assessment, development, and reflection.
I have taught activities based on If You Hopped Like a Frog with diverse students ages 8 to 11. As a third-grade teacher, I used this book in the spring to teach a mathematics class designed to provide additional acceleration and enrichment within our curriculum. At the beginning of the next school year, I co-planned and taught four lessons connected to the book with a fourth-grade mathematics teacher, Jeanne Barnes. This article primarily focuses on my experiences with the accelerated third-grade class. It also highlights the ways in which I changed or extended the activities with other students. My goal is to share students' particular understandings and the reflection that guided my choices.
The NCTM Content Standards (2000) most directly connected to the book are the Grades 3-5 Standards for Measurement, Number and Operations, and Algebra, with a particular focus on linear, metric measurement; the comparative model for multiplication; and patterns, rules/functions, variables, and equations. The activities with the third-grade class took four hour-long lessons and an additional week of partial lessons. The activities with the fourth-grade class took only four hour-long lessons. Teachers can adapt the activities to better match their students' strengths and the local curriculum.
About the Book
Best known for his books How Much Is a Million? (1985) and If You Made a Million (1989), David Schwartz has created yet another high-quality picture book that presents engaging, worthwhile mathematics concepts.
If You Hopped Like a Frog is both highly accessible and conceptually rich. Children possessing a wide range of skills in reading and mathematics immediately feel comfortable and able to comprehend the basics while also feeling emboldened to explore more challenging ideas.
Each page uses a single sentence and bright, detailed illustrations to help students imagine the consequences of sharing traits with animals. Schwartz writes about objects and experiences that are familiar to children, including baseball, cars, and elephants. Connecting to background knowledge not only supports the children's reading comprehension but also helps them understand measurement concepts. The sentence "A shrew eats 3 times its own weight daily" may not mean much to most children if it is presented by itself, but Schwartz's words--"If you ate like a shrew ... you could devour over 700 hamburgers in a day" (p. 12)--better equip children to construct a sense of how much heavier the food is than the eater.
As with Schwartz's previous books, If You Hopped Like a Frog includes resources for teachers and students to focus their mathematics explorations. Schwartz begins with a letter to the reader that shares how he asked the mathematics questions that led to the writing of the book. His appendix includes more detailed, specific facts about the animals, as well as problem-solving scenarios (pp. 27-30).
Third-Grade Students Draw Themselves with Animal Proportions
Reading aloud with sensory imagery
Research supports teachers in striving to "understand the cognitive processes used most frequently by proficient readers and ... provide explicit and in-depth instruction focused over a long period of time on these strategies" (Keene and Zimmerman 1997, p. 23). Teachers should model a comprehension strategy as part of any literature-based study in any discipline. I chose to focus on the sensory-imagery strategy during the third-grade read-aloud because the students were familiar with this strategy and it allowed them to use their imaginations to make abstract concepts more tangible. …