If you watched any of the 2014 Sochi Winter Olympics, also known as the XXII Olympic Winter Games, you know how important numbers are to the athletes, officials, and spectators, both in terms of understanding the events and determining the outcomes. In fact, each sport has numbers or units peculiar to its type of competition. Here are a few examples from some popular events.
2 minutes and 50 seconds—length of the “Short Program”
4-4 ½ minutes—length of the “Long Program”
200 ft. x 100 ft.– Rink dimensions (compared to 200 x 85 in the NHL)
Curling (one of my favorites)
16 stones are thrown in each of 10 ends
42-44 pounds—weight of curling stone
36 inches—maximum circumference of a curling stone
10,000 meter event—25 laps around track
.22–caliber of rifle used
50 meters—distance to target
150 meters—length of penalty lap for each missed target
3:45.39—gold medal winning time (in minutes)
3:46.05—silver medal winning time
3:46.27—bronze medal winning time
0:00.88—time separating gold from bronze
(BTW–The Olympics (not a stunning revelation) is an amazingly rich resource for practical applications of math vocabulary and concepts found in CC math standards: problem solving, place value, decimals, fractions, a range of calculations/computations, terminology, telling time, conversions, Roman numerals, ordinal/cardinal numbers, etc. Wow!)
The book Lifetime: The Amazing Numbers in Animal Lives, by Lola Schaefer (one of my favorites from my holiday break reading), has nothing to do with the many different kinds of competition found in the Winter Olympics. But it has everything to do with important numbers in the ultimate competition in the lives of animals—survival!
Lifetime: The Amazing Numbers in Animal Lives. 2013. Lola Schaefer. Illustrated by Christopher Silas Neal. San Francisco: Chronicle Books.
Genre: Informational picture/counting book, mixing math and science
Grade Levels: K and up
Features: Back matter—extended information on each featured animal, including scientific name, average–defined/explained mathematically, practice with concept of averaging.
40 pages (including back matter)
Visit lolaschaefer.com to find out more about Lola M. Shaefer and her books.
Each page in Lifetime begins with the phrase “In one lifetime,” matter-of-factly introducing an animal to readers by name, then offering a numerical fact about a specific physical characteristic or behavior. Young readers will want to pay close attention to the mixed-media illustrations—they match the animal’s important number! On one page, for instance, the author informs us that, “In one lifetime, this caribou will grow and shed 10 sets of antlers.” Look carefully at the illustration and you will count ten antler sets. We learn that the alligator will lay 550 eggs in its lifetime—Yep! All 550 are there. And the male seahorse, we are informed, will lay 1,000 eggs—have fun counting them! (I didn’t, but I’m sure illustrator Neal did.) Flip to the back of the book and you will find more detailed information about each of the eleven animals and their important numbers.
The book opens with an informative statement/disclaimer from the author to clarify how she came up with her numbers. She tells us that she based her calculations on the “average adult life span of each wild animal” and researched information on each animal’s behaviors and physical characteristics. I appreciated that author Shaefer let’s us know that even though each animal belonging to a species may be different, because of her in-depth research and her attention to the math, she feels very confident about the accuracy of her averages and approximations—her numbers. In a back section, she informs readers, “Math gives you answers you can’t find any other way. Without math, I wouldn’t have been able to write this book.” She speaks confidently to readers with the voice of an “expert,” and her confidence becomes a reader’s confidence in her as an authority.
In the Classroom
1. Preparing for Reading. As always, take time to preview and read the book prior to sharing or involving students in independent reading. You will want to read the back matter, as well, so you are aware of the more detailed content of the informative passages about each of the animals. If you plan to use this as a complete read-aloud, the illustrations could be shown to students using a document camera. I believe students will call for a second reading, especially if they want to try and count the antlers, spots, flowers, roosting holes, rattles, babies, etc.
2. As You Read (Ideas/Word Choice). Because there are only one or two sentences on each page (and the first sentence always begins with the pattern “In one lifetime…”), the author has to make strong word choices to make sure her message comes through focused and clear. A limited amount of text puts extra pressure on each word choice—choosing the most specific noun, the right adjective (if necessary), and the most precise verb to make sure readers are seeing and feeling the author’s ideas. I suggest doing a second reading of the book to keep track on chart paper of the nouns, adjectives, and verbs the author has used on each page. It could be done like this:
Noun Adjective/noun Verb
Spider papery egg sac spin
Caribou, antlers grow, shed
You could do this in so many ways depending on the age level of your students (and the specific CCSS you may be focusing on). This would give your students a platform for understanding parts of speech and for sentence building in their own writing. An immediate practice for younger students could be to imitate the book’s pattern—In one lifetime—changing it to In one recess, or In one day, etc. The emphasis would be on communicating an idea in one or two sentences by choosing the most descriptive nouns, adjectives, and verbs. Convention Alert!!—this would be an opportunity to talk about commas and why there needs to be one in sentences following this pattern.
In one recess, Cruz blasted the black and green soccer ball against the wall one hundred times.
3. Math One. This book is about animals and some of their important numbers—so let’s not forget about the math opportunities to be found. As you are reading the book, have your students help you keep a chart of the numbers. I suggest writing both the numerals and the number words spelled out. Ask your students to look for patterns, make predictions, etc. Conventions Alert!!—Discuss/practice/apply the conventions for spelling out numbers versus using numerals. (Notice how the author applied the conventions, staying consistent throughout.)
4. Math Two. The author has included in the back matter a section called, “What is an average?” Here she defines/explains the word as she has used it—a way to describe a typical or usual amount, and her reasoning for choosing the mathematical average (an expression of central tendency) for the purpose of calculating each animal’s number. To help readers understand, she uses the example of finding the average number of times a person might brush his/her teeth in a week. Younger writers might be interested in writing about themselves and their important number, not focused on a lifetime but based on an hour, day, week, month, year or a particular year in school (e.g. 2nd grade). Their numbers might be about saying the Pledge of Allegiance, lining up, school lunches eaten, tying shoes, hanging up a coat, sharpening a pencil, etc.
In a section called, “I Love Math,” Shaefer explains the importance of applying math to her scientific curiosity to help express what she wanted to say about animals’ lives. For older students, I would ask them to choose a mathematical concept—something from a standard they had been focusing on—and explain it using both words and number examples. Their audience could be another student, a parent, etc. These two sections serve as great examples of a focused message, clear communication through word choice, and being an “expert” on your topic.
5. Math Three. Younger students could use her examples in the “I Love Math” section to write their own “story” or word problems. Student writers would need to be sure to include all the necessary information and word clues to guide readers to the appropriate operation(s) and an opportunity to correctly solve the problem. Convention Alert!!—Writers will need to know the difference between a telling sentence—ending with a period—and a question sentence—ending with a question mark.
Example (Actual word problem written by a 2nd grader I happen to know.)
Martin has 24 chocolate chip cookies. His best friend Ahmed has 20 oatmeal raisin cookies. How many cookies do they have all together?
6. Average—Without the Math. Though the concept of average is steeped in its mathematical roots, we often use the word as a synonym for usual, typical, normal, regular, or as another way to say mediocre, plain, or unexciting. Choose one of these meanings to launch students into explanatory writing of a different kind. Instead of explaining a concept or procedure, students could take a more personal path and write about—the “average” 6th grader interests, their activities on an average weekend or day off from school, what it means to be an “average” student, the traits of an “average” soccer player compared to a “skilled” player, etc. The writing could even head down the path of persuasive/argument (See STG post from January 31, 2014)—why being called an “average kid” might be a good thing but being called an “average student” might not, for example.
7. Research and Voice. Take a moment to discuss with your students how they as readers know when writers are “experts” on their topics— how, as a reader, they can tell when writers know what they’re talking about. What happens to readers when they are in the hands of an expert? Are they able to tell when writers are faking it or stretching their limited knowledge too thin? What happens to readers when they don’t have confidence that the writer is an expert?
Lola Schaefer says, “I was curious about the lives of animals.” Her curiosity led to research—observation, reading, speaking with/listening to/digging into the work of known experts, etc. Following her lead, have your students select an animal they are curious about to begin “researching.” Depending on the grade level, the research could be done as a class, in small groups, or as individuals. It might involve some computer time, visits to the library, or a field trip to a zoo. As readers, we have confidence in Ms. Shaefer’s writing; her writer’s voice comes through because of her research efforts–she has become an “expert” and writes with that voice, just like your students will need to be for the sake of their readers. Their writing could follow the author’s pattern—finding the animal’s interesting/important number, with the outcome being a few sentences or stretching all the way to a few paragraphs or pages. The length might be connected to the purpose and audience of the writing—a class book written for a younger audience, a science fair-type display for adults, a full-blown research project aimed at convincing lawmakers to help protect a particular animal, etc.
8. Research—Narrative writing. The same research described above could be used to lead students into a piece of narrative/informational writing. In this writing, students would share what they have learned about their animal, including that animal’s significant number, by telling a “story,” fictional but factual story, based on research. The writer’s voice would be that of an expert but because of the created story, more personal, too.
9. Math Four. Since I’ve been so immersed in the Winter Olympics, I can’t help making one more math and writing connection between Lifetime and the Sochi Games. The unit of time in Lola Shaefer’s book is a lifetime—a unit of time varying in length depending on the type of animal and a myriad of other conditions. The events of the Olympics, Winter or Summer, deal with time broken down into units and sub-units so small they’re almost impossible to imagine—tenths, hundredths, thousandths of seconds. What could possibly happen in such a teeny amount of time? Older students might be interested in writing answers to this question (sentences, paragraphs, poetry) both in terms of Olympic outcomes—medals earned, dreams realized or shattered, etc., and in terms of human events, moments, and emotions.
10. Resources. Here are a few other highly recommended books—directly/indirectly relating to math, math writing, animals, or writing about animals—that you or your students might find useful.
Math Talk: Mathematical Ideas in Poems for Two Voices. 1991. Theoni Pappas. San Carlos: Wide World Publishing/Tetras.
How Fast is It? (How Strong is It?, How Big is It?). 2008. Ben Hillman. New York: Scholastic.
Math Poetry: Linking Language and Math in a Fresh Way. 2006. Betsy Franco. Culver City: Good Year Books.
Mathematicles. 2006. Betsy Franco. New York: Simon & Schuster.
Coming up on Gurus . . .
Vicki will be reviewing Holly Goldberg Sloan’s Counting by 7’s. Don’t forget, we are here for you and your student writers! Are you are thinking about professional development in writing during the remainder of this school year? Whether your focus is on complying with the Common Core writing standards or making students strong writers for life, we can help. Let us design a seminar or series of classroom demo’s to meet your needs at the classroom, building, or district level. We can incorporate any combination of the following: Common Core Standards for writing, the 6 traits, writing strong narrative, exposition, or argument, and the best in literature for young people. Please contact us for details or with questions at any time: 503-579-3034. Thanks for stopping by. Come back—and bring friends. And remember . . . Give every child a voice.