by Jacqueline Ventura
As a teacher of sixth-grade mathematics, reading, and language arts, I shared the book I Can Count the Petals of a Flower by John Wahl and Stacey Wahl (Reston, Va.: National Council of Teachers of Mathematics, 1976) with my students. The book has a direct link to science, and it furnishes a meaningful context for mathematics. It invites readers to count the number of petals on flowers to show the numbers 1 to 10. The second part of the book shows the numbers 1 to 15, but some illustrations include multiple photographs. For instance, six is shown as one yellow day lily (one flower with six petals, or 1 × 6), two painted trilliums (two flowers, each with three petals, or 2 × 3), and three crowns of thorns (three flowers with two petals each, or 3 × 2). Students remarked that 6 × 1 was not likely, because six flowers would not normally each have one petal.
While we discussed the book, the children noticed that even numbers always had more than one picture. They predicted the pictures that would appear for the numbers 7 and 8. When they saw the page for 9, one child declared, "Nine is the first odd to have more than one picture because combinations that make nine are 1 × 9 and 3 × 3." "Why is that?" I asked. The children then discussed prime and composite numbers. "Ten will have three pictures: one for 1 × 10, one for 2 × 5, and one for 5 × 2." "Twelve will have five pictures." "Fifteen has three pictures." The children then made a game out of how many pictures would come for the next numbers and often shouted out the answer before I turned the page. They were eager to see whether their predictions were correct.
Other interesting observations were made along the way. "White, yellow, and orange are common colors for petals." "Sixteen has a pink dogwood. There are Chinese dogwoods and pink dogwoods." I added, "I wonder if there are any other dogwoods?" One boy asked, "Are there any flowers you can eat?" I replied, "That's a very interesting question. In fact, I believe that certain flowers are edible. It would be interesting to find out what kinds." The wide variety of questions led one student to muse, "This is more of a science book than a math book."
As we ended the book I asked, "Let's suppose the authors continued the book to 100. What problems might they encounter?" A response included "There might not be a flower with 50 or 100 petals." "Or even 17 because they stopped at 16." "Is there really a flower with 20 petals?" "What's the largest number of petals on a flower?" "I think a rose has a lot of petals. How come there were no roses in the book?"
As I went home that day, I remembered one student's comment that pleased all the children: "Ms. Ventura, can we go to the greenhouse and actually count the number of petals that flowers really have?" Her idea seemed a perfect way to extend their interest, so I arranged a trip to the school's greenhouse.
The horticulture teacher brought to life both the mathematical and the scientific perspectives of I Can Count the Petals of a Flower. Children touched real flowers and learned about complete and incomplete flowers. They learned about Fibonacci's investigation of patterns in nature and how brightly colored petals attract insects that are seeking nectar. After visiting the greenhouse, the children spent time writing in their journals some of the things that they wondered about or noticed throughout the book or on the trip. I then encouraged them to explore further. Some children used Microsoft Encarta to research edible flowers. A few students did research on roses to find out how many petals they have. Several students created a graph on Microsoft Excel and compared different flowers and their numbers of petals. Students then used a spreadsheet to find the average number of petals among their data. Students grew more and more eager as they prepared presentations to share with their classmates. They even invited the horticulture teacher to hear their reports.
Encouraged by my asking open-ended questions and sharing my own curiosity and excitement, the class was led by the book into a wide range of investigations and discussions. I was happy with the experience because I am always looking for ways to connect mathematics and science. The students recognized that mathematics is in nature. It is all around us, every day, and it is real!
|Jacqueline Ventura is currently teaching mathematics and language arts in the Hewlett-Woodmere School District, New York. She has been an instructor in the middle school for six years. She is completing her master's degree in elementary education with a specialization in children's literature at Queens College.