Put the VT to work in your classroom
Where Math Meets Poetry
Lesson Question:How can students apply Fibonacci's sequence of numbers to write "Word Fib" poems that expand their vocabularies?
Lesson Overview:In this lesson, students identify the algorithm behind Fibonacci's sequence of numbers and then read a New York Times article about how blogger Gregory K. Pincus invented a poetry form based on this number sequence. Students then synthesize their knowledge of the Fibonacci sequence and the VT to create their own "Word Fib" poems that explore the multiple connotations of some challenging one-syllable vocabulary words.
Length of Lesson:One hour to one hour and a half
Instructional Objectives:Students will:
- identify the algorithm behind Fibonacci's sequence of numbers
- evaluate a news article about a Fibonacci-inspired poetry form
- research some unfamiliar one-syllable vocabulary words by using the VT
- write and share their own "Word Fib" poems based on vocabulary words
- student notebooks
- white board
- computers with Internet access
- copies of the New York Times article "Fibonacci Poems Multiply on the Web After Blog's Invitation" (one per student), available at the following URL: http://www.nytimes.com/2006/04/14/books/14fibo.html.
- "Word Fib Starters" [click here to download]
Warm-up:Identifying the pattern behind the Fibonacci sequence:
- Write the following number sequence on the board: 0, 1, 1, 2, 3, 5, 8, ?
- Inform students that these numbers follow a special sequence or pattern, and it is their job to try to figure out the next number in this sequence.
- Give students a few minutes to consult with one another and to try to determine how this sequence of numbers was formed (and to predict the next number in the pattern).
- Elicit students' theories about the number pattern and establish that the next number in the sequence is 13 [since it is the sum of the previous two numbers in the sequence (i.e., 5 + 8 = 13)].
Instruction:Learning about Leonardo Fibonacci's work as a mathematician:
- Inform students that the term in mathematics for a rule that one follows to determine the numbers in a sequence is called an "algorithm," and that they just discovered the algorithm behind the Fibonacci sequence of numbers.
- Explain that this number sequence became famous in the early 13th century when the Italian mathematician Leonardo Fibonacci used it to try to predict the population growth of a single pair of rabbits over time (i.e., one pair of rabbits produced another pair of rabbits, then two pairs of rabbits, and so on). In addition to the number sequence, Fibonacci also studied the "golden ratio" formed between two consecutive numbers in this sequence (approximately 1.618). This golden ratio has been associated with certain aspects of music, art, architecture, and even nature.
- Distribute copies of the April 14, 2006 New York Times article "Fibonacci Poems Multiply on the Web After Blog's Invitation" or have students access the article on-line, available at the following URL: http://www.nytimes.com/2006/04/14/books/14fibo.html.
- Have students read the article with the following guided reading questions in mind: How did Gregory K. Pincus apply the Fibonacci sequence to writing? How else has the influence of Fibonacci's work become evident? According to the article, why have "Fibs" become increasingly popular?
- Hold a brief discussion about the article "Fibonacci Poems Multiply on the Web After Blog's Invitation," eliciting students' responses to your previous set of reading questions. In your discussion, you can point to the examples of how Fibonacci's work relates to the music, knitting, the shape of the Nautilus shell, and to popular culture (e.g., "Da Vinci Code" and the metal band "Tool"). You might also discuss why some writers have embraced Pincus's "Fibs" as a popular form of poetry (since it is a "simple, yet restricted" form that is puzzle-like and fun).
- Explain to students that they can use Pincus's "Fib" format and the VT as a way to explore the various meanings and connotations of some tricky one-syllable words (not all SAT-caliber words are polysyllabic!).
- Demonstrate the process of composing a "Word Fib" by beginning with a one-syllable vocabulary word with which your students may not be familiar, and then continuing the rest of the poem according to the Fibonacci sequence (i.e., line 2: one syllable; line 3: two syllables; line 4: three syllables; line 5: five syllables; line 6: eight syllables).
- For example, type in the word "yearn" into the Visual Thesaurus search box and display its "word web" on the white board. Then, use the different words in the "yearn" display (in the web or in the meanings list) as lines of your original fib or as sources of inspiration for lines. Here is a sample Fib that uses different words related to "yearn" found on the VT display but then ends in a more personal association with "yearn" in the last three lines:
how I feel
for the Nintendo
sitting in the Gamestop window.
Writing original "Word Fibs" using the VT:
- Organize the class in partners or in small groups (depending on how many computers with Internet access are available) and distribute the "Word Fib Starter" sheet to each set of students [click here to download].
- Explain to students that they will be composing "Word Fib" poems that explore the different meanings and/or associations that are related to some challenging one-syllable words.
- Have each partnership or small group choose an unfamiliar one-syllable word from the "Word Fib Starter" chart (or from somewhere else), look it up on the Visual Thesaurus, and then create a Fib that incorporates different associations with that "starter" word.
- Circulate around the room as students compose their Word Fib poems, ensuring that students are adhering to the Fibonacci sequence in determining the number of syllables in each line of their Word Fibs.
Wrap-up:Sharing Word Fib poems:
- Have a representative of each group or partnership share his or her Word Fib poem with the class. Ideally, students could read aloud their poems in class and also display their poems on the white board or on large drawing paper.
- After each poem is shared, discuss with presenting poets their composition process. Which lines in their poems came directly from the VT? Did their poems express one meaning of their starter word or did they also include multiple meanings of that word? How did the VT display help them think about their word in different ways? How did the Fibonacci sequence influence their composition process?
Extending the Lesson:
- If you would like students to learn more about the Fibonacci sequence or about how the golden ratio is evident in nature, direct them to the interactive Annenberg Media "Learner.org" site where they can use interactive graphics to solve the puzzle of the seashell spiral (http://www.learner.org/interactives/renaissance/fibonacci/).
- If your students would like to read more Fibs or even share their Word Fib poems with Gregory K. Pincus himself (the subject of the New York Times article), direct them to his "GottaBook" blog: (http://gottabook.blogspot.com/).
- You could assess each student's comprehension of the New York Times article "Fibonacci Poems Multiply on the Web After Blog's Invitation" by having them write responses to the guided reading questions mentioned in this lesson.
- Assess each partnership or group's Word Fib poem to see if it explores different meanings or associations with a particular word and to see if it follows the Fibonacci sequence (in terms of the number of syllables contained in each of its lines).
Standard 1. Uses a variety of strategies in the problem-solving process
Level IV (Grades: 9-12)
2. Constructs algorithms for multi-step and non-routine problems
4. Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems (i.e., uses deductive reasoning)
Standard 3. Uses basic and advanced procedures while performing the processes of computation
Level III (Grade: 6-8)
9. Understands how different algorithms work for arithmetic computations and operations
Level IV (Grade: 9-12)
6. Uses recurrence relations (i.e., formulas expressing each term as a function of one or more of the previous terms, such as the Fibonacci sequence or the compound interest equation) to model and to solve real-world problems (e.g., home mortgages, annuities)
Standard 2. Uses the stylistic and rhetorical aspects of writing
Level III (Grades 6-8)
1. Uses descriptive language that clarifies and enhances ideas (e.g., establishes tone and mood, uses figurative language, uses sensory images and comparisons, uses a thesaurus to choose effective wording)
Level IV (Grades 9-12)
1. Uses precise and descriptive language that clarifies and enhances ideas and supports different purposes (e.g., to stimulate the imagination of the reader, to translate concepts into simpler or more easily understood terms, to achieve a specific tone, to explain concepts in literature)
Standard 6. Uses reading skills and strategies to understand and interpret a variety of literary texts
Level III (Grades 6-8)
1. Uses reading skills and strategies to understand a variety of literary passages and texts (e.g., fiction, nonfiction, myths, poems, fantasies, biographies, autobiographies, science fiction, drama)
2. Knows the defining characteristics of a variety of literary forms and genres (e.g., fiction, nonfiction, myths, poems, fantasies, biographies, autobiographies, science fiction, drama)
Level IV (Grades 9-12)
1. Uses reading skills and strategies to understand a variety of literary texts (e.g., fiction, nonfiction, myths, poems, biographies, autobiographies, science fiction, supernatural tales, satires, parodies, plays, American literature, British literature, world and ancient literature)
2. Knows the defining characteristics of a variety of literary forms and genres (e.g., fiction, nonfiction, myths, poems, biographies, autobiographies, science fiction, supernatural tales, satires, parodies, plays, drama, American literature, British literature, world and ancient literature, the Bible)