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Counting the Spirals on a Sunflower

6th grade nonfiction passage about fibonacci number pattern: 204 words, six questions, an answer key and vocabulary.

6th grade nonfiction fibonacci number pattern 204 words

Counting the Spirals on a Sunflower

Start with 1 and 1. Add them to make 2. Add 1 and 2 to make 3, then 2 and 3 to make 5. Keep going and you get 1, 1, 2, 3, 5, 8, 13, 21, 34. Every number is the sum of the two numbers before it. This pattern is called the Fibonacci sequence, after an Italian mathematician who wrote about it about eight hundred years ago.

What makes the sequence famous is that it turns up in plants. Look closely at the seeds in the middle of a sunflower. They are packed into curved rows that spiral in two directions, one clockwise and one counterclockwise. If you count the rows going each way, the two counts are often neighbors in the sequence, such as 21 and 34. Pinecones and pineapples often show the same thing, with counts like 8 and 13.

Scientists think plants grow this way because spiral packing lets a great many seeds or scales fit into a small space with very little wasted room.

Still, not every plant follows the pattern exactly, and counts can vary from one flower to the next. The sequence is a helpful guide, not a strict law of nature. To test the idea yourself, find a pinecone and count the spirals going each way. Then see whether your two numbers are neighbors in the sequence.

Questions

  1. What are the first two numbers of the Fibonacci sequence? in the text

  2. How is each number in the sequence made? in the text

  3. What number comes after 21 in the sequence? in the text

  4. Where in a sunflower do the spirals appear? in the text

  5. Why do scientists think plants grow in spirals? think about it

  6. Why does the passage call the sequence a guide and not a strict law? think about it

Words to know

sequence
a list of numbers that follow a pattern
mathematician
a person who studies numbers and shapes
spiral
a curve that winds around a center point
clockwise
moving in the same direction as clock hands
scales
the small overlapping parts that cover a pinecone
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One passage, three levels

The same topic and facts written three ways, so a mixed class can read and talk about one text. Each group’s sheet shows only a shape; the key says which is which.

● Easier · 150 words · Flesch-Kincaid grade 2.5

Start with 1 and 1. Add them to make 2. Add 1 and 2 to make 3. Add 2 and 3 to make 5. Keep going. You get 1, 1, 2, 3, 5, 8, 13, 21, 34. Each number is the sum of the two before it. This is the Fibonacci sequence. It is named for an Italian mathematician who wrote about it about eight hundred years ago.

This pattern shows up in plants. Look at the seeds in the middle of a sunflower. They sit in curved rows. The rows spiral two ways, clockwise and counterclockwise. Count the rows each way. The two counts are often neighbors in the sequence, like 21 and 34. Pinecones and pineapples often show it too, with counts like 8 and 13.

Scientists think plants grow this way because spirals fit many seeds into a small space.

But not every plant follows the pattern. Counts can differ. The sequence is a guide, not a law. Try it yourself. Find a pinecone. Count the spirals each way.

▲ This passage · 204 words · Flesch-Kincaid grade 5.5

Start with 1 and 1. Add them to make 2. Add 1 and 2 to make 3, then 2 and 3 to make 5. Keep going and you get 1, 1, 2, 3, 5, 8, 13, 21, 34. Every number is the sum of the two numbers before it. This pattern is called the Fibonacci sequence, after an Italian mathematician who wrote about it about eight hundred years ago.

What makes the sequence famous is that it turns up in plants. Look closely at the seeds in the middle of a sunflower. They are packed into curved rows that spiral in two directions, one clockwise and one counterclockwise. If you count the rows going each way, the two counts are often neighbors in the sequence, such as 21 and 34. Pinecones and pineapples often show the same thing, with counts like 8 and 13.

Scientists think plants grow this way because spiral packing lets a great many seeds or scales fit into a small space with very little wasted room.

Still, not every plant follows the pattern exactly, and counts can vary from one flower to the next. The sequence is a helpful guide, not a strict law of nature. To test the idea yourself, find a pinecone and count the spirals going each way. Then see whether your two numbers are neighbors in the sequence.

■ Harder · 232 words · Flesch-Kincaid grade 8.2

Begin with the numbers 1 and 1. Add them together to make 2. Add 1 and 2 to make 3, and then add 2 and 3 to make 5. If you continue in this way, you generate the list 1, 1, 2, 3, 5, 8, 13, 21, 34. Every number in the list is the sum of the two numbers that precede it. This pattern is called the Fibonacci sequence, after an Italian mathematician who described it roughly eight hundred years ago.

What has made the sequence so famous is its tendency to appear in plants. Examine the seeds at the center of a sunflower closely, and you will notice that they are packed into curved rows that spiral in two directions, one clockwise and the other counterclockwise. When you count the rows running each way, the two totals are frequently neighbors in the sequence, such as 21 and 34. Pinecones and pineapples often display the same feature, with totals like 8 and 13.

Scientists believe that plants grow in this manner because spiral packing allows an enormous number of seeds or scales to fit into a small space with very little room wasted.

Nevertheless, not every plant follows the pattern precisely, and the counts may vary from one flower to the next. The sequence is a useful guide rather than a strict law of nature. To test the idea for yourself, find a pinecone and count the spirals running in each direction, then check whether your two numbers are neighbors in the sequence.

Download as one PDF

How to use it

  1. Press Read it big (or B) to put the text on the projector, or Full screen (F) to fill the whole screen.
  2. Ask the questions one at a time and use Show answer when the class has decided. A shows or hides every answer.
  3. Print student copy for the class, or Print with answers for yourself.

Ideas for class

  • Before reading, put sequence, mathematician, spiral, clockwise and scales on the board with their meanings from the Words to know section and have students predict what the text will be about.
  • Read it aloud once while students follow along, then have them reread it alone or with a partner. At a calm 100 words a minute it takes about 2 minutes to read aloud.
  • Use the Read it big button (or B) to put the text on the projector, and Show answer on one question at a time so the class commits to an answer first.
  • Question 5 asks the reader to infer. Ask students to point to the words in the passage that led them to their answer.
  • Ask students to write one question the passage did not answer, then look for the answer in a book or on a classroom screen.
  • Print the student copy for independent work and keep the answer-key copy for yourself.

Related

Questions

What reading level is "Counting the Spirals on a Sunflower"?

It was written for 6th grade. It has 204 words and works out to a Flesch-Kincaid grade level of about 5.5. That is a formula's estimate from sentence length and syllables, and it is not a Lexile or a guided reading level, so check it against your students.

What do the questions ask?

There are six. 4 ask for something the text says directly and 2 ask the reader to work something out from clues. Each has an answer in the key, and the answers are written as a teacher would accept them, not as the only possible wording.

How long does it take to read?

About 2 minutes read aloud at 100 words a minute. For a one-minute fluency check, paste it into the fluency timer and use the word count.

Can I print it?

Yes. Print student copy gives the passage, the questions with lines to write on, and the word meanings. Print with answers gives the same page with the answers filled in. Both are made in your browser.

Is this passage from a published book?

No. It was written for Peabody Teach, so there is no book to buy and no login to read it.

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