Fibonacci Flowers

Watch a garden of Fibonacci flowers spring to life in the classroom as students discover a mathematical pattern in nature!

  • 1.

    Students arrange a display of flowers with various numbers of petals. Use photographs if the actual samples are difficult to obtain.

  • 2.

    Distribute one flower to each student and invite them to carefully count the number of petals on their flowers.

  • 3.

    Ask students to report the number of petals counted and record the numbers prominently where all can see them.

  • 4.

    While a few flowers may have 4, 6, or 7 petals, most students will report numbers from the following sequence: 1, 2, 3, 5, 8, 13, 21, 34….. Ask students to copy this series of numbers on paper at their seats. Then invite them to look for a pattern to this series. How are each of the terms in this sequence arrived at? (Factor = add two adjacent terms together to arrive at the next term; 2 + 3 = 5.) If they were to extend the series by one more number, what would it be? (answer: 55) What would the following 3 terms be? (89, 144, 233)

  • 5.

    Invite students to investigate the 13th century mathematician, Fibonacci and his famous number sequence. The pattern appears often in nature such as in the seed spirals of a sunflower and the pattern on a pineapple as well as in the number of petals on a flower.

  • 6.

    Invite the class to create a garden of Fibonacci flowers! Ask each student to create a three dimensional paper flower that fits the Fibonacci pattern with 1, 2, 3, 5, 8, 13, 21, or 34 petals. It can be a replica of a real flower (the calla lily has 1 petal, the buttercup has 5, black eyed Susans have 13, etc.); or it can be an imaginary one as long as the number of petals equals a Fibonacci number.

  • 7.

    Encourage students to experiment to see how they can create three dimensional effects by bending and/or curling various pieces of paper. Allow them to use additional materials for special effects such as curled ribbons, or glitter glue, if they are available.

  • 8.

    Demonstrate how to create various hues by mixing Crayola® Watercolors or using various layers of Crayola® Crayons or Crayola® Colored Pencils or a mixture of mediums. Encourage the use of vivid colors and interesting textures. Remind them to count their petals carefully!

  • 9.

    Engage students in a discussion about how and where to display their flowers so that others can learn about Fibonnaci patterns in nature. Work together to mount the display. Encourage interested students to explain the display to visitors.

Standards

  • LA: Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grade level reading and content, choosing flexibly from a range of strategies.
  • LA: Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade level topics, texts, and issues, building on others’ ideas and expressing their own clearly.
  • LA: Present claims and findings, sequencing ideas logically and using pertinent descriptions, facts, and details to accentuate main ideas or themes; use appropriate eye contact, adequate volume, and clear pronunciation.
  • MATH: Use random sampling to draw inferences about a population.
  • MATH: Represent and interpret data.
  • MATH: Analyze patterns and relationships.
  • VA: Students will initiate making works of art and design by experimenting, imagining and identifying content.
  • VA: Students will use a variety of methods for preparing their artwork and the work of others for presentation.

Adaptations

  • Encourage students to explore Fibonacci patterns in other areas of nature. What about the scales on a fish, the markings on a pineapple, the patterns on a turtle’s shell…?
  • Invite interested students to learn more about Fibonacci and his mathematical ideas. Ask them to share what they learn with the class.
  • Invite students to investigate other applications of Fibonacci numbers such as in the Golden Ratio.