By: Alannah Mcgregor, Brittany Kozak, and Gudrun Mackness

To explore complex number patterns that reflects a sequence that is found in nature and has been translated into art

● Index cards with “warm-up” number patterns (Appendix A)

● Set of Cue cards with a picture of a flower and its name (Appendix B)

● Graph paper, markers, and pencils● Picture book: Fibonacci Numbers in Nature● Natural objects showing Fibonacci pattern (i.e.

Apples cut horizontally through the centre, Pineapples, Pinecones)

Fibonacci Sequence Goals Curriculum Expectations: Grade 6

Mathematics: ● Patterning and Algebra & Patterns and

Relationships: identify geometric patterns, through investigation using concrete materials or drawings, and represent them numerically

● Data Management and Probability & Collecting and Organization of Data: collect and organize data and display the data in tables that have appropriate titles and labels

● Data Relationships: read, interpret, and draw conclusions from primary data presented in tables

Materials

Lesson

Introduction (5 minutes)● Hand out number pattern cards to students (Appendix A) and have them discover the pattern● Give students a brief history on Fibonacci. Please see http://www.brainpickings.org/2011/07/21/the-

man-of-numbers-keith-devlin-fibonacci/

Lesson (20 minutes)● Ask students to explore the number of petals on the flowers on cue cards (Appendix B) and the pre-cut

sections of the fruit provided. Go through the first flower and fruit as a class to ensure all students know what a petal of a flower is and what is meant by ‘sections’ of a fruit.

● Have students document the numbers they find on a t-chart (Appendix C). Use tape to trace the spirals found in pineapples. Have students draw the rows of spirals they see in the pine cones.

● Debrief as a class and put the documented numbers in order from smallest to largest. ● Show patterns by measuring the way things grow. It’s called the Golden Spiral (Nautilus example,

Appendix D). By using the numbers in the pattern, we can all draw the Golden Spiral.● Give students materials to draw spiral and guide them just for the first couple of squares. Be sure to

explain that the number determines the length and width (not the number of square units).

Closure (10 minutes)● Ask students “Why do you think the 1s column (right) only goes up to 9?” ● Together in small groups, begin to represent numbers one by one to ensure that every student

understands the basics. ● Begin by representing one digit numbers moving our way up to 5 digit numbers, as follows: 2, 7, 13,

69, 325, 6479, and 10000.

Possible Extensions

● Sometimes we can see the Golden Spiral in art and photography. The center of the spiral is the focal point of the picture. Have students use the iPad app “Awesome Camera” to take one photo where the focal point is in the center of the spiral and one without the use of the spiral. Compare photos & vote on which one is more aesthetically pleasing. (Example, Appendix E)

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Appendix A - Example of index card number patterns

Appendix B - Set of flower cue cards. Photocopy and cut out to create set of cue cards.

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Appendix C - Patterns in Nature

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Appendix D - Nautilus example of a Golden Spiral

Appendix E - Example of pictures taken on the iPad App “Awesome Camera”

Extension: To construct a “Golden Rectangle” please see: www.wikihow.com/Construct-a-Golden-Rectangle.

The focal point (pineapple) is in the center of the spiral.

The focal point (pineapple) is not in the center of the spiral.

Example of the app “Awesome Camera”. When you are ready to take a photo the black background is removed allowed you to place the object at the centre of the spiral.

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