Curriculum – Patterning and Algebra; Data Management and Probability
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.
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)
- 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/
- 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).
- 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.
- 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)
*Download the lesson to see all appendices.
The Robertson Program has chosen to place Fibonacci in quotes as per research by Rochelle Gutierrez:
I place Fibonacci in quotes to highlight the presence of settler colonialism. That is, although the Italian Leonardo Pisano (Fibonacci) receives credit for the pattern, many cultures and persons throughout the world, including Pingala in 200BC in India, had already known/performed the same pattern many years earlier. In fact, if humans are no longer the center, we might credit nautilus pompilius (Nautilus shell), pinus coulteri (pinecone), or helianthus annus (sunflower) with the “discovery” (p. 12, Footnote 6).
Gutiérrez, R. (2017). Living mathematx: Towards a vision for the future. Philosophy of Mathematics 12 Education, 32(1).