Encourage tinkering with ideas, relationships, connections. Set up situations where students have to find information not readily available in school texts. Provide opportunity for students to design open-ended explorations of the concept. Provide multiple options so students can plan a unique "proof" of learning.
Students select a project and design a plan for its completion.
Objective: Students will personalize their learning through a choice of learning activities.
Activity: Students select one of the following projects and design a plan for its completion (correlate with the Fibonacci Sequence):
Research and report on the life of Fibonacci.
Make and demonstrate an abacus.
Research how the Moslem's invented their number system. Include a diagram of the number system.
Complete a detailed, colored drawing or design using spirals or helices.
Research the spiral and its meaning in ancient art, philosophy, and architecture.
Research and diagram or build the DNA double helix molecule. ï Research and report on infinity. ï Research and report on Einstein and his theory of relativity. ï Research and construct a model of the Leaning Tower of Pisa. ï Research and report on the town of Pisa, Italy. ï Create a detailed, colored drawing of fantasy flowers that shows Fibonacci numbers operating on them in different ways. ï Make a display of climates and soils that encourage growth of different species of sunflowers and daisies. Use a flower field guide as a resource. ï Count the clockwise and counterclockwise spirals and petals of different species of daisies. Record and diagram your findings. ï Find at least three different pine cone species. Paint the scales of each helix a different color. Try to paint four cones of the same species to show the four Fibonacci Numbers for that sequence. Create a display of your work. ï Check the hexagons on a pineapple for number sequences. Chart or diagram your results for a display. ï Draw and color at least five different species of Fibonacci flowers. Take notes on their Fibonacci Sequences and numbers. Use the notes and drawings to create a display. ï Report why ancient Greeks and Egyptians considered "7" a number of "completion." ï Report on the dawning of the modern scientific age with the discovery of Uranus in 1781, by William Herschel. ï Visit a beekeeper and secure a honeycomb to be used in connection with a report on the life of bees. ï Research and report on the "Sieve of Eratosthenes." Students will select one of the following projects and design a plan for its completion (correlates with the Golden Ratio): ï Measure and diagram the ratios of your family's bodies. ï Find at least ten pictures of animals for a booklet. Measure each for the Golden Ratio. Report your findings. ï Measure and diagram at least five real statues for the Golden Ratio. ï Design and build a "Golden Ratio Robot." ï Draw and color five strange faces for a booklet full of Golden Ratios. ï Draw, color and redesign a Greed face and statue so they have no Golden Ratios. ï Create a new ratio, name it, and write about how you discovered it. Draw a diagram showing how it would be used. ï Find faces of at least five different nationalities in magazines. Measure to see which have more or fewer Golden Ratios. Diagram your results. ï Diagram animal species that have spiral or helical horns, tusks, teeth, etc. Include animal parts that would grow in the spiral curve it continued: rhino horn, wolf fang, beaver tooth, fingernail. ï Compare and contrast (include diagrams) spirals of five different shells. ï Make a bulletin board exhibit of spirals in nature. Use pictures or tracings that are colored. Make the exhibit in spiral form. ï Using a ruler and calculator, check at least ten common rectangular objects, both big (door, playground, school wall) and small (light switch, page) to determine if they are Golden Rectangles. Document findings, both negative and positive). ï Report on the United Nations building, its architect, when it was built, how it was built, its floor plan, etc. Was it designed to be a Golden Rectangle? ï Research and report on "calculus" a kind of closer-and-closer study approach to a number. What is a "limit"?
