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# Finding Fibonacci

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• 1. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] A WebQuest for 8th Grade Mathematics Designed by Brooke Jacobson [email_address] Based on a template from The WebQuest Page
• 2. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] You are on an investigation to discover the golden ratio within architecture, art, nature, and the human body. I am sending you to Greece to discover the uses of the Fibonacci sequence, the golden ratio, and the golden spiral. Can you find Fibonacci? Leonardo Fibonacci was born in 1175. His discoveries of the Fibonacci Sequence, the Golden Ratio, and the Golden spiral are significant in the connections that it makes to nature and the real world. Although his discovery was not made until nearly 1200, we can find amazing architecture from Greece dating back to the 500’s BC.
• 3. Student Page Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Students will need to compile their data and organize it in a file on notepad. They will be required to show three examples of Fibonacci found in architecture, art, nature, and the human body. Once they compile all of this information, they will create either a piece of artwork or blue prints to describe what they learned. Title
• 4. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Students will have 2 class periods to explore Fibonacci and the Golden Ratio in Art, Architecture, Nature, and the Human Body. After these 2 days, all additional research will be for homework. The next 3 days will be spend designing a project, either a piece of artwork or blueprints for a structure that utilizes the Golden Ratio or the Fibonacci Sequence. Day 1-2 Breakdown: Step 1: Students will separate into pairs. Step 2: Together partners will select a computer and begin researching. Step 3: Students will select available links and explore the Golden Ratio in a variety of settings. Step 4: Students will take “travel notes” in notepad and print when finished. Step 5: Together, students will decide on which project they would prefer to do. Click here to learn about: A Fibonacci Overview Architecture Art Art 2 Nature Nature 2 Human Body Day 3-5 Breakdown: Step 1: Students will pair off at the beginning of class and begin the rough design of their projects. This should be detailed and organized, but can be in rough form. Step 2: Students will present their project proposal to the teacher, and once they have received the “okay” they are free to work. Step 3: Students will work in groups until complete. Step 4: Once the project is complete, students will turn it in to the teacher and take a short comprehension quiz on Fibonacci.
• 5. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Exemplary 4 Accomplished 3 Developing 2 Beginning 1 Score Quality of work Project is creative and original. It meets all of the criteria. The project is good, but could be more creative. The project is lacking creativity and it does not meet some criteria. The project has met little to no criteria. Understands the material Project clearly uses Fibonacci concepts. Project uses Fibonacci concepts but may be confusing. Barely demonstrates comprehension. Project does not show any level of comprehension of the subject. Time Management The students were on task, utilized their time, and finished the project on time or early. Students were mostly on task, and finished the project on time or early. Students were somewhat on task and finished the project within one day of the due date. Students were not on task and failed to meet the deadline.
• 6. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Congratulations! You have effectively explored Fibonacci’s work throughout history. With your help, historians were able to find more information than ever before about this inventive mathematician.
• 7. Student Page Title Introduction Task Process Evaluation Conclusion Credits [ Teacher Page ] Cites Used: http://faculty.oxy.edu/jquinn/home/fibonacci/homecoming/art1.html http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#arch http://techcenter.davidson.k12.nc.us/Group2/art.htm http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#plants http://milan.milanovic.org/math/english/golden/golden2.html
• 8. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page Based on a template from The WebQuest Page Evaluation Teacher Script Conclusion A WebQuest for 8th Grade Mathematics Designed by Brooke Jacobson [email_address] Based on a template from The WebQuest Page
• 9. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This lesson was developed at Colorado State University. The purpose of the lesson is to encourage students to discover the Fibonacci Sequence on their own, and find examples of it in every day life. Evaluation Teacher Script Conclusion
• 10. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This lesson is designed for 8 th grade geometry. Students will need to have background in measurement and scaling in order to make their projects. If students are able to, discussion of irrational numbers could pertain to this topic. Evaluation Teacher Script Conclusion
• 11. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page Standard 1 Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems. Standard 3 Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems. Standard 4 Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems. Standard 5 Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems. Evaluation Teacher Script Conclusion
• 12. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page Evaluation Teacher Script Conclusion Students will have 2 class periods to explore Fibonacci and the Golden Ratio in Art, Architecture, Nature, and the Human Body. After these 2 days, all additional research will be for homework. The next 3 days will be spend designing a project, either a piece of artwork or blueprints for a structure that utilizes the Golden Ratio or the Fibonacci Sequence. Day 1-2 Breakdown: Step 1: Students will separate into pairs. Step 2: Together partners will select a computer and begin researching. Step 3: Students will select available links and explore the Golden Ratio in a variety of settings. Step 4: Students will take “travel notes” in notepad and print when finished. Step 5: Together, students will decide on which project they would prefer to do. Click here to learn about: A Fibonacci Overview Architecture Art Art 2 Nature Nature 2 Human Body Day 3-5 Breakdown: Step 1: Students will pair off at the beginning of class and begin the rough design of their projects. This should be detailed and organized, but can be in rough form. Step 2: Students will present their project proposal to the teacher, and once they have received the “okay” they are free to work. Step 3: Students will work in groups until complete. Step 4: Once the project is complete, students will turn it in to the teacher and take a short comprehension quiz on Fibonacci.
• 13. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page The teacher will need: A set of computers for half the class. An available printer Graphing paper for designs Yard sticks, markers, etc. Internet connection This can all be done at school with only one teacher present. It may be fun to bring in the Art teacher to talk about designs that the students can do, but this is not necessary. Evaluation Teacher Script Conclusion
• 14. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This can be defined as successful if student artwork and blueprints reflect the concepts of Fibonacci. Also, students should be asking questions and getting engaged with this material. If students finish early, they can use butcher paper to map their bodies and describe the ratio on themselves. Evaluation Teacher Script Conclusion Exemplary 4 Accomplished 3 Developing 2 Beginning 1 Score Quality of work Project is creative and original. It meets all of the criteria. The project is good, but could be more creative. The project is lacking creativity and it does not meet some criteria. The project has met little to no criteria. Understands the material Project clearly uses Fibonacci concepts. Project uses Fibonacci concepts but may be confusing. Barely demonstrates comprehension. Project does not show any level of comprehension of the subject. Time Management The students were on task, utilized their time, and finished the project on time or early. Students were mostly on task, and finished the project on time or early. Students were somewhat on task and finished the project within one day of the due date. Students were not on task and failed to meet the deadline.
• 15. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page The teacher can read the introduction to the students and let them go from there. Part of this assignment is to encourage students to problem solve individually and ask questions when necessary. Evaluation Teacher Script Conclusion Leonardo Fibonacci was born in 1175. His discoveries of the Fibonacci Sequence, the Golden Ratio, and the Golden spiral are significant in the connections that it makes to nature and the real world. Although his discovery was not made until nearly 1200, we can find amazing architecture from Greece dating back to the 500’s BC. You are on an investigation to discover the golden ratio within architecture, art, nature, and the human body. I am sending you to Greece to discover the uses of the Fibonacci sequence, the golden ratio, and the golden spiral. Can you find Fibonacci?
• 16. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page This will teach students about Fibonacci, but hopefully, it will strike an interested in kids who are not “mathy” and are generally uninterested in math. This is a great way to connect mathematics to all other realms of life, and it should be utilized in class! Evaluation Teacher Script Conclusion
• 17. [ Student Page ] Title Introduction Learners Standards Process Resources Credits Teacher Page Evaluation Teacher Script Conclusion Cites Used: http://faculty.oxy.edu/jquinn/home/fibonacci/homecoming/art1.html http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#rabeecow http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#arch http://techcenter.davidson.k12.nc.us/Group2/art.htm http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#plants http://milan.milanovic.org/math/english/golden/golden2.html