### Submitted by: Blake VanWinkle

In this lesson plan which is adaptable for grades 6-8, students will use BrainPOP resources to explore the Fibonacci sequence, learning what it is and where it originated from. Students will then determine how sequences are found in nature.

### Students will:

1. Students will understand what the Fibonacci sequence is and where it originated from.
2. Students will determine how sequences are found in nature.

### Materials:

• Computer with internet access for BrainPOP
• Interactive whiteboard (or just an LCD projector)
• Images of examples of the Fiboncci sequence (online, from books, etc.)

### Vocabulary:

sequence, term, algorithm, logarithmic spirl.

### Lesson Procedure:

1. Introduce students to Fibonacci by showing images about his life and work. Explain that Leonardo Fibonacci was born in Pisa, Italy, around 1175. His father was Guilielmo Bonacci, a secretary of the Republic of Pisa.His father was also a customs officer for the North African city of Bugia. Sometime after 1192. Bonacci brought his son with him to Bugia. Guilielmo wanted for Leonardo to become a merchant and so arranged for his instruction in calculation techniques, especially those involving the Hindu - Arabic numerals which had not yet been introduced into Europe. Since Fibonacci was the son of a merchant, he was able to travel freely all over the Byzantine Empire. Merchants at the time were immuned, so they were allowed to move about freely. As a result of this, he was able to travel to Greece as well.
2. Show students examples of different items in nature that may or may not follow certain mathematical patterns. This will help identify what the students already know and where you will need to spend additional time. Specifically, find out if students are aware of any mathematical patterns in nature.
3. Ask students what they have seen in nature that could be modeled by a mathematical pattern. Build on their responses to include nautilus shells, flower petals, and of course tree growth.
4. Inform the students that they will be studying different patterns of math in nature, specifically the Fibonacci series. Play the Fibonacci movie on BrainPOP.
5. Again, ask now that they have had an example, if they know of any other situations in nature that would be modeled by a mathematical pattern.
6. Have students explore vocabulary related to Fibonacci. Split students into groups of 4 where possible and have them jigsaw. Within the home group, have each student assigned one term (sequence, term, algorithm, or logarithmic spiral). Then have them group with others who have the same term. Let them discuss then return to home group and relay the definition they settled on. Only have the students switch from home once into the specialty group, and have them spend no longer than 4-5 minutes per group.
7. Have students write down the chosen definition for each vocabulary word. Then correct or guide where there may be some confusion so everyone then has the correct definitions. Show examples of each of the terms so students will have an image to go by.
8. Play a quick review game where you put up an example and the students have to identify which vocabulary word is being shown. Where possible, use the terms in sentences not directly math centered to give the students some contextual meaning to the terms.
9. Ask students to do more research on patterns in nature for homework.
10. The following day, have students discuss some of the different types of patterns that are in nature that can be represented mathematically. Do a jigsaw like before, but this time, instead of doing definitions and each group having a single term, have them all split up and discuss what patterns they found and what they think they mean. Also, split the groups a couple of times and have them all discuss what the other group had decided on. After this have them get back into home group and see if everyone feels the same way about it as they did at the start.
11. Go back and target specifically the Fibonacci sequence and how it got started by the merchant Fibonacci wanting to determine the rate of rabbit reproduction. Then relate how this has since become a major part of modern mathematics. Also, build that up and show how it also occurs in multiple different places in nature. Then show pictures of various nature scenarios that incorporate the Fibonacci sequence. Also, explain that during his travels, he introduced this to the Greek mathematicians who then were able to include it in many of their calculations and helped evolve math as we know it today.
12. Have the students continue to construct the ratio and have them answer some questions involving the use of the Fibonacci sequence. Then discuss what the students thought about the sequence and if they could think of any other applications of it than what had already been discussed.
13. For homework, assign students to locate the Fibonacci number in given picture. What is the value of the nth term of the Fibonacci sequence? Construct the sequence to “however many” terms.