# Fibonacci and Leonardo

#### 1 Teacher Background

Teacher background that’s helpful is a great TED Talk by Arthur Benjamin, “The Magic of Fibonacci Numbers.” It provides a deeper understanding and you can utilize some of the additional items for higher level learners.

#### 2 Building Background Knowledge

Fibonacci was a mathematician that noticed and observed interesting patterns in nature eventually leading to creating a sequence of numbers. Write the numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, ____ up for students and see if they can see a pattern.

The pattern is the two previous numbers are added to create the next.

Prior to showing the movie, I write up the number sequence and see if the students notice any patterns. They usually love this challenge and within a few minutes can continue the pattern. This way, when it comes up in the movie, that understanding gets confirmed and they can focus a bit more on how it occurs in nature.

Show the movie, “Fibonacci Sequence.” To utilize Brainpop movies, there is a fee. I always like to watch the movie prior to showing it to my students so, depending on their level of understanding, I can pause at the important points. It talks about the mathematician that discovered it, Leonardo di Pisa, and how he took a pondering about rabbits, to come upon the Fibonacci Sequence. It would be helpful to familiarize yourself with this story as it's pretty unusual, nowadays, for people to just sit around and ponder things like this. I pointed out that he lived during the time of no television, etc. and people did do things like this back then.

#### 3 Direct Instruction

Select the lesson “Leonardo Numbers.” Go through the slides and utilize the student handouts as is appropriate for your class and time limit. I found the handouts a bit small for my students to write on, so I enlarged them on the copy machine.

There are clear examples of how they are found in nature and if you have any real-life samples (pinecones, circular cactus, Natilus shells, flowers, etc) to bring in, it's more helpful. The thing I noticed about Fibonacci numbers is students don't have the awareness that they exist and, once they do, they become easily identifiable in so many different places.

I broke this activity over a two-day, forty-five minute period, so I gave a prize (candy) after the first day to students who went home and brought in a real world example showing the Fibonacci Sequence.Since the activity showed a pinecone, sunflower, and flower, they couldn't use those examples. This really showed a level of understanding and helped the second day to showcase real examples and discuss what could or couldn't be within a sequence.

#### 4 Drawing your own Fibonacci Spiral

Provide students with ½” graph paper and have them replicate the Fibonacci rectangles. A one-by-one square, connected to a one-by-one square, with a two-by-two square beneath, etc. Show when you start in the initial square and spiral out, you get that Fibonacci spiral.

This provided really tricky for some of my fourth grade students so I modeled this and then paired them up with some fifth graders or other students who understood.

If there is time, starting in the center, you spiral out going through the center of each of the colored squares to show a clear spiral. When usuing colored pencils, as we did, using a permanent black marker to do the spiral allowed it to be more readily seen.

#### 5 Optional: Coding out the Spiral

In partners have students try to create a Fibonacci spiral within Hopscotch. Starting in the center and then spiraling from there. My students were already comfortable with using Hopscotch to code. If not this would require some additional time to play around with the application. I find that there is always a student "expert" in the midst that is more than willing to help the class start up and explain the initial way to begin this project.

Then, have them share their designs.