# Bunnies, Bunnies, Bunnies: A quick lesson in exploring the Fibonacci Sequence

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## Objective

SWBAT calculate Fibonacci numbers.

#### Big Idea

After reading Rabbits, Rabbits, Everywhere A Fibonacci Tale, students will explore and experiment with Fibonacci numbers. We will take a look at nature where the pattern comes to realization.

## Take a look at these shells! An introduction to nature and its patterns.

10 minutes

Today was just too much winter! We had had enough of learning to divide and needed a well deserved break. I was looking for something that would be spirit lifting and amazing to connect to mathematics. The wind was blowing up snow devils in full force outside our window and we were all dressed in our Hawaiian shirts ready for a beach party anyway. Who wants to drill more division on a day like today? I know that number patterns was a standard I wanted to touch on again and so I chose CCSS 4.OA.C.5 to work some magic around on this blustery subzero  day.

I got out my seashells to put on my makeshift beach on the classroom floor. Beach Boys music was blaring as students entered from recess. They knew something was up! I love creating a mathematics classroom that keeps their curiousity at peak levels. Students swarmed to look at the sheels. CCSS gives us plenty of room to master standards in an atmosphere of discovery and amazement. It just takes a little creativity.

I gave each of my students a shell that had a spiral shape and one ammonite. I wanted them to discover that mathematics is in nature. I have a poster telling them that it's everywhere. I feel obligated to show them as often as I can because I always want them to connect everything they learn to the real world.

I opened up the lesson by saying: Aren't shells just amazing? Who thought of these? How can they be so different and so amazing at the same time? Can you find patterns in the shell you are holding? I wanted to set the mood for wonder and thoughtfulness.

Several students offered up their observations. One talked about the ammonite sections. Another ran her finger around the spiral shell and talked about how it got increasingly "pointier" at the tip. It reminded her of a spiral staircase.

I brought up the SB to show them how Fibonacci Is Amazing! and asked them to put their shells down on their desks for a moment. We discussed the patterns and the word "Fibonacci." We marveled at the photos and tried to understand the nautilus pattern. I spoke about how amazing the earth is and that mathematics is a part of the natural world. It helps us explain patterns we see in nature, and helps us understand the dynamics of how math helps a plant or animal exist.

I asked them if they had ever heard of Fibonacci? Several students had heard of him and knew he had something to do with numbers, but couldn't explain.

I told them that today, we would play with Fibonacci's numbers a little bit after we read a story.

## Rabbits Rabbits Rabbits

10 minutes

I showed my students the cover of the book Rabbits, Rabbits, Everywhere , a Fibonacci Tale, by Ann McCallum.

I asked them what they knew about rabbits. They laughed. They knew they multiplied. And fast! It helped me lead right into the book. I read them the story using different voices for the Pied Piper, the mayor and Amanda, to make the characters come alive. I wrote down the number pattern on the white board as Amanda presented it in the dirt. I stopped and asked them to predict what would happen every day. They kept telling me the rabbits were doubling. One student said that they were tripling. I kept smiling and told them no...to keep looking for the pattern. I didn't expect any of them to understand the pattern just yet, but I wanted them to keep looking.

We finished the book and discussed the pattern I had written on the board. I taught them how it worked. Every new sum was derived from adding the two sums before. I heard lots of "oh's!"

I realized that students will get this! I wanted to explore it further and found this video that I think does a good job of summing it all up. ( No pun intended.)

I like how he ends with telling us that math can be beautiful too. This is exactly what I wanted them to understand...besides figuring out  a Fibonacci pattern!

## Playing with the pattern.

10 minutes

I had written the Fibonacci pattern up to 55 on the whiteboard. I asked my students to practice calculating it by going for 10 more sums. Fibonacci sample. They worked for several minutes. I asked them to trade notebooks and check each other's work. Did your sums match your buddy's? Correcting her work.This lesson turned into great addition practice right before my very eyes! Patterns, addition skills and critically looking at others work was keeping them engaged and amazed. They couldn't believe how fast the numbers got so large. Work Sample: Lining up numbers and using standard algorithms  Most students worked the problems out using a standard algorithm. But, a few tried to do it in their heads. No one was accurate trying to mentally calculate, so I made them go back and figure it out on paper. I encourage mental math, and I appreciate that they tried it. But, I stressed accuracy as Math Practice Standard 6 demands

I closed the lesson with a short discussion about saving money. I asked them how much money they could save in a year if they started with saving one dollar per week and applying the Fibonacci sequence.

Eyes got really big. The answer was "millions!". I challenged them to figure it out over the weekend. I wonder who will bring me the answer?

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## Practicing Patterns

10 minutes

I wanted my students to practice more number patterns. I assigned IXL math Section F L.1 through L.5. They could choose any of those activities over the weekend to play with. I presented it as "play", but explained that I wanted them to think carefully and draw out patterns on paper to solve. My advanced students are always encouraged to look for a higher level if they feel that the level I assigned was not challenging enough. Because I can track their progress on this site, I can easily monitor how long it takes them and how many they are getting correct.

I hope they enjoy their work this weekend. Working with these patterns will help satisfy another facet of the standard.