Amazing Math Enrichment!

Are you looking for something to fill time towards the end of the school year? Do this amazing group of activities revolving around the Fibonacci sequence. For a classroom teacher this would probably take about a week. I did this with higher level learners in fifth grade. They were intrigued.

Lesson 1: First we watched this video:

Then we added Fibonacci numbers up to sequence 30. This was good for students who needed to add some larger digit numbers since they get large rather fast. We talked about what Fibonacci numbers were and where they were located on our bodies, such as in the spiral of our ears, hair, and fingerprints. I brought a few pinecones to examine.

Lesson 2: We watched this video.

Then we went outside and found pine cones, I brought some raw broccoli, and I got some daisies at the local grocery store. We examined these items for Fibonacci spirals and counted the number of petals and looked for spirals.

Lesson 3: We drew a Fibonacci Spiral and talked again about where we could find it on our own body. This video shows how to draw a Fibonacci Spiral more slowly.

Lesson 4: We found the golden ratio. I had students pull out their Fibonacci numbers that they had figured out in the first lesson. Students need to divide the larger Fibonacci number by the smaller preceding one all the way down the sequences. I allowed them to use calculators to do this. I had them record 10 decimal places after the decimal. Eventually students end up seeing the pattern.

Lesson 5: (This took 2 classes) We measured our body parts with a measuring tape and ruler. If you want these measurements to be more accurate, I figured out the second time that I wanted students to use the centimeter side of the measuring tape so that the Golden Ratio would turn out more accurately. This way students don’t have to keep up with fractions of an inch. I did use a product on TPT for students to do this. There are several which have places for students to fill the measurements of their body. They actually did get 1.6 on some of their measurements!!!

Lesson 6: We made an angletron with 137.5 degrees which also is related to the Fibonacci sequences.

Then we went outside with our angletron and tried to find Golden Angles. I found one and asked the children if it was truly a Golden angle. They confirmed the veins in the leaf of an oak tree were a Golden Angle!! WOW!!!!!WOW!!!