| Read Fibbing Can Be Fun! ~ Celebrating Fibonacci Day to find resources and activities designed to introduce and explore the Fibonacci sequence with students and to celebrate Fibonacci Day. |
I remember being ASTOUNDED when I first learned about the Fibonacci sequence and its prevalence in nature – in trees, flowers, galaxies!
It changed the way I see the world. It helped me better understand Pythagoras, who was so mesmerized by the mathematical patterns all around him that he thought numbers were the divine building blocks of life. He may have been wrong about many things, but he’s credited with being the first to connect math to everything in the universe.
The 3-minute video below reinforces this fascination with a “secret universe” of mathematical patterns and I would share it with students! The puzzle shown here is another related resource your students might enjoy.
PLAYING with PATTERNS
Here are some sequences you can introduce to students to encourage math exploration.
Tribonacci Sequence This sequence is like the Fibonacci sequence, but it begins with three numbers rather than two. Each successive number is the sum of the three previous numbers. The sequence starts with 0, 0, 1 and the fourth number is 1, the sum of those three (0 + 0 + 1). The fifth number in the sequence is 2, the sum of the previous three (0 + 1 + 1), and so on. Math enthusiasts might enjoy finding patterns in the N-bonacci sequences listed below. This video explains them, but students who understand the Fibonacci sequence will quickly catch on to these.
| # of Digits Added | Name of Sequence |
| 2 (begin with 0, 1) | Fibonacci |
| 3 (begin with 0, 0, 1) | Tribonacci |
| 4 (begin with 0, 0, 0, 1) | Tetranacci |
| 5 (begin with 0, 0, 0, 0, 1) | Pentanacci |
| 6 (begin with 0, 0, 0, 0, 0, 1) | Hexanacci |
| 7 (begin with 0, 0, 0, 0, 0, 0, 1) | Heptanacci |
| 8 (begin with 0, 0, 0, 0, 0, 0, 0, 1) | Octanacci |
Ulam Sequence
I loved learning about this one! Like the Fibonacci sequence, this sequence is named after the person who devised it. It was introduced in 1964 by mathematician Stanislaw Ulam who moved from his home in Poland to the United States just before the start of WW2. He was a professor at Princeton during the same years Albert Einstein was there. The video below (also found HERE) can be shared directly with students. (NOTE: When your students are ready to check themselves, just do a quick online search to find the next numbers in the sequence.)
If your students enjoy exploring the Ulam sequence, you’ll eventually want to share that there is no overarching pattern to discover. It has an erratic pattern. However, mathematicians continue to study patterns found within segments of the sequence. You may also want to introduce your students to Ulam’s Spiral. I recently discovered Minds on Math, an organization “specializing in education and neuroscience research” and I’m interested in learning more. The free lessons and activities they share are focused on developing “math minds” and “equipping students to solve challenging problems.” Don’t miss the mosaic tile activities which are also all about patterns!
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