The essence of mathematics is not to make simple things complicated, but to make complicated things simple.
Hi! Welcome to our very FIRST post of the year! It’s an EXCITING one! Why? Because we have been looking at PATTERNS! What’s the big deal? Well, patterns are EVERYWHERE! Patterns aren’t just about math … we can find them in nature and they also help us to make sense of and organize the WORLD! They keep animals SAFE through CAMOUFLAGE and they WARN us from DANGER! They help us keep track of time through days and nights, weeks and months; through the passage of seasons. Patterns are AMAZING!
We began our learning adventure by looking at patterns on our September calendar. It was amazing how even THIS simple task generated MORE wonders:
Moving beyond the simple repeating patterns we could see, ONE of our classmates came up with a complex NUMBER pattern and then we worked hard to try to figure out how to EXTEND that pattern:
Oh, oh! When Mrs. Renton could see that we looked like “Pattern PROs” … THAT’S when she put a number pattern up that had NOTHING to do with our Calendar. We talked about it with partners. We grabbed the mini whiteboards and persevered through her challenge:
Now … you MAY notice one or two calculation errors on our whiteboards … because we were beginning to add some pretty HUGE numbers! We learned a LOT about rechecking our calculations because … when each new number relies on the LAST … one small error can change the entire pattern! What matters is that we were on the RIGHT track … we had decoded the pattern, which is NO small feat!
You WON’T believe this, but … SOME of us BEGGED to take our whiteboards outside at RECESS to CONTINUE this mathematical journey:
Then, Mrs. Renton surprised us with some SPECIAL information about this pattern. It is called the Fibonacci Sequence! What’s even MORE amazing? This pattern can be found in NATURE!!! WHAT? Yup. You read that right. MANY plants … and even some ANIMALS … grow using the Fibonacci Sequence! We decided we needed to find out MORE!
We NEEDED to try and PROVE that Fibonacci could be found in nature. See if you can SPOT Fibonacci in some of the things we found outside:
That’s when we hit a roadblock! Yes, we DEFINITELY found some flowers with FIVE petals … and a WHOLE bunch of THREE leaf clovers … but … when we counted the swirls on our PINE CONES … we were NOT getting Fibonacci numbers like in the YouTube video below:
Hmm. We thought ALL pine cones would follow this amazing sequence of numbers. While we were perplexed … we were NOT dissuaded … THIS adventure had pulled us DEEPER into our learning journey! What did we discover, you may be asking yourselves? Well … there is a LESSER known sequence that some plants follow. It’s call the LUCAS sequence:
2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843 … and on and on and on
If you are wondering … we managed to figure out THIS sequence pretty quickly TOO! And, SOME of us BEGGED to work on it at RECESS again! Since then, we’ve been coming up with our OWN complicated number patterns and we’ve been challenging one another to SOLVE them. We’ve ALSO begun to notice the Fibonacci and Lucas sequences ALL around us … even during breakfast and dinner:
We met FIB the PINEAPPLE and discovered that FIB followed the Fibonacci Sequence … we EVEN shared our pineapple adventure with the Grade Twos in Mrs. JENSEN’S class:
So … the NEXT time you’re at the grocery store, or out for a walk or eating dinner … think about what you are seeing! You may be SURPRISED:
Wonders lead to the quest for answers. Answers lead us to MORE wonders … oh, oh! Do you see what WE see? Wonders, answers, wonders, answers … MORE wonders, MORE answers … it’s … a … PATTERN! But, don’t get us started … it’s like the song that has NO end!
Go down deep enough into anything and you will find mathematics.
- Why is the Fibonacci Sequence named after an Italian when it was discovered in another country LONG before that?
- How many things are there that have Fibonacci numbers in the world?
- How did anyone even figure OUT that 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 … was IN plants and nature?
- Why do SO many plants grow using the Fibonacci OR the Lucas number sequences?