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What’s the BIG Deal About PATTERNS?

Posted by on October 1, 2016

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. 

~S. Gudder

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:

Patterns ... looking at the September calendar.

Patterns … looking at the September calendar.

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:

Okay ... who's up for a NUMERICAL pattern challenge? Apparently we ALL are!

Okay … who’s up for a NUMERICAL pattern challenge? Apparently we ALL are!

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:

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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:

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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!

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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:

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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:

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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:

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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:

Is it really JUST a pretty flower? Or ... is it something MORE!

Is it really JUST a pretty flower? Or … is it something MORE! Photo courtesy of MR. Renton.

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. 

~Dean Schlicter

We wonder:

  • 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?

28 Responses to What’s the BIG Deal About PATTERNS?

  1. Caroline

    Your study of Fibonacci and Lucas sequences is FASCINATING. I love your enthusiasm and the way you grasped the concepts so quickly – I, too, learned something today!!! Isn’t nature amazing? I will never look at a banana or a flower the same again!! Well done!

    • The BPS Bloggers

      Hi Caroline!

      Thank you for leaving a comment on our blog! We also found it fascinating learning about the Fibonacci and Lucas sequences! Some of us will often catch ourselves looking deeply at our food or the plants around us to see if we can spot Fibonacci or Lucas anywhere now!

      The BPS Bloggers 🙂

  2. Ms. Jensen

    Woweee Zowee Holy Coweee Grade 3’s!! This is amazing thinking and wondering. The grade 2’s were so surprised that you noticed our bit of work work and all of these discoveries have made us very curious!! I can hardly wait to share this post with them next week! Keep up the exploring…and sharing!

    • Maxine

      Colby really loved counting Fib the Pineapple. It ended up being a Fibonacci number!!!

      I have learned so much from Colby and this blog! It is all so interesting!!! Thank you for continuing our learning journey together too!

      -Maxine

    • The BPS Bloggers

      Hi Ms. Jensen!

      Thank you for leaving a comment on our BPS blog and for the awesome compliment! We will keep exploring Fibonacci and if we find anything new we can send it to you and your class! We can even send you a photo if we make some new discoveries! Fibonacci is fun, isn’t it, even though it’s a hard pattern to figure out! We wonder if some of the Grade Twos want to try some of these experiments … like the one with the pine cone?

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  3. Patricia

    Love the blog!

    • The BPS Bloggers

      Hi Patricia!

      Thank you for this lovely comment! We love the blog too!

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  4. Brooklyn

    I really like to do Fibonacci numbers, bye bye

    • The BPS Bloggers

      Hi Brooklyn!

      Thank you for your comment! Keep up the good work … we LOVE when you leave comments! We like doing Fibonacci too because it’s cool! The numbers added together equal the next one! We think it’s fun math!

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  5. Rowen

    I wonder if SnowFlakes follow a Fibonacci sequence?

    • The BPS Bloggers

      Hi Rowen!

      Thank you for leaving this comment! We think it might depend on the snowflake! We really LIKE the wonder! Some of us think we might try to do some more research on this wonder!

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  6. Crystal

    I do not think we learned about the Fibonacci pattern in grade 3 ! Or maybe I just don’t remember ??? They say you learn something new everyday day and today I did ! What a creative way to learn. Crystal

    • The BPS Bloggers

      Hi Crystal!

      Thank you for leaving a comment! We’re glad we learned Fibonacci this year! Mrs. Renton didn’t even learn about Fibonacci when SHE was in Grade Three! Mrs. Renton and The BPS Bloggers learn new things every day too!

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  7. Renee

    Hi this is Renee, Payton’s mom. I really enjoyed reading the blog about Fibonacci and Payton telling about how much she is enjoying learning about Fibonacci and she is teaching me. I look forward to exploring many more adventures with the Grade 3 class.

    • The BPS Bloggers

      Hi Renee!

      Thank you for leaving this comment! We are enjoying Fibonacci too! How much is Payton teaching you? We think she’d be a GREAT teacher! We wonder what your FAVOURITE part of Fibonacci?

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  8. Leah

    My parents had never even heard of Fibonacci, and they were so impressed! I wonder if pumpkins have Fibonacci… now I can teach them about the Lucas Numbers. Thanks Ms. Renton!

    • The BPS Bloggers

      Hi Leah!

      Thanks for leaving a comment! Lots of our parents had never heard of the Fibonacci or the Lucas sequence before! We were ALSO impressed with Fibonacci! Many of us think that a pumpkin MIGHT follow the Fibonacci or the Lucas sequence but we’re not sure! We are glad that Mrs. Renton taught us about these number sequences too!

      Keep checking back! Have a great day!

      The BPS Bloggers 🙂

  9. Mr R

    WOW! What a great blog post! I learned so much. I understand why we have been picking up pine cones … buying pineapples. Pretty much analyzing anything in nature we can find. Thank you for the awesome lesson. Oh yeah…nice picture of the sunflower!
    Mr R

    • The BPS Bloggers

      Hi Mr. R!

      Thank you for leaving a comment! We know that pineapples and pine cones are pretty hard to find Fibonacci on … but pine cones usually follow the LUCAS sequence instead of the Fibonacci! Thank you, Mr. R., for helping us to figure out Fibonacci … and taking the nice picture of the sunflower!

      Have a nice day! Keep checking back!

      The BPS Bloggers 🙂

  10. Reid

    I love Patterns!!!!

    • The BPS Bloggers

      Hi Reid!

      Thank you for leaving a comment! We also love patterns because they are EVERYWHERE!!! Today we even learned about a pattern with on a CORAL .. s-s-s-snake!!! It wasn’t ANY pattern … it was a WARNING pattern! So BEWARE! What is YOUR favourite kind of pattern?

      Keep checking back! Have a great day!

      The OTHER BPS Bloggers 😉

      • Reid

        Hi class mates

        I like all patterns.what’s your favourite kind of pattern?

        Have a lovely day.bye.

        Reid

        • The BPS Bloggers

          Hi Reid!

          Thanks for leaving a comment! We also love patterns. We can not decide which ones are our favourites … some of us really love using our brains to figure out number patterns … but others really like shape patterns! Some patterns really make our BRAINS hurt! What is your favourite type of pattern?

          Have a great day! Keep checking back!

          The OTHER BPS Bloggers 🙂

  11. Vivian

    I LOVE learning the Fibonacci and the Lucas sequence! it is so much fun! Okay, gotta go to training right now! Toddles! Vivian. 🙂

    • The BPS Bloggers

      Hi Vivian!

      Thank you for this lovely comment! We love learning about the Fibonacci and Lucas sequence too! It is fun for us to learn about them. Some of us can’t even look at a sunflower or other plants without wondering if it fits one of those sequences!

      Have a great day! Keep checking back!

      The OTHER BPS Bloggers 🙂

  12. Eric

    Patterns are interesting! Are there are sequences beside the Lucas sequence and Fibonacci sequence?

    • The BPS Bloggers

      Hi Eric!

      Thank you for the cool comment! We triple doggy dare you to try to find that wonder out because we don’t know for sure! It’s a good wonder. When we started off with the Fibonacci and the Lucas numbers it was hard … but … we worked hard to figure the sequences out! Then we got better!

      Keep checking back! Have a great day … of … researching!

      The OTHER BPS Bloggers 🙂

  13. Vivian

    I wonder if you can find Fibonacci or the Lucas sequence in your clothing??? 🙂 Have a good day! Bye I have to got to sleep.

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