Fibonacci's Sequence: The Wonderful Asynchrony of Young Gifted Learners

As Seabury Head of School Sandi Wollum says, "You never know what age they are when you're talking with them." 

Here is a peek into the first grade classroom as they discover the Fibonacci Sequence.

What "age" are they in each picture? 

Listening to the ocean in a shell

Figuring out the Fibonacci Sequence

Taking it to very high numbers

(Also taking the clipboard outside to recess!)

"Hey, we both have astronomy t-shirts on today!

Can you see the flag of my Lego astronaut on the moon of yours?"

Such is life in a classroom of highly-capable first graders with curriculum designed specifically for them. 

Interested in finding out more? Click here for some parental tips 

from NAGC - National Association for Gifted Children.

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Here are some more snapshots of what our Fibonacci day was like.

Much like the discoverer of the Fibonacci Sequence, 

the Navigators are keen observers. 

We love making connections. 

We begin to see something in common. 

We look at other things from nature 

and notice that "they all have a spiral!"

We then read a biography about a man named Leonardo Fibonacci. 

He lived during the Middle Ages

(hey, we know what that means!) 

and he also noticed the spiral pattern in nature.

And he noticed this number pattern: 

1, 1, 2, 3, 5, 8, 13...

We  set off to figure out the code.

This student uses the analogy of the famous rabbit 

problem found in our book, 

but also found in 1202 in Fibonacci's book Liber Abaci. 

Collaborating to figure it out. 

Some students discover it by looking at the numbers. 

Once we know the code, we proceed to take it further and further. 

As the number get bigger, it requires a lot of mental math.

And a quick lesson on using semi-colons. 

Using graph paper, we make our own spirals with the pattern 1,1,2,3,5...

Again, we love to go big, bigger, biggest!

This was inquiry-based instruction at its finest - the students asked the questions, did the observations, and discovered for themselves what Leonardo Fibonacci discovered about 850 years ago.

He could have been a Seabury Student!

Have you figured it out?

Scroll down for answer. 

Invention Quest #3: How Does This Work?

How does a wind-up toy work?

That was the important question for the quest of the day. 

First, we looked at the outside of the toy and drew it on our lab report.

We each came up with a hypothesis as to how it works. 

Another hypothesis. 

Then we got out the screwdrivers and did some

reverse engineering. 

We learned how to use Phillips screwdrivers. 

We used flathead screwdrivers to pry them open.

When we got inside the toy, we discovered another box 

that needed to be opened. 

As we opened them up, we laid out the parts, 

drew them, and labeled them. 

 

With a lot of twisting and turning and prying, 

we discovered the most important part - the torsion spring!

Notice the sprung torsion spring.

We tried to put them back together and had no success.

What a wonderful, complicated, fun little toy!

So many skills practiced. Here are a few:

• curiosity
• prediction
• observation
• small motor 
• innovation
• filling out a lab report
• collaboration
• analytical/critical thinking 

These skills might come in handy 

for when we come up 

with our own inventions!

Invention Quest #2: Discover Resourcefulness

 What if there were no toys? 

That was the question of the day. 

We started with one pipe cleaner. 

Could we make a toy out of it?

A toy person

A toy ring

A toy bracelet

What can you do with two pipe cleaners?

A handle for a book?

A jewelry container?

What if you had more than two pipe cleaners

 plus some some buttons and pop can tabs 

and any garbage you can find on the floor?

A fidget toy!

A math manipulative counting toy

We then read Galimoto, a book about children in Malawi who collect wires and odds and ends and make their own toys.

Galimoto: a Malawi word for car

The galimoto is steered from behind by the child.

The long wire is attached to the front axle. 

Children are ingenious!

What if there were no toys?

Gather some resources, use your ingenuity, and invent your own!

Invention Quest #1: Discover Your Inner Inventor with S.C.A.M.P.E.R.

Children are natural inventors. The key is to not squelch that natural bent, but to draw on it.

To get the creative, invention juices flowing, the Navigators have done several mind stretching activities. We started with a whisk. 

What can you do with an ordinary kitchen whisk? Stir, whip, blend, mix....

What else can you do with an ordinary kitchen whisk? The creative juices started to flow. It can be used as a:

What if we changed the whisk? Introducing S.C.A.M.P.E.R., a way of stretching our ideas to come up with even more innovative, inventive ideas.

S. Substitute: What if we put a pencil in it (and hung it from our mask!)? 

A Pencil Whisk!

C. Combine: What if we combined it with other things in the kitchen?

A Multi-Item Kitchen Set!

A. Adapt: What if we adapted the wires?

The Magic Claw!

What if we added batteries?

An Electric Whisk

M. Modify: What if we put a button on it and when you push the button, it grabs garbage?

A Super Garbage Grabber!

P. Parody: What if you hang it from your ear?

A Whisk Earring That Holds Important Things...

...like Mrs. Towne's marker. And her mask can hold her keys

E. Eliminate: What if we take away the tips and the handle?

A Scrubby!

R. Rearrange: What if you need something to hold all your candy?

The Candy Feeder

So many ideas...so many potential inventions...

Here are some variations on a theme:

A Masked Marker Holder

An Everything You Can Write With Holder

A Handy Dandy Cupcake Holder Earring

An everything in school holder

Stay tuned. The juices are flowing and who knows where it will lead the Navigators. Watch out world!