In this activity we will expand our knowledge of geometric shapes and patterns and see how many of these are naturally occuring in our own backyards...we may be surprised by what we find!

Fibonacci's Mic Drop on Nature...

Before we even begin looking for a boatload of crazy shapes and patterns, we need to get an understanding for how our natural world is organized - and we can't do that without Fibonacci. In its simplest form, this sequence follows the pattern of adding numbers together in sequence. For example, 1, 1, 2, 3, 5, 8 is the start of the Fibonacci sequence. Can you see the pattern? First number added to second, second added to third, third added to fourth, and so on. Pretty cool! But it doesn't stop there.

Take a look at the video below to see how deep this whole Fibonacci thing goes...be warned...it's everywhere! As you are watching, see if you can find out the following things:

• In what century did Fibonacci live?

• What animals caused him to develop this particular sequence?

• How large can the spiral patterns get on some sunflowers?

• What is the measurement of the Golden Angle?

Fibonacci and Beyond...

I know, it can be a little unsettling to come to the realization that nature seems to be ruled by MATH! But here at Nuhop, math is our jam and we love seeing all of the amazingness that comes from the Golden Angle and Golden Ratio! But what about all of the natural things that are not sunflowers? What kind of geometric connection do they have?

Let's take a minute to look at a wide range of natural elements and see if you can identify the hidden geometric shapes. Use the scrolling arrows to check out all of the images. Write down what you can find in each image. Here are some shape suggestions: alternate lines, right angles, parallel lines, cubes, spirals, circles, octagons, tangents, opposite lines, right triangles, Fibonacci sequence, hexagons, obtuse triangles, straight angles, intersecting lines, obtuse angles, squares, acute triangles, spheres, cones, cylinders, acute angles, perpendicular lines, overlapping patterns, whorls, and cones. Whew!

Let's compare some notes to see if we found some similar things:

1. Starfish - star (obviously), acute angles, obtuse angles, a pentagon

2. Stones - hexagons, parallel lines, obtuse angles

3. Leaves - alternate lines

4. Log - circles, intersecting lines

5. Fern - parallel lines

6. Grapefruit - circles, straight, acute and obtuse angles

7. Ice - hexagons, parallel lines, straight, acute and obtuse angles, intersecting lines

8. Spiderweb - circles, straight, acute and obtuse angles

9. Honeycomb - hexagons, parallel lines, obtuse angles

10. Atlas Shell - spiral

I am sure you found even more! Now that we have you all prepped and ready to identify naturally occurring shapes in the blink of an eye, let's see if you have what it takes to find the real thing in your real world!

I’d tell you a Fibonacci joke,

but it’s probably as bad

as the last two you’ve heard combined.

Outdoor Adventure Challenge

*Teachers, this activity is an adaptation of one found in Schoolyard Enhanced Learning by Herb Broda, and the Nature Shape Audit sheet is adapted from the original version created by Dalton Local School's STEAM Educator, Laura Grimm.

It's time to venture outside and see if all these shapes actually exist in our own backyards. To do this we are going to complete a Nature Shape Audit (it's getting close to tax season so your caregivers will get that joke). To complete our audit, we will need to do the following:

• Print out the Nature Shape Audit linked below. This has 25 2D shapes that we will be challenging to find.

• Take the sheet with you outside and start searching!

• How many of the 25 can you find? You need to show the match to someone (or take a picture of it with your phone) for it to count.

• How many of the 25 can you find on one plant? You need to show the match to someone (or take a picture of it with your phone) for it to count.

• Race against a sibling or friend to see who can find the most the fastest. You need to show your competitor your match for it to count.

• On the back of the sheet, draw your own shapes that we missed.

• When you are done, come back so we can do the Reflection and Quick Quiz below.

• HAVE FUN!

Review and Reflection

What? You are back already? This means that we are looking at someone who has found 25 distinctive geometric shapes in their own yard! Who would have thought that so much variety exists right before our eyes.

1. Which of the shapes were easiest to find? Why do you think that is so?

2. Which of the shapes were hardest to find? Why do you think that is so?

3. Were you able to find all 25 shapes on one plant? If not, do you think that is even possible? What plant might work (even if it is not naturally occurring)?

4. What shapes did we miss in our grid above? Were you able to find the missing shapes on more than one natural object?

Quick Quiz

It's go time! You have done all the hard work, now let's see how much you remember from your deep dive into nature's geometry. Feel free to look back and review for each of the questions. Good luck!

About the Author

Matthew

Dr. Matthew Broda is an Assistant Professor of Education at The College of Wooster and is currently on sabbatical studying innovative pedagogies. His research and teaching interests include instructional technology, outdoor, and experiential education. When not teaching his students, he can usually be found somewhere outside – smiling.