### Fibonacci Spider Webs

Time Required: Two 45-60 minute sessions
Skill Level: Intermediate

Transform your classroom into a creepy, crawly fabrication lab (FABLAB). Students will explore the mathematics and design of Fibonacci's golden spiral in nature and then innovate and fabricating spider webs for a new type of spider based on the Fibonacci sequence. *This is a great math activity for Halloween!

Note: Any links outside of the3doodler.com are optional resources. We can’t ensure their upkeep or accuracy.

### Lesson Plan

#### Instructions

Step 1

PREPARATION:

Set up a table with natural Fibonacci items displayed, e.g., plant leaves, snail shells, pinecones, pineapple, sunflowers, sliced banana, rose petals, starfish, daisy, cauliflower, conch shell, etc.

If your students do not have computers, print out graph paper before this lesson.

Step 2

Whole group: Brainstorm and record a list of plants and organisms with Fibonacci numbers, e.g., plant leaves, snail shells, pinecones, sunflowers, sliced banana, rose petals.

Step 3

Ask: "What is the next number in this Fibonacci sequence? 0, 1, 1, 2, 3, 5...?"
See how far students can take this pattern of numbers. "What is the next number?"

Step 4

Ask how they determined the next number in the sequence. *Add the previous two numbers together.

Step 5

Note the spiral in a pine cone. Ask: How this spiral forms from the Fibonacci sequence?

Step 6

Project computer screen to display the webs of the Cat Face and Garden Spiders

Step 7

Discuss how the Fibonacci sequence affects the structure of an orb spider's web. (Possible responses: Allows web to be compact, strong, thin but harder than steel, durable, allows for growth, elasticity and length of the web.)

Step 8

Explain how Fibonacci numbers form a golden spiral.
(Option to use the illustrations on this site )

Step 9

Model how to create a Fibonacci spider web using online graph paper.

Create a Google Doc and click, "insert a drawing." Insert screenshot of graph paper. Using square shapes, follow grid lines to create boxes for 1, 1, 2, 3, 5, 8 and 13. )
*Alternative: Use construction paper and scissors to create golden spiral.

Step 10

Place a blank white paper over computer screen and trace online spiral with pencil. Trace over spiral on paper with 3Doodler. Sketch a template for a spider to add to it. Incorporate principles of Fibonacci pattern. Weld spider to the web. Write a poem about your Fibonacci spider and web. Incorporate 2-3 facts about the Fibonacci sequence in your poem. *See Appendix.

Step 11

Divide students into pairs to work together. Hand out computers or tablets, blank paper, pencils, and 3Doodlers. Remind students to plan first. Discuss. Make changes, if needed. Then 3Doodle. Circle to guide assist and assess as students work.

#### Wrap Up

Students share their Fibonacci webs and poetry. (Option: Turn out lights to surprise students with glow of spiders made with Ghostly Glow filament!) Weld webs to stick in corners of classroom windows and walls. Share on Twitter #3DoodlerEDU

#### Assessment

Review students' webs, spiders and poetry. Assess their feedback during discussions.

#### Possible Extensions

Students will design webs based on an original number pattern of their own design.

#### Resources

Example of Poems in free verse and in rhyme:

The Fibosnatchy Spider
by Julia Dweck

There upon my window sill, a tiny spider doodles.
Weaving a spiral with numbers as it turns, round and round.
1, 1, 2, 3, 5, 8, 13, 21. Oops! It's out of room.
The Fibosnatchy Spider wiggles its two horns, one by one.
Its arms are grouped in sets of 2's and 3's.
With its 8 stickly legs, it scurries back and forth between its gooey strands.
A golden spiral forms against my window pane.
This yellow and orange web looks so fragile,
But don't be fooled.
It is a sticky trap for catching numbers!

My 3Doodled Fibonacci Spider
by Julia Dweck

There upon my windowsill a tiny spider spins.
Two matching horns upon its head, as similar as twins.
Its weavings look like doodles based on numbers set in groups.
Two furry arms to paint its web and three to tie its loops.
Eight nimble leg goes scurrying across the gooey strands.
Amazing what an artist it can be without two hands.
A golden spiral forms against my kitchen's window pane.
And droplets gleam upon each thread that highlight morning's rain.
As numbers stick between its strands, it gives a gentle tug.
This spiral spinning spider is a number eating bug!

#### Vocabulary

• Doodle - An object we “draw” using a 3Doodler.

• Extrude - The act of plastic being melted and then ejected from the 3Doodler as a steady stream, similar to a thread until stopped.

• Retracing - The fine and delicate lines created with the 3Doodler are great, but sometimes you want your creation to be a little stronger or you didn’t get it exactly right the first time. Retracing is exactly what it sounds like. You simply extrude back over the lines you've already created to make welded sections stronger or reinforce thinner areas, or just make some small adjustments.

• Stencil - A stencil is a guide that you can draw or print on regular paper and then trace over the lines with the 3Doodler. Stencils can be of simple shapes or very complicated ones. Stencils are useful for making more than one of the same shape.

• Welding - Freshly extruded plastic can be used to weld two already finished pieces. The hotter the plastic used to weld two pieces, the better they will stick together. Touching the hot nozzle of the 3Doodler to the two pieces being joined just before beginning to extrude can remelt the pieces and help create an even stronger connection.

#### Educational Standards

Common Core
CCSS.MATH.CONTENT.4.OA.C.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

In This Lesson

Students will design spider webs using the Fibonacci sequence and display an understanding of the pattern rule: Add the previous two numbers together.

Students will incorporate aspects of the Fibonacci pattern into the design of their spiders.

Common Core
CCSS.ELA-LITERACY.W.5.4

Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience.

In This Lesson

Students will write poetry about their Fibonacci spiders that integrates principles of its sequence, origin or pattern.

Next Gen Science
3-5-ETS1-1.

Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost.

In This Lesson

Students will work in pairs to meet selected criteria to construct a concrete example of a Fibonacci spiral.

CS Teachers
1A-A-5-3

Plan and create a design document to illustrate thoughts, ideas, and stories in a sequential (step-by-step) manner (e.g., story map, storyboard, sequential graphic organizer).

In This Lesson

Students will create stencils that reflect their thoughts and ideas about the Fibonacci sequence for spider webs and spiders.

Students will write poetry based on their sketches/stencils and designs.

CS Teachers
1A-A-3-5

Decompose (break down) a larger problem into smaller sub-problems with teacher guidance or independently.

In This Lesson

Students will break down the process of exploring the Fibonacci sequence into brainstorm, planning and design work.

ISTE
1C

Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

In This Lesson

Students will use the 3Doodler to visually demonstrate the Fibonacci sequence as a web and spider.

ISTE
4D

Exhibit a tolerance for ambiguity, perseverance and the capacity to work with open-ended problems.

In This Lesson

Students will demonstrate willingness and competency within an open-ended task with more than one possible outcome.

ISTE
6B

Create original works or responsibly repurpose or remix digital resources into new creations.

In This Lesson

Students will create original webs and spiders with a 3Doodler.

ISTE
7A

Use collaborative technologies to work with others, including peers, experts or community members, to examine issues and problems from multiple viewpoints.

In This Lesson

Students will seek feedback from peers before designing web and spider with a 3Doodler.

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