Add

to your math classroomwith Origami artPresented by:

Norma BoakesEan Boakes7 th Grader at Hess School

& my protégé

Today’s agenda• Learn a little bit of background about the art of Origami• Explore Origami’s link to science and technology• Develop some of the basic written and verbal language of Origami• Create Origami art• Consider the application of math, science and art within the act of

folding and creating Origami art

Origami Ori- to fold

Gami or Kami- paperIt is literally the “art of paperfolding”.

When you think of Origami, what comes to mind?

?

http://www.popsci.com/article/science/robots-retinas-9-amazing-origami-applications

Origami is accepted as an art form

Origami is practiced throughout the world

By Eric Joisel

Spain- “Pajarita”Germany- “Papierdrache”France- “Cocotte”

PBS featured a

documentary on the art

of Origami and its’ range

of significance in

everyday life…..

There are national and international Origami associations including Origami USA that actively promote the value of Origami Art

See this tree in

the American

Natural History

Museum!

As a K-12 mathematics teacher…

• My students struggled with visualizing geometry concepts• The mathematics was often from the book

and didn’t engage students. (They were bored!)Then I attended a workshop on Origami in the classroom and it all changed!…..

Grade 1…..“Students can learn to use their intuitive understandings of measurement, congruence, and symmetry to guide their work on tasks such as puzzles and making simple origami construction.” p. 9Grade 3…. “More advanced paper-folding (origami) tasks afford the same mathematical practices of seeing and using structure, conjecturing and justifying conjectures.” p.13

Excerpts from the Progressions for the Common Core State Standards (2012)

Need

additional

convincing?

Common Core Math Standards• Geometry- Gr.1-3- Reason with shapes and their attributes• Geometry- Gr.6- Represent three-dimensional figures using nets and

use the nets… in the context of real world problems• Geometry- Gr.8- Understand congruence & similarity using physical

models• HS- “Make formal geometric constructions with a variety of tools and

methods (compass & straightedge, string, reflective devices, paper folding, dynamic software, etc.)” p.76• Math Practices- Make sense of problems… “younger students might

use concrete objects or pictures to conceptualize and solve”

So what about

STEAM?• “Though the arts, students learn to observe, visualize, manipulate

materials, and develop the creative confidence to imagine new possibilities.”• “Exposure to the arts teaches observation, or deep noticing. Students

learn to see tiny differences and to record them”…. like a scientist does!• “By taking things apart and tinkering or through manipulating art

materials, students learn comfort with open-ended questions and process.”

ASCD Express, Generation STEM, January 30, 2014….. The art of thinking like a scientist by L. Yokana

The most important reasons to use Origami

Origami TypesTraditional

Unit or Modular

Kirigami

Origami as Art

Unique Material

Origami has its own language and symbols

• Specialty folds• Valley• Mountain• Step• Reverse, etc

• Bases• Preliminary• Waterbomb• Bird • Frog, etc.

“Rabbit Ear”

“Petal fold”

“Waterbomb Base”“Preliminary Base”

Thanks to Akira Yoshizawa

Symbols of Origami

It’s time! Ready?

Before we fold….. A few tips so you have fun• Watch and listen to me THEN fold your paper• Pay close attention to the visual cues in the diagrams!

More tips….

• Be patient if you are stuck. A neighbor or I will be there to help you as soon as we can.• Don’t worry! You may not be able to do all the

models today. It takes PRACTICE.• Don’t rush. Be neat with your folds and check

around you to see if your model looks like those around you.

Origami Traditional Box

connections for the Box• Math• Use the folding steps to teach about fractional parts• Discuss area, surface area and/or volume• Explore 2-D and 3-D terminology such as planes, axes, skew lines, etc• How do you plan to make a template so you can put designs that’s visible on

the bottom of the box?• Science• Let kids create a lid for their box (*done by making a similar, but smaller

rectangle to start with)• Experiment with different materials and host a “book challenge”. What

could hold a whole stack of books?• Art• Use plain paper and decorate the box• Make a sculpture using various boxes and media

Link to video & other sources

Jumping Frog

Can you see…. -Vertical angles-Supplementary angles-Perpendicular lines-Isosceles triangles…..

Discuss the relationships of angles when you fold the acute angles to the right angle. Do you notice the angle is bisected?

Can you see…. -Square formed-Symmetry-Congruent trapezoids

connections for the Frog

• Math• Explore the polygons and fold lines of the model by completely unfolding it and darkening in

the lines• Practice math terminology as you complete the folding process• Have a frog contest tracking the height and distance of jumps (easily done using slow mo on

iPhone & meter stick in camera view). Graph your results!• Apply frog facts… did you know a frog can jump 20 times its body length? If you were a frog,

how far could you jump in one leap?

• Science• Research cool frog facts• Study the mechanics of a frog jump and compare to the Origami frog

• Art• Look at frog skin patterns and decorate a frog to blend with its environment

Sumo Wrestler

connections to the sumo wrestler

• Math• Explore the math of the folding process & finished model• Research and calculate the cost of a sumo wrestler diet• Design the perfect 3-D prism “ring” for the wrestlers. Build it

as a net and assemble it!• Design a point system for the sumo game (tip left, tip left, fall

forward- like Pigs game) then plan & calculate your scores!

• Science• Explore the concept of force (friction, push, pull)• Check out “sports” science…..the rebound challenge-

Kevin Love vs. Sumo Wrestler (force & center of gravity)

• Art• Explore Japanese drawing of sumo wrestlers

Helicopter

Instructions are a little tougher on this one but it’s because the calendar teaches you along the

way. Buy one! It’s a great way to learn more!

connections to a helicopter

• Math• Explore the lines and angles of the “square” base you start with• Discuss the polygon types of the final helicopter form• Discuss and explore the properties of a square • Make a target for the floor with point rings. Drop from a ladder and track

the scores.• Science

• Add weight to the helicopter. Does it effect the flight?• How does the helicopter design compare to a maple seed’s flight? What’s

the purpose of the spinning motion?• Art

• Add designs to the “blades” of the helicopter so when it spins it makes cool patterns. (Use larger square paper- Origami paper not needed!)

Business Card Cubex6Business

card

connections to the business card cube

• Math• Explore the fractal that can be made with these cubes

called Menger’s sponge!• Calculate how many cards it would take to build a

structure. (The Menger sponge, level 3, takes 66,048!)• Explore the properties of a cube

• Science• Experiment with cubes from other rectangular shapes

then test its strength (ie. playing card vs. cardboard)

• Art• Make a cube sculpture• Create cubes with lids and hinges

Need more inspiration?• Websites

• Origami Club- http://en.origami-club.com/ • Origami Resource Center-

http://www.origami-resource-center.com/easy-origami.html

• Organization• Origami USA- https://origamiusa.org

• Favorite books for seeing the STEAM connections• Origami Math by Scholastic (lower elementary friendly!)• Geometric Origami by M. LaFosse• Math in Motion by B. Pearl (lower elementary friendly!)• Unfolding Math w/Unit Origami by B.Franco• Paper Square Geometry: The mathematics of Origami by M. Youngs

• Favorite paper brands!• Toyo • Aitoh

Email: Norma.Boakes@stockton.edu Linkedin: www.linkedin.com/in/boakes-norma-6380174

I love hearing about teachers’ Origami adventures and helping others add Origami to their classrooms! Don’t hesitate to reach out to me!