Participants of this workshop learned how Origami is integrated into a mathematics classroom. Links to STEAM areas were highlighted with each model!

1. to your math classroom
with Origami artPresented by:
Norma Boakes & my protégé

2. 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

3. Origami
Ori- to fold
Gami or Kami- paper
It is literally the “art of paperfolding”.

4. When you think of Origami,
what comes to mind?
?

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

6. Origami is accepted as an art form
Origami is practiced throughout the world
By Eric Joisel
Spain- “Pajarita”
Germany- “Papierdrache”
France- “Cocotte”

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

11. 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!…..

13. 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. 9
Grade 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)

14. 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”

15. • “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

16. The most important
reasons to use Origami

17. Origami Types

18. 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

19. Symbols of Origami

20. It’s time! Ready?

21. 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!

22. 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.

23. Origami Traditional Box

24. 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

25. Jumping Frog

26. 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

27. 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

28. Sumo Wrestler

29. 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

30. 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!

31. 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!)

32. Business Card Cube
x6Business
card

33. 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

34. 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

35. 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!