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Jump Start Questions
What Do You Think These Objects Are Called?
How Do You Think They Are Made?
How is Geometry Used to Develop These Shapes?
Interdisciplinary Unit Origami
By: Cheryl Gaynor, Bayshore HS, Bradenton, FL
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Where Will I Use This?
Integrating Math, Science, Art, Architecture, Business, Engineering Design, Language Arts, World Cultures, Critical Thinking, Writing, Study Of Design And Structure, Science/Mineralogy, Solid Geometry, Writing, Critical Thinking, Problem Solving and…
EOC Review
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Origami Origin
Traditional Origami makes objects like the tsuru (crane) out of a single piece of paper.
In Unit Origami, many pieces of paper are folded the same way and assembled in various ways to create many different geometric shapes.
Today, we will learn the Sonobe Cube. A simple cube made with six units designed by Sonobe Mitsunobu.
The word 'Ori' in Japanese means “to fold.” The word 'gami' means paper. The art of Origami was believed to have
originated 1400 years ago.
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Shapes of Mineral Crystals
Cubic crystals are not always cube shaped! There are many that are shaped like octahedrons (eight faces), and some that are shaped like dodecahedrons (12 faces). The cube is composed of 6 square faces at 90 degree angles to each other. Each face intersects one of the crystallographic axes and is parallel to the other two. Think of sugar, salt/halite , and galena [above] as natural cubes!
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Shapes of Mineral Crystals
OCTAHEDRON-- The octahedron is a form composed of 8 equilateral triangles. These triangle-shaped faces intersect all 3 crystallographic axes at the same distance.
Can you think of a natural octahedron you see every day?
Diamonds and gold are minerals that commonly exhibit the simple octahedral form. Sometimes fluorite and pyrite [fools gold] also take this form.
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First…Origami Basics
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Let’s Make a Sonobe Cube
Step One… What shape is this paper? Fold the paper in half [hot
dog]. What shape is this now? Could the shape be
classified as any other? How does the folded area
compare to the original shape?
How about the perimeter?
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Sonobe Cube
Step Two… Open up the first fold and
fold the quarters into the middle.
What shape is this? What word in geometry
describes shapes of the exact size?
How does this area compare to the fold in step one?
How about this perimeter?
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Sonobe Cube
Step Three… Open up to the original
square. Fold the lower right corner to the first crease line.
What is the new shape? Does anyone know the
word in geometry for all equal sides and all equal angles?
Is this shape a regular polygon?
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Sonobe Cube
Step Four… Rotate the unit 180°and
fold the lower right corner again.
What is the new shape?
Is this shape a regular polygon?
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Sonobe Cube
Step Five… Fold "doors" back into
the center
What is this new shape?
Is it regular?
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Sonobe Cube
Step Six… Fold top right corner
all the way across to the left hand side. Tuck the fold under left-hand “door."
What is the new shape?
Is this a special one?
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Sonobe Cube
Step Seven… Rotate 180° Fold top right corner
all the way across to the left hand side. Tuck the fold under left-hand “door." Make sure that ALL the flaps are tucked in like an envelope.
What shape is this?
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Sonobe Cube
Step Eight… Flip over to the smooth side. Smooth or iron the unit FLAT. Then stand the unit “tall.” What new shape is this?
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Sonobe Cube
Step Nine… Fold the lower right
tip to the consecutive upper right corner.
What is the new shape?
What is the area? Notice that you have
created two pockets and flaps.
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Sonobe Cube
Step Ten… Rotate the unit 180°. Fold the lower right
tip to the consecutive upper right corner.
What is the new shape?
How is new area related to the original piece of paper?
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Sonobe Cube
Step Eleven… We now have a
square. An origami unit has
been created! This was our practice
unit fold. Now we’ll repeat this
“fold” with your remaining colored papers.
Flap
Flap
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Sonobe Cube…Refresher Steps
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Returning To Crystals…
Crystals form geometric shapes because of the orderly arrangement of atoms…sometimes at right angles, other times at acute angles.
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Shapes of Mineral Crystals
Tetragonal - The difference between the isometric system and the tetragonal system is that one of the three axes is longer or shorter than the other two.
The isometric crystal system is the most symmetrical. In it there three axes, all of equal length and at right angles to each other…our Halite crystal for example.
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Shapes of Mineral Crystals
Orthorhombic crystals are often shaped like rhombic prisms or dipyramids (two pyramids stuck together).
• They often look a bit like tetragonal crystals except that they are square in cross section (when you look at the crystal on end).
• Remember…rhombus means?• Ortho means?
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Shapes of Mineral Crystals
Hexagonal crystals often look like six-sided prisms. When you look at the crystal on end, it looks like a hexagon shape in cross section.
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Shapes of Mineral Crystals
Monoclinic crystals look like tetragonal crystals that have been skewed. Often, they form prism shapes and double pyramids.
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Shapes of Mineral Crystals
Triclinic crystals are sometimes very strange shapes! They are usually not symmetrical from one side to the other
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Sonobe Cube…Critical Thinking
Step Twelve… Repeat the above steps
six more times with the colored paper so you have six “units.”
Put the six origami units together to form the cube.
Can you figure out how to do this?
HINT…Every “flap” is in a pocket, and every pocket has a “flap”
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Vocabulary Check…
We learned or reviewed a number of terms. Can you define the following words?
• Square• Rhombus• Rectangle• Parallelogram• Quadrilateral• Regular• Polygon• Consecutive • Congruent• Area• Perimeter
• Closed figure• Origami• Tetrahedron• Pentagon• Isosceles Triangle• Dodecahedron• Trapezoid• Obtuse Angle• Symmetrical• Right Angle• Acute Angle
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Integrated Business Example…
Concepts which have six or seven elements can be modeled using the Sonobe Cube.
Seven Habits of Highly Successful Teens by Sean Covey… which habit do you find most difficult?
Use the six outside cube faces to remember the habits, and put the one you need to work on most inside the cube!!!
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Integrated Business Example…
Seven Habits of Highly Successful Teens by Sean Covey…
#1 – Be Proactive & The Personal Bank Account#2 – Begin With The End In Mind#3 – Put First Things First & The Relationship Bank
Account#4 – Think Win-Win#5 – Seek First To Understand, Then To Be Understood#6 – Synergize… 1+1=3#7 – Sharpen The Saw… Renewal/Refresh Yourself http://www.amazon.com/Habits-Highly-Effective-Teens-ebook/dp/B004IK92RA#reader_B004IK92RA
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Integrated Business Example…
Creating A Business Plan*…#1 – Executive Summary
#2 – Business Vision & Description
#3 – Definition of Industry & Target Market
#4 – Description of Products & Services
#5 – Organization & Management
#6 – Marketing & Sales Strategy
#7 – Financial Plan & Pro Forma Statements* Small Business Association… http://web.sba.gov/busplantemplate/BizPlanStart.cfm
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Integrated Language Arts…
Now that you have learned about origami, geometry, crystals & minerals, business uses, etc…
WRITE a few sentences about what you learned and how you might use this knowledge in the future
Don’t forget to use a Graphic Organizer first to map out how you plan to write your sentences
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Integrated Business & Science …
When you go to your classes, try to find ways you can further explore and apply the concepts learned in this lesson.
Share these concepts with your other classmates and instructors.
GOOD LUCK on the EOC…we hope you find that this refresher or unit introduction lesson was fun…and helpful!
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References & Resources
Origami & Papercraft—A Step-by-Step Guide; Paul Jackson & Vivien Frank; Crescent Books; New York; ISBN 0-517-66804-1; 1988
3-D Geometric Origami—Modular Polyhedra; Rona Gurkewitz & Bennett Arnstein; Dover Publications; New York; ISBN 0-486-28863-3; 1995
Unfolding Mathematics With Unit Origami; Betsy Franco; Key Curriculum Press; Berkeley; ISBN 1-55953-275-0; 1999
Multidimensional Transforms—Unit Origami; Tomoko Fuse’; Japan Publications, New York; 1990; ISBN 0-87040-852-6
Small Business Association Business Plan…http://web.sba.gov/busplantemplate/BizPlanStart.cfm
Seven Habits of Highly Effective Teens by Sean Covey http://www.amazon.com/Habits-Highly-Effective-Teens-ebook/dp/B004IK92RA#reader_B004IK92RA
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The End—Thank YouThe End—Thank You
Any Questions???