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Jump Start Questions

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. Where Will I Use This?.

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Jump Start Questions

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  1. 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?

  2. Interdisciplinary Unit Origami By: Cheryl Gaynor, Bayshore HS, Bradenton, FL

  3. 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

  4. 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.

  5. 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!

  6. 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.

  7. First…Origami Basics

  8. 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?

  9. 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?

  10. 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?

  11. 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?

  12. Sonobe Cube Step Five… • Fold "doors" back into the center • What is this new shape? • Is it regular?

  13. 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?

  14. 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?

  15. 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?

  16. 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.

  17. 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?

  18. Pocket Flap Flap Pocket 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.

  19. Sonobe Cube…Refresher Steps 8 5 7 10 6 9 11 12 13

  20. Returning To Crystals… Crystals form geometric shapes because of the orderly arrangement of atoms…sometimes at right angles, other times at acute angles.

  21. 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.

  22. 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?

  23. 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.

  24. Shapes of Mineral Crystals Monoclinic crystals look like tetragonal crystals that have been skewed. Often, they form prism shapes and double pyramids.

  25. Shapes of Mineral Crystals Triclinic crystals are sometimes very strange shapes! They are usually not symmetrical from one side to the other

  26. 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”

  27. 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

  28. Integrated Business Example… • Concepts which have six or seven elements can be modeled using the Sonobe Cube. • Seven Habits of Highly Successful Teensby 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!!!

  29. Integrated Business Example… Seven Habits of Highly Successful Teensby 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

  30. 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

  31. 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

  32. 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!

  33. 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 Coveyhttp://www.amazon.com/Habits-Highly-Effective-Teens-ebook/dp/B004IK92RA#reader_B004IK92RA

  34. The End—Thank You Any Questions???

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