Origami

Origami• Origami (pronounced or-i-GA-me) is the traditional

Japanese folk art of paper folding.

• "Ori" is the Japanese word for folding and "kami" is the Japanese word for paper.

• Meigi Period (1868-1912)

• Friedrich Froebel (1782-1852)

• Akira Yoshizawa (1930s)

Social Studies

Kids Web Japan - http://web-japan.org/kidsweb/

Japan

In Japan the crane is the symbol for long life, prosperity and good health. Recently the crane has become a symbol of peace.

English Language Arts

Visual Arts

http://www.janm.org/exhibits/foldingpaper/

Visual Arts

http://www.langorigami.com/

Science, Mathematics and Technology• Origami mathematics

– includes the mathematics that describes the underlying laws of origami

• Computational origami– comprises algorithms and theory devoted to the

solution of origami problems by mathematical means

• Origami technology– the application of origami (and folding in general)

to the solution of problems arising in engineering, industrial design, and technology in general.

Science

• More and more scientists are integrating origami into studies.

• Folding and unfolding problems have applications in robotics, hydraulic tube bending, and have connections to protein folding, sheet-metal bending, packaging, and air-bag folding.

http://theory.csail.mit.edu/~edemaine/folding/

Paper Manufacturing• Although paper manufacture itself was invented and

refined in China between 2000 and 1500 years ago it is from Japan that the first references come that relate to using paper to create folded models.

http://www.pbs.org/independentlens/between-the-folds/film.html

Michael LaFosse

A Closer LookIntegrating the Common Core

State Standards for Mathematics

• Selecting and Unpacking Standard• Determining Learning Goals• Identifying Learning Progressions and Scale• Engaging Students in Meaningful Dialogue

and Activities• Assessing Student Progress

Geometry

Standards

Making an Origami Cup

Identify the Geometry Standard(s)

Handout #14

Grade: Subject:Standard(s):

Skills – Students should be able to do Concepts – Student should know

Critical Area of Focus:

Learning Goal:

Essential Question:

Target Learning Progression:

5th Mathematics Classify two-dimensional figures in a hierarchy based on properties.MACC.5.G.2.4

Classify • Two-dimensional figures• Properties• Hierarchy

Classify two-dimensional figures into categories based on their properties.

Classify two‐dimensional figures in a hierarchy based on properties.

How are two-dimensional figures classified?

Students will classify two-dimensional figures in a hierarchy based on properties.

Making an Origami Cup

Origami House

Counting Shapes

• What shape is the origami paper?• When you fold the paper in half, what shapes

do you see?

Counting Shapes

• Fold the paper again.

• Open up the paper and count the number of rectangular regions you see.

How many rectangular regions do you see?

1 2

43

Count each section1234

Next, combine sections that touch1,22, 43,41,3

Last combine all the sections1, 2, 3, 4

How many rectangular regions do you see how?

• Fold the paper another time.

How many rectangular regions do you see how?

• Unfold the paper and count all of the rectangular regions. Remember to make a list.

3

5 7

1 2 4

6 8

Count each section1 2 3 45 6 7 8Next, combine sections that touch1,2 1,5 5,6,7 2,3,4,6,7,83,7 2,6 6,7,82,3 3,7 5,6,7,83,4 4,8 1,2,5,65,6 1,2,3 2,3,6,76,7 2,3,4 3,4,7,87,8 1,2,3,4 1,2,3,5,6,7Last combine all the sections1, 2, 3, 4, 5, 6, 7, 8,

Origami Fish

Origami Fish: Triangles• Scalene

• No side equal• Isosceles

• at least two sides equal• Equilateral

• all sides equal• Acute

• 3 acute angles • (all less than 90°)

• Obtuse• 1 obtuse angle • (greater than 90 °)

• Right • One 90° angle

• Equiangular • all angles equal

Origami Fish: TrianglesIdentify Triangles1+22+31+2+31+2+3+42+3+43+45+66+75+6+78+910+1110+11+1211+12

1. Obtuse Scalene 25, 110, 452. Right Scalene 20, 90, 703. Right Scalene 15, 75, 904. Obtuse Scalene 30, 45, 1055. Obtuse Scalene 30, 105, 456. Right Scalene 15, 90, 757. Right Isosceles 45, 45, 908. Right Isosceles 45, 45, 909. Right Isosceles 45, 90, 4510. Right Isosceles 45, 45, 9011. Right Scalene 20, 90, 70 12. Obtuse Scalene 25, 110, 45

Planning Integrated Lessons 1. Generate ideas2. Identify Standards 3. Identify Learning Goals

and Progressions Scale4. Identify Resources5. Develop Lesson6. Develop Formative

Assessment tasks7. Teach 8. Monitor Progress