Develop a multicultural lesson that brings together the teaching of subject matter through a cultural context aligned with Transformative or Social Action Approaches from Banks or Culturall

Origami Lesson Plan (Day 1&2)

I. Description of Students

This lesson will be used with a Geometry class. This class includes twenty-four 9th grade students.

Each student is unique, but shares the commonality of learning together in a respectful and

comfortable class environment. Of the students 33% are Asian including 3 with Japanese

backgrounds, 25% Latino students, and the rest are from White Anglo backgrounds. Four are English

Language Learners (ELL) and two have a learning disability.

Grade: 9th-10th

II. Content Progression

Beginning in Kindergarten, CCSS for Geometry include Identify and describe shapes regardless of

their orientation; Analyze and compare two- and three-dimensional shapes using informal language to

compare similarities and differences; Model shapes in the world by building shapes from components

or drawing shapes; Compose simple shapes to form larger shapes.

In Grade 1, 2, & 3, CCSS include–Reason with shapes and their attributes. Grade 1–Compose two-

dimensional shapes or three dimensional shapes to create composite shapes and compose new shapes

from composite shapes. Grade 2—Recognize and draw shapes having specified attributes; Identify

triangles, quadrilaterals, pentagons, hexagons, and cubes.

In Grade 4, CCSS includes–Draw and identify lines and angles, and classify shapes by properties of

their lines and angles; Classify two-dimensional figures based on the presence or absence of parallel

or perpendicular lines or of angles of specified size (e.g., right, obtuse, acute, etc.); Recognize a line of

symmetry for a two-dimensional figure.

In Grade 5, CCSS includes Classify two-dimensional figures into categories based on their properties.

In Grade 6, CCSS includes Represent three dimensional figures using nets made up of rectangles and

triangles; Apply these techniques in the context of solving real-world and mathematical problems.

In Grade 7 & 8, CCSS includes Draw, construct and describe geometrical figures and describe the

relationships between them.

CCSS for this high school Geometry lesson:

 G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment.

 G.MG.1: Use geometric shapes, their measures, and their properties to describe objects (e.g.,

modeling a tree truck or a human torso as a cylinder).

CCSS Mathematical Practices for lesson and across Grades levels: Attend to precision; construct

viable arguments and critique the reasoning of others.

III. Lesson Plan

Overarching (Long-term) Goal(s):

Affective:

 Students will value the cultural traditions of other’s, and appreciate the merits that others’

traditions bring to today’s society.

Practice/Process:

 Students will attend to precision, using clear definitions of geometric concepts in discussion

with others and in their own reasoning.

 Students will construct viable arguments and critique the reasoning of others in developing

steps involving geometry properties and shapes for creating varied origami figures.

Common Core Standards: Geometry

 G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment.

 G.MG.1: Use geometric shapes, their measures, and their properties to describe objects (e.g.,

modeling a tree truck or a human torso as a cylinder).

Objective(s):

 Students will be able to use paper-folding techniques to explore geometric patterns.

 Students will be able to make origami models.

 Students will be able to use the language of geometry to explain how to make an origami

model.

 Students will be able to explore and compare problem solving between the use of origami and

traditional algorithms in various academic fields.

Materials:

 PowerPoint

 8.5” x 11” Sheets of Paper

 Computers with Internet access on Day 2

 Handouts: Day 1–Easy Origami Heart Handout, Day 2–Origami Research Handout

Time: Two 50-minute periods

Procedures:

Day 1

1. Have a visual origami swan on PowerPoint display when students walk into class.

2. Bell Ringer: On a half sheet of paper, have students reflect on the origami swan. Have them reflect

on what it is, and how they think it was made.

3. Once all students are seated and a few minutes have passed, discuss the above questions with the

students.

(5 minute mark)

4. On PowerPoint slides, show numerous images of origami from the Japanese culture. Observe

students’ reactions. Explain to students that the Japanese culture has used origami, the art of paper-

folding, for centuries to make beautiful figures and this ancient art has in recent years been used as a

basis for functional creations such as automobile airbags and expandable space telescopes.

5. Preplan—ask any of the Japanese students to share any experiences with origami that they have

had and to share any origami figures from home.

Teacher asks: “What do you think about the origami images/figures we have seen?”

Possible student answers: “They are really cool”. “How did they make it?”

6. Using PowerPoint slides including the following information, discuss with students a brief history of

origami:

a) Paper is thought to have originated in China around 105 A.D., where very few examples of folded

paper designs were known; one example are paper-folded to look like gold nuggets burned as

offerings to the deceased. Around the 6 th

Century, paper was brought to other Asian countries

including Japan where paper-folding was initially used for religious and other formal ceremonies

and celebrations and grew to become a popular art-form, known as Origami.

b) “Ori” means folding and “kami” means paper in Japanese.

c) Origami was first used by only the elite who could afford paper

i. as a good luck token

ii. for religious rituals and formal ceremonies

iii. at celebrations to represent the guest of honor (bride and groom)

d) During the 17 th

Century as paper became mass produced and thus less expensive, Origami began to

fully develop into the art form we know it today.

e) During this time, origami grew very quickly in Japan because the Japanese culture emphasized

saving everything, even paper. Also, following tradition, the people gave origami pieces as good

luck charms following in the traditions of the Samuri, used folded-paper butterflies for good luck

at weddings following Shinto Wedding traditions, and as the crane was considered a sacred bird in

Japanese mythology, the custom of folding 1000 paper cranes to receive good luck or receive a

wish grew in popularity.

Picture of Origami Crane from

http://www.instructables.com/id/How-to-make-

a-Paper-Crane-1/ )

f) Origami became a form of art as people began to make their own models.

g) It was first passed down from generation to generation by word-of-mouth, and then was written

about in books with recorded steps including visual diagrams for recreation (creating and recording

Origami designs involves problem solving and spatial reasoning with shapes.

Picture from “Tsutsumi-no Ki”:

The first book published about Origami was in 1764, the

"Tsutsumi-no Ki" by Sadatake Ise. It contained 13 ceremonial

folds.

In 1797 came the first published book documenting

recreational paper-folding: “Folding of 1000 Cranes“ by

Senbazuru Orikata.

Information from: http://www.origami-resource-

center.com/history-of-origami.html

h) Origami was introduced to Africa from Japan, then to Spain, then to South America, then to

Europe, and then to the United States.

i) The Japanese origami crane is now a global peace symbol

j) In the 1950, Akira Yoshizana and Sam Randlett developed a standard set of origami symbols to

describe how to fold paper into models. These symbols continue to be used today.

k) In recent years, a variety of Origami has become the bases for modern technological advances,

including airbags, a NASA solar array sent into space folded and expanded in space, a stent to

open up diseased arteries that are entered into the body folded and expanded in the artery.

i. Heart stent prototype, designed by Zhong You and Kaori

Kuribayashi-Shigetomi in 2003, made of stainless steel.

Picture from:

origami-changed-science-from-heart-stents-to-airbags-

2372322

ii. Diagram below is of an airbag based on origami techniques:

QuickTime animation for airbag:

http://www.langorigami.com/science/technology/airbag/airbag.php

Teacher asks: “What do you think about origami and its contribution to society?”

Possible student answers: “That is cool”. “I didn’t know about it.” “It is so useful.”

Teacher asks: “What mathematics is involved in Origami?

Possible student answers: “Making shapes.” “Geometry.” “Spatial thinking.” “Problem solving.”

Teacher explains: We often hear the term, “Western Mathematics,” and think of mathematics ideas

coming from European countries; however, mathematical ideas have been created around the world.

(15 minute mark)

7. Explain to students that today, as a class, we will be constructing an origami heart using the

techniques of origami and will then connect the origami techniques to geometric terms and ideas.

8. Show students the short video of what they will be doing as an overview using the following link:

http://www.origami-instructions.com/easy-origami-heart.html. The video will help students visualize

what the instructions mean prior to having to follow the instructions.

Teacher asks: “What are some geometric terms that we can used to create the origami heart?”

Possible student answers: “Midpoint” “Diagonal” “Parallel” “Triangle”

9. Distribute a sheet of paper to each student.

10. Pair students with a partner and give each pair an Easy Origami Heart Handout. Explain to

students that they are to work together assisting one another as you walk them thoroughly through

each step. (Pictures of each step available on the website above). While going through each step, ask

students to describe each fold using the language of geometry. Ask students to identify geometric

patterns being repeated through the construction of the origami heart. Discuss with students how the

folds relate to different lines, angles, polygons/shapes, and planes in geometry. Write out the

geometric terms being used on the board while partners take turns recording them on their Handout.

Have students refer to their Geometry: Common Core textbook for help.

(35 minute mark)

11. Give student pairs time to work with their partner to change the steps on the origami heart

handout so that the steps use geometric terms and properties they are learning. Students should refer

to the class discussion earlier to come up with the new instructions. Have each pair write out the new

instructions on a separate sheet of paper to be turned in at the end of the period.

12. Teacher walks around and checks for understanding.

Teacher asks: “How are you and your partner applying geometric terms?

Possible student answers: “We know that these horizontal and vertical folds are diagonals of the

square.” “We know that the steps form shapes like squares, triangles, trapezoids, and rectangles.”

(45 minute mark)

13. Closure: Bring class back together and collect the pairs’ geometry rewording of the Origami

Heart instructions. Ask students to explain what they learned today about origami and its connection

to geometry.

Teacher asks: “What’s the benefit of using origami to learn geometry?”

Possible student answers: “It provides a visual.” “It’s just cool to make. You only need a piece of

paper.” “It’s something hands-on.” “It requires a lot of focus.”

13. Assign homework: Students are to research different origami figures and choose one that they like.

Students may use books, art and craft stores, or the Internet to conduct their research. Then, they are

to practice the construction of their origami and write out the instructions on how to make it using

geometric terms. Students are required to bring in the actual origami that they chose along with the

instructions, typed-up. Tell students to make sure the instructions are clear, accurate, and can be

understood easily. Have students use the origami heart instructions (revised to use geometric terms)

as a reference. This homework assignment will be due in a week.

15. Tell students that during next class, if time permits, students will share their origami with the class,

and discuss what they found difficult in making the origami and in writing the instructions.

*Announce to students that class will meet in the computer lab tomorrow.

(50 minute mark)

Assessment, Accommodations, and Handouts at end of Day 2 lesson below.

Day 2

Materials: Computers (e.g., Computer Lab) and Origami Research Handouts

1. Students report to the computer lab.

2. Bell ringer: On a half sheet of paper, have students reflect on how origami can be used in other

academic fields apart from learning geometry.

3. Once all students are seated and a few minutes have passed, discuss the Bell Ringer with the

students.

Teacher asks: “Besides geometry, how else do you think we can use origami?”

Possible student answers: “For car airbags.“ ”As an art.” “For expanding telescope lenses in space.”

(5 minute mark)

4. Explain to students that origami can be applied for problem solving in academic fields like

mechanical engineering, computer science, and biomedical engineering. Provide brief examples.

Heart Stent (closed and expanded)

Space Solar Panel (closed and expanded)

1.

5. Explain to students that today, as a class, we will be conducting research on how origami is used in

academic fields besides learning geometry.

6. Divide class up into groups of three.

7. Distribute one Origami Research Handout per group.

8. Give directions to assignment:

a. Each group will work together to complete the Origami Research Handout. Students will be

selected at random to represent their group in sharing what their group researched and found and

their responses to the questions on the Origami Research Handout.

b. Each group should find an article that discusses the success of using origami for studying or

problem solving a particular idea in a field of study other than geometry. Students can either find a

concept or idea they have already studied and use their knowledge to make comparisons with

traditional approach, or conduct further research to find the traditional method of studying that

concept.

c. Groups are required to collaboratively work together. Every group member must conduct

research to find a common group topic of study. Once a topic has been agreed upon, each group

member is required to take notes on their findings. Once sufficient information is acquired, each

group member will share their finding with the group, and accurately fill out the worksheet.

d. Remind students that research should be conducted from authentic sources, and the information

should be precise. Students should also be able to provide supporting evidence for their results.

Teacher asks: “What are some sources that are good to use?”

Possible student answers: “Google to initiate research” “journal databases” “dot com if it’s reliable”

(15 minute mark)

9. Have students begin working. Walk around and check for understanding. Repeatedly remind

students to work collaboratively. As teacher walks around be sure to approach groups as a whole and

ask groups what each member is doing.

Teacher asks: “Why do you think the field(s) you are investigating use origami?”

Possible student answers: “It provides a model.” “It can be used for things that need to be smaller to

transport and then expand.”

Teacher asks: “What is each member in your group doing?”

Possible student answers: “Jenny is recording what we are finding, Jose is researching the internet

from authentic websites, and Aki is researching journal articles.

(40 minute mark)

10. Closure: Bring class back together. Randomly call on students from groups to share and discuss

their findings from the Origami Research Handout. Ask students to explain what they learned today

about the use of origami in various fields versus traditional approaches.

11. Cooperative Group Processing: Ask students to explain what strategies were helpful for

successfully working in a small group.

12. Collect the classwork (Origami Research Handout) from each group; any group not finished can

complete for homework.

13. Assign homework: Finish research handout if group needs more time. Otherwise, if handout is

finished and turned-in, there is no homework.

(50 minute mark)

Assessment:

Informally assess students while walking around and asking questions, making observations, and

checking for understanding. Formally assess students through students’ responses to classwork—Easy

Heart Origami’s new instructions using geometry terms and properties, Homework on creating an

Origami of their own choice and generating intructions using geometry terms and preoperties, and

Origami Research Handout.

Extension: For groups finishing early, they can share the origami figures they investigated and

created for Day 1 homework.

Accommodations:

Place ELL students (English Language Learners) and students with learning disabilities or physical

disabilities with specified classmates as needed in order to assure that the best learning is taking

place. The above students will be paired during Day 1 and grouped during Day 2 with those who are

proficient in English, patient, and have the skills to collaboratively work together. Teacher will

provide close attention to these students, and assist them as needed.

Handouts: Attached: Easy Origami Heart Handout and Origami Research Handout.

IV. Sources/Bibliography

http://www.origami-resource-center.com/history-of-origami.html,

http://www.instructables.com/id/How-to-make-a-Paper-Crane-1/ ,

https://origamihistory.wordpress.com/2010/11/16/where-did-origami-come-from/,

to-airbags-2372322, http://www.langorigami.com/science/technology/airbag/airbag.php,

http://www.origami-instructions.com/easy-origami-heart.html, www.pearsonsuccessnet.com,

www.sciencedaily.com, www.foldingtogher.org, www.japan-zone.com, www.thinkquest.org,

www.youtube.com, Geometry: Common Core textbook, Google images

V. Reflection

The origami lesson is aligned with recent theories of learning taking into account the diversity of the

students in the Geometry class as described in section I above. Both Day 1&2 of the lesson,

incorporate the use of learner-centered approaches, cultural and experiential backgrounds of

students, and cooperative learning strategies taking into account the diversity of the student body and

allowing for students to work together accordingly; all aligned with culturally relevant pedagogy.

Students who are ELLs will be paired/grouped with those who are proficient in English, can

communicate with the ELL, and are patient so that they can cooperatively work together. Students who

are above average, collaborative, and patient will be paired/grouped with those students who are

below average and/or have a learning disability. The teacher will monitor the cooperation by walking

around the class and communicating with the small groups as a whole when responding to student

questions or engaging in any discussion about the work or cooperation strategies being used.

The lesson is aligned with Bank’s third level of multicultural curriculum reform, the Transformation

Approach. The transformation approach changes the basic assumptions of the curriculum and gives

students the tools to view concepts, issues, events, and themes from the different perspectives of

various cultural and ethnic groups. This particular lesson connects the mathematical thinking involved

in making origami, a valued tradition in the culture of some students in the class, particularly those

from Japan, with mathematical ideas in Geometry that the students are learning in class. It provides

opportunities for members of the class, such as students from Japanese backgrounds, to share their

experiences with origami; thus, valuing their cultural backgrounds. It student-centered helps students

recognize the contributions that origami has made to recent scientific and mathematical

developments; thus, helping students develop an appreciation of other cultures’ contributions to

mathematics and science and helps the Japanese students recognize the merits of their traditions and

contributions to society. Students also begin to realize that mathematical ideas learned in their

classroom and textbook are not the only ideas that are learned and used throughout the world.

My own reflection of this lesson plan is that it required much time and effort, but it was a good

learning opportunity. It allowed me to use the multicultural mathematics knowledge I’ve gained and

apply it constructively. I hope my students will enjoy learning about origami and its uses as I have

enjoyed it.

Pair Names: ____________________________________ Date:____________ Class Per._________

Easy Origami Heart Handout

Website video and pictures: http://www.origami-instructions.com/easy-origami-heart.html

Directions: Working in pairs, for each step in making the Origami Heart, discuss geometric terms and

properties evidenced in each step and take turns recording these on the handout. After working

through the Origami Heart steps creating a Heart, you will work with your partner to re-word each step

to including the geometric terms and properties you have been learning and have recorded on the

handout.)

1. Create a square piece of paper from a regular

sheet of letter paper (8.5” x 11”):

a) Hold paper portrait style and fold the sheet of paper taking corner on bottom left across to

right-hand side of paper: fold paper to match

the corner and bottom of paper to touch the

right-hand side of the paper.

b) Fold the elongated piece remaining as a single layer over the double layer created in

(a) and crease sufficiently to tear elongated

piece off. Unfold the remaining double layer

to reveal a square piece of paper.

2. Using the square piece of paper, fold the paper

in half (one corner to the opposite corner), and

then unfold.

3. Fold the other side in half (other corner to its

opposite) and then unfold so that you have two

creases that cross in the paper.

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