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## Engaging Elementary Students in Geometry through Origami

Keywords: geometry , Math , origami

School Subject(s): Geometry , Math

## Full Unit Text

3000 BCE Oldest papyrus found – a blank scroll in a tomb at Saqquara, near Cairo

500 BCE Chinese begin writing on silk

252 BCE Dating of the oldest piece of paper ever found in Lu Lan, China

105 BCE Cai Lun of the Chinese Han court is credited with inventing paper

256 CE First known book on paper produced in China

500-600 CE Mayans develop bark paper

610 CE Korean monk takes papermaking to Japan

751 CE Papermaking in Samarkand begins – they are credited for producing

high quality paper exclusively from (linen) rags

1264 CE First record of papermaking in Fabriano, Italy – they are credited

with first using watermarks to identify the papermaker.

1309 CE Paper is first used in England.

1495 CE John Tate establishes the first paper mill in England in Hertfordshire.

1502-20 CE Aztec tribute book lists forty-two papermaking centers. Some villages

produce half a million sheets of paper annually.

1575 CE Spanish build the first paper mill in Mexico.

1729 CE Papermaking in Massachusetts begins.

1833 CE An English patent is granted for making paper from wood.

1863 CE American papermakers start using wood pulp. (Kurlansky 337 – 3446)

- Students will be able to construct two-dimensional shapes in order to analyze the properties of two-dimensional shapes.
- Students will be able to construct multi-step shapes in order to develop perseverance in solving problems.
- Students will be able to construct three-dimensional shapes in order to analyze the properties of three-dimensional shapes.
- Students will be able to analyze characteristics of two and three-dimensional shapes in order to develop mathematical arguments about geometric relationships.
- Students will be able to develop basic geometric principles in order to construct and deconstruct models.

## Lesson Plans

## Lesson One: History of Origami and basic terms

- document camera
- short history of Origami taken from the Background
- Origami Math – see resources
- Smart board

- Short History of Origami – origins given in the History of Origami above
- Why origami? Ask students to turn and talk to a partner about why origami would be beneficial to use in math lessons. Show images of origami used in science today.
- Basic terms – review and model symbols page given above: mountain, valley, crease, and fold, which is pictured under Basics of Origami. Or you can view this YouTube video on making a square: youtube.com/watch?v=gLrKrHgAI40 . Note to the students that the presenter is carefully folding and creasing his paper.
- Share Tips for success –patience, sharp and precise folds, perseverance, following step by step procedures
- Model and practice – have students make a square using a sheet of copy paper. Point out that the two triangles that are created when folding the top portion of the paper are isosceles right triangles. Define an isosceles triangle and start an anchor chart. You can tape an example of an isosceles triangle to the chart.
- The strip of paper left over can be used to create a simple heart shape using rectangular strips of paper. Use the procedure used on page 9 of Origami Math. Or you can use this website to create a heart using origami paper. youtube.com/watch?v=nnV262Egucw . Students can design one side of the paper to make it their own. Students can also write a message to a friend, family member to write inside the heart and share it with them.
- Exit Slip-given a square sheet of paper, students will fold the paper to create two isosceles triangles and label the two right angles.

## Lesson Two: Geometric Shapes

Objective: Students will be able to use a square sheet of paper to create a 3-dimensional pinwheel.

- Square paper – 6” x 6”
- Instructions for a Basic Form, Net I, and Net II in the appendix
- Pins or wire
- Document Camera
- Diagonal cross
- Horizontal lines
- Vertical lines
- Review properties of a square, including four right angles and four equal sides. Although this may sound basic, asking students to turn and talk to discuss the difference between a rectangle and a square is a good way to check for understanding. Introduce vocabulary words and add to the anchor chart in Lesson one.
- Model with students how to fold Basic I, a straight and diagonal cross using the document camera. This Basic form can be found on page 16 of Easy & Fun Paper Folding . As students fold, refer to geometric shapes that the creases create. Ask students what they notice about the shapes they are creating from the Basic I folds.
- Model with students how to fold Net I and Net II, which is a basic form for many shapes. These forms can be found on pages 17 and 18 of Easy & Fun Paper Folding . Use the document camera again so students can see the folds and creases. As students fold, ask them what they notice about the shapes the creases are creating.
- Use Basic form, Net I, and Net II to create a pinwheel in the appendix using the pinwheel design, straws, and pins/wires. Remind students to be careful with the pins.
- Exit Slip-given a square sheet of paper, students will fold to create horizontal and vertical lines and label each line.

## Lesson Three: Jumping Frog

Objective: Students will be able to use origami procedures to create a moving 3-dimensional shape.

- 3” x 5” index cards
- Math in Motion instructions on pages 52, 53, and 54.
- Document camera
- Line segment
- Perpendicular lines
- Introduce vocabulary words and add to the anchor chart from Lesson one. Students could draw these terms on the chart using a straight edge.
- Introduce motion/action origami – shapes that can be folded in a way that when “prodded” can move
- Use Pearl’s instructions on pages 53 and 54 using a document camera so students can watch each step. As you model the first time (students watch you make the entire frog and then you make it step-by-step together), use vocabulary term while modeling. Or you can show this YouTube video which is about 10 minutes long:
- youtube.com/watch?v=PR_AI3CM2-A.
- Unfold your frog and model step-by-step instructions while students follow along. Allow students time to practice moving their frog.
- Ask students what other movable origami shapes they could make that would move. Allow students to work in pairs to design a shape that would move.

Exit Slip-students will draw perpendicular lines, intersecting lines, and line segments.

## [Please see PDF above for additional activities & appendices]

The following represent Pennsylvania standards for fourth graders:

CC.2.3.4.A.2 Classify two-dimensional figures by properties of their lines and angles.

CC.2.3.4.A.3 Recognize symmetric shapes and draw lines of symmetry.

Hull, T. (2006). Project Origami: Ideas for Exploring Mathematics . Wellesley, PA: A.K. Peters.

Kurlansky, M. (2016). Paper: Paging through history . New York: W.W. Norton & Company.

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## You are here

Origami in the geometry classroom, by ophir feldman, wentworth institute of technology.

1. Hull, Thomas, 2006, Project Origami , A.K. Peters.

## About the Author

The Innovative Teaching Exchange is edited by Bonnie Gold .

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## Connect with MAA

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## SMART Space

Video of solution for calculating the surface area on an origami fold.

If you (carefully) pull on the points of the star, it transforms into this donut-shaped figure!

Trang Ngo & Will Luna, Tufts University CEEO 2016

## Leave a Reply Cancel reply

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## Origami and Geometry Lesson Plan

- Worksheets By Grade
- Math Tutorials
- Pre Algebra & Algebra
- Exponential Decay
- Ph.D., Education, University of Illinois at Urbana-Champaign
- M.A., Curriculum and Instruction, University of Illinois at Urbana-Champaign

## Key Vocabulary

Use origami to develop an understanding of geometric properties.

## Standards Met

## Lesson Introduction

## Step-By-Step Procedure

- Once the airplanes are gone (or confiscated), tell students that math and art are combined in the traditional Japanese art of origami. Paper folding has been around for hundreds of years, and there is much geometry to be found in this beautiful art.
- Read The Paper Crane to them before starting the lesson. If this book can't be found in your school or local library, find another picture book that features origami. The goal here is to give students a visual image of origami so that they know what they'll be creating in the lesson.
- Visit a website, or use the book you selected for the class to find an easy origami design. You can project these steps for students, or just refer to the instructions as you go, but this boat is a very easy first step.
- Rather than square paper, which you usually need for origami designs, the boat referenced above begins with rectangles. Pass one sheet of paper out to each student.
- As students begin to fold, using this method for the origami boat, stop them at each step to talk about the geometry involved. First of all, they are starting with a rectangle. Then they are folding their rectangle in half. Have them open it up so that they can see the line of symmetry, then fold it again.
- When they reach the step where they are folding down the two triangles, tell them that those triangles are congruent, which means they are the same size and shape.
- When they are bringing the sides of the hat together to make a square, review this with students. It is fascinating to see shapes change with a little folding here and there, and they have just changed a hat shape into a square. You can also highlight the line of symmetry down the center of the square.
- Create another figure with your students. If they have reached the point where you think they can make their own, you can allow them to choose from a variety of designs.

## Homework/Assessment

## Origami - Made With Math

## Introduction: Origami - Made With Math

## Step 1: Basics: Creating an Origami Fortune Teller for Kids

A paper fortune teller can be constructed with these steps using a plain A4 paper:

## Attachments

## Step 2: Intermediate: Creating an Origami Flasher

Modern technology is trying to make everything smaller.

We will now create an Origami Flasher.

Satellite solar panels are delicate and not forgive mistake while handling them.

I have attached a pdf file for you to download if you want to follow along.

In order to make the Origami flasher you need to follow these steps:

## Step 3: Introduction to Origami Mathematical Design

In order to understand the math behind Origami we have to take a trip to Ancient Greece.

Euclid’ axioms basically tell us what’s possible geometry.

It turns out that we just need two very simple tools to be able to sketch Origami on paper:

Axioms 4 and 5 are about comparing properties of shapes, rather than designing.

## Step 4: Advanced:Creating the Crease of an Origami Scorpion (How Artists and Scientists Do It)

I think it is time to delve inside the mathematical thinking process of Origami.

Pictures were taken from Robert J. Lang 's amazing work . You can also download a pdf version the Scorpion. Also from this excellent youtube video of Veritasium about Origami.

## Step 5: What to Do Next:

There are a few Resources I can offer to help you in your journey:

1. Software for creating origami

2. Origami Designs and Creases

I am participating in Made by math contest. If you enjoyed this content please leave an Upvote. Thank you!

Participated in the Made with Math Contest

## Be the First to Share

Did you make this project? Share it with us!

## IMAGES

## VIDEO

## COMMENTS

Project Origami: Ideas for Exploring Mathematics. Wellesley, PA: A.K. Peters. This is a technical book for teachers who are looking for more complex origami designs along with ideas for math lessons for older students. There are many suggestions for lessons plans and essential questions for students to write their reflections. Kurlansky, M. (2016).

You really don’t have to be an origami master to bring origami to your math class. Reference 1. Hull, Thomas, 2006, Project Origami, A.K. Peters. About the Author Ophir Feldman ( [email protected]) received his B.S. in Mathematics from Hofstra University in Hempstead, New York.

The origami project can also be used to teach 3D geometry using available 3D origami modules. Using 3D modules would allow students to practice calculating volume of different 3D shapes. If some students finish early, have them trade shapes with another student, and see if they come up with the same answer. Refining the Challenge

In order to make the Origami flasher you need to follow these steps: You fold you paper horizontally. Then you fold your paper vertically. Follow the lines. Fold and unfold your paper in half. Fold the top edge and then the bottom edge to the line in the center. Now fold top and bottom then flip and fold top and bottom to the center line.