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January 22, 2016

# Teaching Math With Modular Origami

Several years ago, I had the good fortune to attend a workshop by Rachel McAnallen (aka Ms. Math) about teaching geometry with a fun and tactile method: origami! Since then, introducing my students to modular geometric origami is one of my favorite teaching moments each year. Origami math gives my tactile and spatially gifted students a chance to shine, it helps students with sequencing and direction following, and it’s a fun way to introduce a wide range of geometry terms and concepts.

I had NEVER created origami before the abovementioned two-hour workshop. You absolutely do not need to be a talented origami artist to pull off these lessons with your students. With the straight-forward tips below and a few minutes of practice, you’ll be ready to guide your students through an origami math experience that will have them clamoring for more. (That’s when you can hand them an origami book and challenge them to figure it out!)

I was bursting with pride upon making my first "skeletal octahedron." Students feel a similar sense of accomplishment when completing their origami structures.

## What is Modular Origami?

Modular origami is the fancy name for geometric origami that is made up of many repeating “units” that are then assembled to create a more complex geometric form. Unlike traditional origami that uses a single sheet of paper to fold a figure, modular origami uses many sheets of paper that are folded into basic modules or units. Once you learn how to make the basic unit for a design, you repeat the process to make enough copies of the unit to assemble your final form. (For a look at some modular origami projects, check out my Pinterest board.)

Although the process of making the units is repetitive, I find that many students enjoy it as a calming, almost meditative process. I often introduce this activity right before standardized tests, because the repetitive folding soothes some students and gives them a purposeful active for jittery hands. I always have a few students who find folding the units to be a chore. I team these students up to divide and conquer the unit folding work and then assemble a joint final product. I’ve had so many students become nearly obsessed with folding units — they bring origami paper to lunch and recess (especially on rainy days) to get in extra folding time.

A student shows off his first modular origami creations: sonobe cubes. (See the video tutorial below to make these simple cubes.)

## What Supplies Will We Need?

I buy very inexpensive origami paper for my students since we go through a fair amount of it, like this 500-sheet pack of 6”x6” paper. I keep a pack or two of fancier paper on hand for special projects that individual students tackle. Colored copier paper cut into squares also works well.

The only other supplies you’ll need are a Popsicle stick and a Ziploc bag for each student. The students use the Popsicle sticks to press “crispy creases” into the paper, and the bag to hold all of their units before they assemble the modules into the final design.

## How Do I Incorporate Math Into Origami?

The math comes entirely through the discussion as you guide the students through making a module/unit. I sit all of my students down and VERY slowly go through the stepwise process of making the first module for a design. I model the process using the document camera, and I have a couple of student experts circulate to help other students who get stuck. (I pre-teach the folding process to these student experts so they are available to be my assistants.)

Before, during and after each fold, we discuss the shapes that we are pressing into the paper, we classify the angles, and I invite the students to name each step to help them remember the sequence of paper folding. This way, students can remember that “the large trapezoid comes after the double horizontal rectangle step.” By folding while discussing geometry, students are also more likely to memorize vocabulary-heavy geometry; they create kinesthetic associations to go along with the geometry terms.

Two of my student experts show off their icosahedrons. Empowering these guys to assist their peers not only helps to build their confidence, it also means that struggling students get timely hands-on support.

## How Do I Get Started With Modular Origami?

The sonobe cube uses a very simple modular origami unit: the aptly named Sonobe unit. As a cube with six faces, this design requires six units. That makes for a pretty short project. Students can get the feel for modular origami without having to create dozens of units for a single project. And Sonobe cubes are so much fun to assemble! You can find plenty of online tutorials about the Sonobe cube, or follow along with my video below. Plus, once your students have mastered the Sonobe cube, they can use the same units to make octahedrons and icosahedrons.

## What Do We Do After Our First Project?

After you teach your students how to make the Sonobe cube (and possibly the other Sonobe shapes), you might like to help them through one other project. An octagon-star is another favorite because it is a transforming shape — the final design transforms from a star to an octagon and back. For the second project, I provide written directions, but I still walk them through the process step by step. I have the students refer to the written directions (and diagrams) so they can learn to follow origami directions independently.

Students who caught the modular origami bug will be so motivated after learning the first two projects, that they will likely want to figure out other origami designs. I provide a basket of modular origami books and printouts that they can peruse to choose other projects. At that point I step back and let my students become the expert origami crafters — their skills soon surpass my basic ones, and I am very happy to take on the role of appreciative spectator.

If you give modular origami a try in your classroom, I’d love to hear about it! Connect with me on Twitter or Facebook, or leave me comments or questions below.

One year ago: “Division S.O.S.: What To Do About Remainders

Two years ago: “Classroom Crafts to Celebrate the Chinese New Year

Three years ago: “Four Ways to Learn About Lincoln

Four years ago: “Total Recall: Helping Our Students Memorize Multiplication Facts

Several years ago, I had the good fortune to attend a workshop by Rachel McAnallen (aka Ms. Math) about teaching geometry with a fun and tactile method: origami! Since then, introducing my students to modular geometric origami is one of my favorite teaching moments each year. Origami math gives my tactile and spatially gifted students a chance to shine, it helps students with sequencing and direction following, and it’s a fun way to introduce a wide range of geometry terms and concepts.

I had NEVER created origami before the abovementioned two-hour workshop. You absolutely do not need to be a talented origami artist to pull off these lessons with your students. With the straight-forward tips below and a few minutes of practice, you’ll be ready to guide your students through an origami math experience that will have them clamoring for more. (That’s when you can hand them an origami book and challenge them to figure it out!)

I was bursting with pride upon making my first "skeletal octahedron." Students feel a similar sense of accomplishment when completing their origami structures.

## What is Modular Origami?

Modular origami is the fancy name for geometric origami that is made up of many repeating “units” that are then assembled to create a more complex geometric form. Unlike traditional origami that uses a single sheet of paper to fold a figure, modular origami uses many sheets of paper that are folded into basic modules or units. Once you learn how to make the basic unit for a design, you repeat the process to make enough copies of the unit to assemble your final form. (For a look at some modular origami projects, check out my Pinterest board.)

Although the process of making the units is repetitive, I find that many students enjoy it as a calming, almost meditative process. I often introduce this activity right before standardized tests, because the repetitive folding soothes some students and gives them a purposeful active for jittery hands. I always have a few students who find folding the units to be a chore. I team these students up to divide and conquer the unit folding work and then assemble a joint final product. I’ve had so many students become nearly obsessed with folding units — they bring origami paper to lunch and recess (especially on rainy days) to get in extra folding time.

A student shows off his first modular origami creations: sonobe cubes. (See the video tutorial below to make these simple cubes.)

## What Supplies Will We Need?

I buy very inexpensive origami paper for my students since we go through a fair amount of it, like this 500-sheet pack of 6”x6” paper. I keep a pack or two of fancier paper on hand for special projects that individual students tackle. Colored copier paper cut into squares also works well.

The only other supplies you’ll need are a Popsicle stick and a Ziploc bag for each student. The students use the Popsicle sticks to press “crispy creases” into the paper, and the bag to hold all of their units before they assemble the modules into the final design.

## How Do I Incorporate Math Into Origami?

The math comes entirely through the discussion as you guide the students through making a module/unit. I sit all of my students down and VERY slowly go through the stepwise process of making the first module for a design. I model the process using the document camera, and I have a couple of student experts circulate to help other students who get stuck. (I pre-teach the folding process to these student experts so they are available to be my assistants.)

Before, during and after each fold, we discuss the shapes that we are pressing into the paper, we classify the angles, and I invite the students to name each step to help them remember the sequence of paper folding. This way, students can remember that “the large trapezoid comes after the double horizontal rectangle step.” By folding while discussing geometry, students are also more likely to memorize vocabulary-heavy geometry; they create kinesthetic associations to go along with the geometry terms.

Two of my student experts show off their icosahedrons. Empowering these guys to assist their peers not only helps to build their confidence, it also means that struggling students get timely hands-on support.

## How Do I Get Started With Modular Origami?

The sonobe cube uses a very simple modular origami unit: the aptly named Sonobe unit. As a cube with six faces, this design requires six units. That makes for a pretty short project. Students can get the feel for modular origami without having to create dozens of units for a single project. And Sonobe cubes are so much fun to assemble! You can find plenty of online tutorials about the Sonobe cube, or follow along with my video below. Plus, once your students have mastered the Sonobe cube, they can use the same units to make octahedrons and icosahedrons.

## What Do We Do After Our First Project?

After you teach your students how to make the Sonobe cube (and possibly the other Sonobe shapes), you might like to help them through one other project. An octagon-star is another favorite because it is a transforming shape — the final design transforms from a star to an octagon and back. For the second project, I provide written directions, but I still walk them through the process step by step. I have the students refer to the written directions (and diagrams) so they can learn to follow origami directions independently.

Students who caught the modular origami bug will be so motivated after learning the first two projects, that they will likely want to figure out other origami designs. I provide a basket of modular origami books and printouts that they can peruse to choose other projects. At that point I step back and let my students become the expert origami crafters — their skills soon surpass my basic ones, and I am very happy to take on the role of appreciative spectator.

If you give modular origami a try in your classroom, I’d love to hear about it! Connect with me on Twitter or Facebook, or leave me comments or questions below.

One year ago: “Division S.O.S.: What To Do About Remainders

Two years ago: “Classroom Crafts to Celebrate the Chinese New Year

Three years ago: “Four Ways to Learn About Lincoln

Four years ago: “Total Recall: Helping Our Students Memorize Multiplication Facts

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