Using Origami to Promote Math Talk

Have you ever tried origami? Origami is a traditional Japanese art that is created by simply folding a piece of paper. Origami can be used as a fun and engaging educational tool in mathematics. Creating two- and three-dimensional shapes out of various sized square papers can help teachers address number, geometric, and fractional concepts. It supports developing pattern recognition, sequencing skills, visual-motor skills, and temporal-spatial concepts. Using origami encourages students to use their creativity, problem-solving skills, and reasoning abilities.

Working with origami also involves spatial thinking as you follow folding instructions and problem-solve. Spatial awareness is the ability to visualize yourself in relation to the environment around you. Research suggests that origami can be beneficial for training spatial reasoning skills.

Discussing their thoughts and ideas about origami helps students construct their own mathematical understanding and provides a fun and safe learning environment in which they communicate with others. Communication is one of the five components for a high-quality school mathematics program recommended by the National Council of Teachers of Mathematics. It is an essential skill to acquire for all students. Here’s how to integrate origami into elementary math lessons.

Getting Started with an Origami Activity

Origami math can be integrated into units of study addressing basic geometric shapes such as squares, rectangles, and triangles in lower grades; and folding paper in half can be a great way to introduce symmetry and fractional concepts in middle grades. Advanced students and students in upper grades may enjoy creating 3-D objects from 2-D origami papers. You can see the basic instructions for how to fold a dog and a house here. I'll use those as examples throughout this article.

The following books can be used to catch students’ attention to get started with origami:

• Fold Me a Poem, by Kristine O’Connell George
• Lissy’s Friends, by Grace Lin
• Yoko’s Paper Cranes, by Rosemary Wells
• Spread Your Wings and Fly: An Origami Fold-and-Tell Story, by Mary Saunders, illustrated by Carla Mihelich
• The Origami Master, by Nathaniel Lachenmeyer, illustrated by Aki Sogabe
• The Paper Crane, by Molly Bang

After the read-aloud, go over these instructions with your students:

1. Use square paper.
2. Fold paper cleanly and carefully, especially at the small points of corners. 
3. Work on a hard surface. 
4. Exactness is achieved by moving your thumbnail sharply along all folds and creases. 
5. Follow each step carefully in the sequence given.

Where is the Math? 

The two-dimensional shapes and geometry vocabulary such as line segment, diagonal, corner, acute angle, right angle, vertex, and line of symmetry can be addressed while creating origami.

Fractions are another concept that can be addressed while folding and unfolding origami papers. In steps 2 and 3 of the handout linked above, the teacher can introduce vocabulary like halves and fourths. Older students can be challenged to find the fraction of a specific shape as compared with the original square or another shape.

Unfolding the completed origami product provides a rich learning opportunity to discuss what students discover and understand, depending on the age of the students. Ask students what they notice and wonder when they unfold the completed origami. Students will find various shapes and lines that the creases created by the folds. Here are some questions you can ask.

Questions to ask during Origami activities 

As you guide your students through the activity, ask them questions that will encourage them to develop their math talk. I like to ask broad questions and to focus on triangles and angles with the dog, and then focus on lines and quadrilaterals with the house.

Broad questions:

• What shape is the origami paper?
• How many sides does a square paper have?
• What else can you say about the sides?
• What is the center vertical line?
• What is a line of symmetry?
• What shape did it create?
• What kind of triangles?

Questions to ask while creating an origami dog:

• What is the top part of the triangle?
• What is the bottom part of the triangle?
• How many sides does a triangle have? Points? Angles?
• Are the sides of the triangle the same length?
• What kind of triangle is it?
• What is an isosceles right triangle?
• What is a right triangle?
• What is the sum of the angles?

Questions to ask while creating an origami house:

• What is a rectangle?
• What is a right angle?
• What is a quadrilateral?
• Can you name other quadrilaterals?
• What kind of line is it?
• How many rectangles did you see?
• How many equal parts?
• What kinds of lines do you see?
• What are parallel lines?
• What are perpendicular lines?
• When the paper is unfolded, how many parts do you see?

Curriculum Integration

Using origami can provide fun and engaging experiences that young students may be inspired to write about. Bridging math with language arts allows for more authentic learning in a student’s classroom experience. You can have the students do a couple of different writing assignments.

In creative writing, students can take the origami character and create a story having the dog as a central character. You can also have them complete a how-to-style writing activity where they explain the steps necessary to create an origami character by using vocabulary words they have learned during the origami activity.  

If students want to explore origami further, they can check out books by John Montroll or visit websites like Very Simple Origami for Kids and Mathigon: Mathematical Origami.

Utilizing origami to teach math and other subject areas is a fun way to engage your students in learning valuable math skills. I hope you give it a try!