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Teaching Geometry Through Paper Folding

Numerous research studies and math initiatives stress the importance of making math more hands-on and engaging for students. Geometry is a subject that lends itself particularly well to a more hands-on approach due to the nature of the subject. Students of all ages can benefit from the use of paper folding to learn geometric concepts and skills.

Paper folding will engage students in learning the material. They'll be able to physically create the different two- or three-dimensional shapes they're studying, analyze and manipulate angles, explore different types of lines, and so much more.

Regardless of the age of the children you are teaching, it is important to encourage students to use math vocabulary when discussing what they are doing and discovering. Teach them age and grade-level appropriate terms as you lead a lesson. Encourage and expect them to use the vocabulary throughout their learning experience. You'll be amazed at how much this can help cement these words into their memory and allow them to apply them more broadly.

Below, we'll share 10 different paper folding tasks that you can implement with your students to help them learn geometric concepts.


Shapes and their Attributes

Each student will need their own sheet of origami paper for this lesson (you can also use copy paper or construction paper). Students should start with a square or a rectangular piece of paper.

Before having students begin folding their paper, ask them to name the shape they see and describe its attributes. The vocabulary you may expect to hear from children will vary depending on their grade-level, but you may expect to hear answers such as: "I see a square," "It has four corners/side," "It is a rectangle," "It is a quadrilateral," or "It has two pairs of parallel lines."

After students have shared their responses, tell them to take one corner of the paper, fold it up (part of the way, not completely to the top), and make a crease. Again, ask them to describe what they see. You can also have students share the various shapes they made and discuss that while everyone made a pentagon, everyone's pentagon looks a little different.

You can continue the steps, having students make one fold at a time and discussing the attributes and name of the new shape that is formed. Students can be encouraged to make predictions about what their next shape will look like/what its attributes will be before they make the fold.


Attributes of Solid Figures

Print out directions (e.g. from ArgoPrep or MathIsFun) to show students how to create solid figures, such as cubes, cylinders, or prisms. Allow students to engage in making the solid figures. After students have finished, have them explore the properties of the different solid figures they created. They can determine how many faces, edges, or vertices the figure has, for example.

As an extension, you could allow students to experiment with origami paper and try to make their own solid figures. They could then describe the attributes of the figures they created.

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Angle Exploration

You may choose to use this idea to introduce angles to students, or to reinforce concepts that have already been covered. Provide students with a piece of paper and have them fold it down the middle and make a crease. You can then have students open their paper to show different angles. Depending on the students' grade level, you may be more specific and ask them the show you a 150° angle, or you may simply ask them to show you an obtuse angle.


Parallel and Perpendicular Lines

After students have received some instruction on parallel and perpendicular lines, give them a piece of paper with a line drawn on it (you can label it line XY, if you wish). Ask them to see if they can fold the paper to create a line that it is either parallel or perpendicular to line XY. Again, depending on their grade level, you could have them prove that the line they created is parallel or perpendicular by using their protractors.

You can make this exercise easier or more challenging based on the starting line you provide for children. If you want to make it a little easier, make your line go straight up and down or across the paper. If you want to make it a little more challenging, make your line go diagonal on the paper.


Finding Area of Shapes

After students have learned how to find the area of rectangles and triangles, challenge them to apply that knowledge to find the area of a shape such as a parallelogram or trapezoid. Provide them with a cut-out of the shape you wish them to work with. Ask them how they could find the area. You can lead a discussion and see if children come up with folding, or you can offer the suggestion. Students can fold their shape to section off a larger rectangular section and smaller triangular sections. Then, they can find the area of each piece and add them together to determine the total area of the shape.


Attribute Match

In this activity, students will be paired with a partner (or a small group). First, each student should fold a few pieces of origami paper to create different two-dimensional shapes. Encourage students to make a few folds to create something unique with various types of angles or visible sections.

Then, students should place all of the shapes in the middle of them and their partners. Each student should pick one of the shapes, and write a description of what they see. Again, the level of their writing will be dependent on their grade level. But you should share that you want students to use the vocabulary they've been learning in class. They might write about the different angles they see, the different types of lines, the different shapes that are formed because of the folds, and so on.

After students have completed their descriptions, they should switch cards with their partner. Then, they will have to figure out which shape their partner was describing based on what they wrote.

*Note: This activity will work better with two-toned paper to allow students to more easily see the folds and lines created.


Diameter of a Circle

Give each student a cut-out circle. Ask them to fold it in half. Discuss how the fold they just made is the diameter. Ask them to fold it in half again (a different way). You can discuss how the point where the two folds meet is the center of the circle. You can then have students fold the circle in half in many different ways to lead a discussion of how a circle's diameter always passes through its center. You could even ask students to show a non-example of a diameter (such as folding just the top portion of the circle, but not far enough to pass through the center).


Fractions and Partitioning

Provide students with a rectangular piece of paper. You can tell them that it represents a pizza or pan of brownies, and that their job is to determine how to equally partition it into fourths (or sixths, or eighths, or whatever else matches your instructional goals). Allow them to explore and see how they can use paper folding to make sure that they create equal shares. You will likely need to have spare paper on hand for students who will need to start over after making a fold that doesn't work.


Lines of Symmetry

Provide students with a variety of paper shapes and objects that have been cut out. Encourage them to find the line of symmetry for each shape by folding. They should then trace their fold to draw the line of symmetry. Challenge students to find all of the lines of symmetry for a given image.


Make My Shape

On the board, write attributes of a shape you are thinking of. The vocabulary used in your description should match your students grade level objectives. You may include information including the types of lines or angles found on your shape, how many corners or sides it has, and so on. Give students a piece of paper and challenge them to fold it to create your shape. You can play another round of the game and pick a student to visualize a shape and share the attributes of the shape they see for others to discover.

As you can see, there are so many different ways to incorporate paper folding into the math classroom. Students will be engaged, learning through doing, and will be able to make lasting connections and learn important math vocabulary words. Hopefully, reading through our ideas has given you some ideas you can implement with your students. Or, perhaps, we have inspired you to design your own creating lessons using paper folding.

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