Patty Paper - It’s Good For More Than Hamburgers

When I first heard about patty paper, I had no idea what it was (I obviously don’t make my own hamburgers), let alone what it had to do with mathematics. Tracing paper, transparencies, patty paper… they can all be used similarly to help students visualize key geometric ideas. Now that I am acquainted with the multifaceted nature of patty paper, I don’t know how I would teach certain concepts without it! Here are a some examples of how patty paper can be used in the classroom:

Transformations.

For “spatially challenged” people like me (yes, I get lost at the mall), patty paper is invaluable for visualizing transformations - particularly rotations and reflections.  Here is how one teacher uses patty paper to demonstrate a rotation. What are some connections the students would be able to make using this visual model? How would you do it differently?

Constructions

Constructions are typically learned with a compass and straightedge. This is important work which helps develop an understanding of constructions and the geometric reasoning that accompanies them. Patty paper can be a nice compliment to the work with a compass, giving students another avenue to “see” the relationships between various figures and thereby solidifying the understanding they started with the compass and straightedge.

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http://www.cpalms.org/Public/PreviewResourceLesson/Preview/51159

Now that we've seen some of the uses of patty paper, two questions commonly arise - Are we allowed to use patty paper? Does using patty paper lower our expectations for students?

First - Yes, we are allowed to use patty paper. In fact, several standards even call for it:

• 8.G Understand congruence and similarity using physical models, transparencies, or geometry software
• G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
• G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another
• G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Second - A tool by itself cannot raise or lower our expectations. How we use the tool defines the cognitive demand of the task. Standard for Mathematical Practice 5 says: “Use Appropriate Tools Strategically.” Patty paper is a tool that, when used strategically, can give many students access to understanding and connections that the students otherwise may have missed. Additionally, students may combine patty paper with other tools and strategies to check their work and to validate their own learning.

How have you used patty paper in your classroom? If it is new to you, are you willing to give it a try?