Mathematical Modeling: Desmos

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The following tutorial allows students to 3D print mathematical graphs using the free-online graphing calculator Desmos. Desmos can be found at https://www.desmos.com/calculator Desmos is a great learning tool because it is free to use and will work on any device that your students have access to. There is a even a iPAD app as well as a chrome extension for those students with Chrome Books. Note: Desmos works well for graphing and printing 2-Dimensional graphs, but for 3-Dimensional mathematical representations read through Henry Segermans paper titled 3D printing for mathematical visualisation which can be found at: http://www.ms.unimelb.edu.au/~segerman/papers/3d_printed_visualisation.pdf Standards NGSS CCSS Overview and Background 3D printing mathematical computations can allow students to visualize, manipulate and better understand the concepts they are learning. Not only can Desmos be used to 3D students computations, but students can be given design challenges to utilize their graphs for various purposes. A simple example of this would be for students learning how to graph circles with specific areas. Students can 3D print their circles that need to fit a certain number of predetermined objects within like jelly beans or skittles. Desmos can be used for the following classes. Pre-Algebra, Algebra 1 and 2, Trigonometry, Geometry, Pre-calculus, Calculus (AP), Statistics Lesson Plan and Activity Step 1) Create a design in Desmos: For Desmos Tutorials visit http://learn.desmos.com/ Step 2) Set up the image for taking a Screen-Shot Remove the background grid (unless you want the grid to be printed) by choosing the wrench in the upper right corner. Un-click the round grid, x-axis and y-axis. If you don’t remove these, they will get converted to part of the 3D design. (Image 1) -Choose "Projector Mode" which will make the graph lines thicker and easier for 3D printing. Step 3) Take a screen shot of just your graph using the commands for the type of computer you are using. You can find how to to do this on your computer by visiting https://www.take-a-screenshot.org/ (Image 2) Image 1 Image 2 Converting Screen Shot to 3D File To be able to 3D print the mathematical graphs you will need to change the screen shot images first into an .SVG file (Scalable Vector Graphic) Step 3) Go to http://picsvg.com/ . Here you will be able to upload your screen shot and convert it to an .SVG file all while being able to view the .SVG before downloading. This is a feature that other converting sites like http://image.online-convert.com/ don't have. (Image 3) Step 4) Once you have downloaded the .SVG file you can now import it into your CAD program of choice. The image below had the model imported into TinkerCAD where a student could not manipulate the model even further if desired. (Image 4) Step 5) Within the CAD program you choose students can add a back to their model, make it thicker, taller or whatever change is necessary for your lessons outcomes. Step 6) Once the students 3D model is finished all that remains is to save the file for 3D printing. This will most often be an .STL or .OBJ file format. (Image 5) Image 3 Image 4