First things first. You can get the Geogebra Augmented Reality app from the App Store. It is free to download and use and the app allows you to take photos with your camera.
The picture to the left, I used two equations: z = sqrt(9-x^2-y^2) and z=-sqrt(9-x^2-y^2) which I got from the manual.
The manual, Augmented Reality: Ideas for Student Exploration, begins by having students input certain equations that form a circle, ellipse, parabola, and hyperbola so students can view them in 3D. I used the two equations they gave me to create two different shapes. The first is above and the second is to the right.
I like the way they've built some play time into the introduction so students can explore a bit while learning to use the app. In addition, there is a short video showing the same things.
The instructional manual begins with an exploration of conic sections before heading off to explore transformations in 3 dimensions which give students a different way of "seeing" the actual shape.
The activities have you create a surface of revolution by rotating the function around the x-axis before creating a surface of revolution using the y-axis. The final activity for this has the student creating a Gabriel horn and more on creating surface of revolutions.
Geogebra has included a section on AR Modeling tips and hints to help students create these awesome shapes. Some of the topics cover domain restrictions, duplicating objects, going from 2 D to 3D and several more. The final sections are filled with easy and harder challenges such as building a square prism with heart shaped cutouts. They provide hints and a silent video showing the completed object in more detail.
The second to last section shows AR demonstrations made by other people with attempts, final equations and questions for people to think about and answer. One of my favorites in this section is the replication of a Pringles potato chip in 3 dimensions. The video includes the equations used so students can do it themselves.
The final section is titled "Quick Illustrations" and goes over topics for teachers. I love this manual because it allows me to familiarize myself with the program before I let my students use it. I've found it helps if I can get them started or at least provide them with the material to get started.
Download it, give it a shot and have fun playing with it. Let me know what you think, I'd love to hear. Have a great day.
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