Doc ver. of the guide

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Activity Guide for GeoGebra 3D Calculator with AR (Surface
Area Project)
About the App:
-GeoGebra 3D Calculator is an app that allows users to create,
share, and test mathematical 3D models.
-It is compatible with the GeoGebra 3D Calculator (accessible on
PC, laptop, or any other device with internet access) available
online.
-However, the most powerful function available only on the app is
its augmented reality.
Getting Started

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Opening the App:
store phone’s home screen
Using the App
As a 3D model app, the GeoGebra 3D Calculator’s creative
potential is endless! While we will go on to make our own
models in future lessons, in this intro activity we will focus
on the following:
1. How to open pre-made projects
2. How to use AR
3. How to experiment with sliders and variables in the
algebra tool
The 3D calculator uses a hyperplane with three axes: the x-axis, y-axis, and z-axis
The project we will be using this time will help strengthen our understanding of surface area.

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How to Open a Pre-made Project

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If you have selected the correct project, the project will load, and your screen will now look like this:
Note: Each GeoGebra 3D project can be identified by two ways: the project title and the project code.
There are many pre-made projects with similar project titles, so while we are in class, the easiest way to
search for the project we want is by inputting the project code.
However, if you feel like exploring other projects in your free time, searching by project title (ex.
typing “Surface Area” into the search bar) can pull up lots of interesting projects!

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How to Use AR
Step 1: Click on the AR button
For the AR to work, the app
must use your front-view
camera, so if you forgot to give
the app media permissions
earlier, go ahead and click
“Allow” now.
Step 2: Detect a surface
The AR needs a floor to “place”
3D figure on. Point your camera
at the ground and walk around
slowly until you see the white
grid on the screen above. Then
tap the screen where you want
the figure to go.
Step 3: Explore the figure in AR
Now that you have placed the
figure, feel free to explore. Walk
around to see the prism’s six
surface faces, view it from the top,
and even try stepping “inside” to
see it from the interior!

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How to Experiment with Sliders and Variables in the Algebra Tool
Each project created in GeoGebra 3D can be built with any quantity of variables. This project has five
changeable variables that change how the rectangular prism model looks. To adjust these variables,
open the Algebra tool.
button
The screen will display only the first three variables, but there are many written into this project
(however, most are fixed and cannot be changed). Touch the variables screen and slide your finger up
or down to go further down or back up the list.

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“LENGTH”,“WIDTH”, and “HEIGHT” are all self-explanatory variables, as they change the dimensions of
the prism as well as the surface area in the process. To experiment with these,grab the grey-and-black dot in the
middle of the slider and move it to the left (to decrease the number) or right (to increase).
LENGTH dot WIDTH dot HEIGHT dot
As you may have noticed when you explored the rectangular prism earlier, this rectangular prism model is color-
coded, with each pair of opposite faces sharing the same color (pink and yellow sides with a white pair of bases).
The transparency of these colors can be adjusted using the “Filler” variable.

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Finally, the “e” variable unpacks surface area for us by transforming our 3D rectangular prism into a
2D net.
Scroll down the variables
screen until you reach e. At
e=0, the rectangular prism is
fully “closed” and still 3D.
Slide the grey-and-black dot to
the right.
When you slide the grey-and-
black dot anywhere between 0
and 1, the rectangular prism
begins to “open”, and you can
begin to see the net.
At e=1, the rectangular prism
has been fully “opened” into a
net. Each face is now flat on the
floor, making it easier to
visualize as “area”.

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Student Assignment
Play around with the variables in the app to answer the following questions.
1. What is the relationship between opposite faces (faces that share the same color)?
2. When you increase/decrease the length of the rectangular prism, which faces change?
By how much do they increase/decrease?
How can you relate this to width/height?
3. When you increase/decrease the width of the rectangular prism, which faces change?
By how much do they increase/decrease?
How can you relate this to length/height?
4. When you increase/decrease the height of the rectangular prism, which faces change?
By how much do they increase/decrease?
How can you relate this to length/width?

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Reflection on Using this AR App in the Classroom
I was pleased to discover this app because it works in conjunction with the GeoGebra site and the cell phone
technology that the students are already familiar with.
Its level and rigor are high enough for me to consider including it in a geometry lesson. In addition, the AR
component can grab students’ interest and help them visualize 3-dimensional math far better than the traditional
textbook, which is limited to 2-dimensional models.
I appreciate the “collaboration” aspect of the app where users can share the projects they’ve created with others,
especially since it helps new users by granting them access to projects they can explore and use while they build
up the skills necessary to create their own projects.