GB+GeoGebra+Tutorials

**Mathematics and Multimedia GeoGebra Step-by-Step Tutorial Series ** The objective of the GeoGebra Step-by-Step Tutorial Series is not only to teach the readers how to use the software, but also to suggest how to use GeoGebra in teaching and learning mathematics. Most of the tutorials are (or will be) linked to related articles containing explanations and proofs about the mathematics discussed in the tutorials. Although, it is advisable to follow the tutorial series chronologically, the reader may opt for any tutorial of choice since each tutorial is designed to be independent from each other. The readers may start from any tutorial, and follow it step-by-step even without learning the tutorials prior to it. Unlike other blogs, all the tutorials in Mathematics and Multimedia, as well as all the articles, are constantly updated and modified for further improvement. This series is not yet complete, its arrangement maybe changed from time to time, but rest assured that more tutorials will be posted. **What's New**
 * The GeoGebra 4.0 Sneak Peek Series. A series about GeoGebra 4.0, the new version of GeoGebra which will be released in August.
 * GeoGebra Applet Central. A blog for GeoGebra applets. It's an open blog. Everyone is invited to upload their applets there. Just email me at mathandmultimedia@gmail.com if you are interested.

**Note:. **Click here to find more GeoGebra resources. **A. FOR BEGINNERS ** **I. GeoGebra Essentials Tutorial Series ** **II. Basic Geometric Figures Constructions ** **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B. FOR BEGINNERS/INTERMEDIATE USERS ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">I. GeoGebra Intermediate Tutorial Series ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to inscribe a polygon in a circle, increase its number of sides, and see the relationship between the area of the circle and the area of the polygon as the number of sides increases. This strategy was done by mathematicians in ancient time to approximate the area of a circle. || <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This tutorial is a continuation of GeoGebra Tutorial 14. In this tutorial, we are going to compare the areas of the circle, its inscribed polygon which we constructed in Tutorial 14 and its circumscribed polygon. || <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to construct point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // on a function, and construct a line tangent to the function and passing through //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A //. We are also going to plot a point whose //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //-coordinate is is the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //-coordinate of point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // and the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //-coordinate is the slope of the tangent line. We are going to get the derivative of the function and relate it to the path of the second point. || <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">We will manually create the endpoints and the arrows. || <span style="color: #008000; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C. FOR ADVANCED USERS ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Advanced Tutorial Series ** <span style="color: #008000; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">D. MISCELLANY
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-0.png?w=202&h=178 height="178"]] || **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[|Introduction to GeoGebra] **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This is the introduction to GeoGra. It contains discussions of the different parts of GeoGebra and the advantages in using it. It also points you out to the system installation requirements and the website where you can download it. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-1.png?w=209&h=160 height="160"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 1 – Locating the Triangle’s Centroid **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This tutorial, we are going to create a triangle and find its centroid or the intersection of its medians. In doing the tutorial, we are going to learn how to use the following tools: use the new point tool, segment between two points tool, midpoint tool, intersect tool and move tool. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-2.png?w=219&h=167 height="167"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 2 – Constructing a Rectangle **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to create a rectangle using the segment tools, the parallel and perpendicular line tools. We are going to learn how to measure the length of segments and angles. In doing the tutorial, we are also going to discuss semi-free objects. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-3.png?w=228&h=185 height="185"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 3 – Triangles, Incircles and CircumCircles **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to show that in any triangle, we can always create a circle passing through its three vertices, and we can always create a circle inscribed in it. The circle that passes through the three vertices of a triangle is called the circumcircle of the triangle, while the circle that inscribed in it is called its incircle. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-4.png?w=223&h=167 height="167"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 4 –Angles, Lengths and Object Properties **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use GeoGebra to investigate if a relationship exists between the interior angles of a triangle and the lengths of its sides. We are going to learn two new tools – the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Angle // and the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Distance or Length //tool. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-5.png?w=222&h=164 height="164"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGEbra Essentials 5 – The Compass Tool and the SSS Congruence **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will mimic compass and straightedge construction using GeoGebra’s compass, and segment between two points and ray through two points tool. We will use the concept of the SSS congruence; that is, we will show that if the three corresponding sides of a triangle are congruent, then the triangles are congruent. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-6.png?w=237&h=153 height="153" link="http://math4allages.files.wordpress.com/2010/04/essentialslist-6.png"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 6 –Sliders and Rhombuses **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will construct a rhombus using two sliders – the angle slider and the number slider. The slider the slider tool. A slider (see figure below) is a dynamic graphical representation of a number. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-7.png?w=255&h=160 height="160"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 7– Using the Keyboard Commands **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this post, we are going to learn how to construct mathematical objects using keyboard commands. We will learn how to In particular, we are going to create an equilateral triangle. ||
 * < [[image:http://math4allages.files.wordpress.com/2011/03/geogebraessentials8-1.png?w=259&h=314&h=169 height="169"]] ||< <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 8 – Graphs and their Properties <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to learn the basics about graphing and how to use GeoGebra command to get the critical points and the derivative of functions. We will also learn how to graph trigonometric, exponential, and logarithmic functions. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/essentialslist-9.png?w=278&h=205 height="205" link="http://math4allages.files.wordpress.com/2010/04/essentialslist-9.png"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Essentials 9 – Texts and Variables **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to learn how to use the text tool of GeoGebra. We will learn about constants and variables and will learn how to concatenate them in Geogebra codes. ||
 * <  ||< GeoGebra Tutorial 10 – Exporting Your Document ||
 * 1) <span style="list-style-position: inside; margin-bottom: 0px; margin-bottom: 0px; margin-left: 0px; margin-left: 0px; margin-right: 0px; margin-right: 0px; margin-top: 0px; margin-top: 0px; padding-bottom: 0px; padding-bottom: 10px; padding-left: 0px; padding-left: 20px; padding-right: 0px; padding-right: 0px; padding-top: 0px; padding-top: 0px;">Introduction to Basic Construction: Construction versus Drawing
 * 2) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 1 – Constructing an Equilateral Triangle
 * 3) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 2 – Constructing an Isosceles Triangle
 * 4) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 3 – Constructing a Right Triangle
 * 5) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 4 – Constructing a Square
 * 6) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 5 – Constructing a Rectangle
 * 7) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 6 - Constructing a Parallelogram
 * 8) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Basic Construction 7 – Constructing a Rhombus
 * 9) <span style="list-style-position: inside; margin-bottom: 0px; margin-bottom: 0px; margin-left: 0px; margin-left: 0px; margin-right: 0px; margin-right: 0px; margin-top: 0px; margin-top: 0px; padding-bottom: 0px; padding-bottom: 10px; padding-left: 0px; padding-left: 20px; padding-right: 0px; padding-right: 0px; padding-top: 0px; padding-top: 0px;">GeoGebra Basic Construction 8 – Constructing a Trapezoid
 * 10) <span style="list-style-position: inside; margin-bottom: 0px; margin-bottom: 0px; margin-left: 0px; margin-left: 0px; margin-right: 0px; margin-right: 0px; margin-top: 0px; margin-top: 0px; padding-bottom: 0px; padding-bottom: 10px; padding-left: 0px; padding-left: 20px; padding-right: 0px; padding-right: 0px; padding-top: 0px; padding-top: 0px;">GeoGebra Basic Construction 9 – Constructing a Kite
 * < [[image:http://math4allages.files.wordpress.com/2010/04/01quadrilateral1.png?w=195&h=185 height="185" align="center"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Tutorial 1 **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;"> – **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Midpoints and Quadrilaterals  **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use GeoGebra to investigate the properties of the polygon formed by connecting consecutive midpoints of sides of a quadrilateral. The tools that we will use in this construction are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">midpoint or center //, and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon, distance tool and angle tool //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/02-equilateral.png?w=211&h=143 height="143"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 2 – Constructing an Equilateral Triangle ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will mimic //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">compass and straightedge // construction by using radii of two congruent circles to construct an equilateral triangle. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">center through point ** //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/03-square1.png?w=167&h=173 height="173" align="center"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Tutorial 3 – Constructing a Square ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This construction is similar to Tutorial 2, mimicking the compass and straightedge construction. In this construction, we will use a circle and perpendicular and parallel lines to construct a square. The tools that we will use in this tutorial are//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with center through point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //,**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line // ** and **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">parallel line // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/04-graphs2.png?w=278&h=207 height="207"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Tutorial 4 – Graphs and Sliders ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we learn how to use the input box to graph linear functions. We will use the sliders to show the effects of the values of //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">m // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">b // to the graph of the function //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y = m x + b //. In this tutorial, you will learn the advantages of GeoGebra over others. The tool use in this tutorial is the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/05-pythagorean.png?w=221&h=168 height="168"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Tutorial 5 – Discovering the Pythorean Theorem ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will investigate the relationship among the area of the squares formed by the three sides of a right triangle. The tool that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">segment between two points //, and**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">regular polygon // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/06-parameterization1.png?w=257&h=208 height="208"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 6 – Parameterization of Area and Length of a Rectangle ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will learn how to write equations, formulas and perform computations in GeoGebra. We will construct a rectangle with a fixed perimeter and a variable length. We will graph the ordered pair (length,area) of a rectangle with a fixed perimeter in the xy-plane and find the dimensions with the maximum area. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">perpendicular line //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">parallel line //, and//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/07-rotation.png?w=184&h=207 height="207"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 7 – Sliders, Rotation and the Angle Sum Theorem ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the slider tool and rotation to replicate triangles, rotate them and show that the angle sum of a triangle is 180 degrees. The tools that we will use in this tutorial are **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">line through two points // **,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> midpoint or center //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">polygon //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider //, and **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">rotate object around a point by angle // **. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/08-tracing1.png?w=279&h=170 height="170"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 8 – Tracing Graphs of Trigonometric Functions ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will trace paths of points formed by coordinates of the distance **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">d // **traveled by a point along the circumference of a circle. We will graph (d,x) and (d,y) where //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y // are the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //-coordinates of the points . The tools that we will use in this construction are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new point //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circle with center through point //, and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">circular // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">arc with center through two points //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/09-translation.png?w=245&h=176 height="176" align="center"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[|GeoGebra Tutorial 9– Vector and Translation] **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the vector tool to translate a triangle. We will explore the relationship among the coordinates of the pre-image of an object, the object of its image, and the direction and magnitude of the vector. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> polygon //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> vector between two points //, //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">translate object by vector //. ||
 * < <span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[[image:http://math4allages.files.wordpress.com/2010/04/10-trigofunctions.png?w=278&h=165 height="165" link="http://math4allages.files.wordpress.com/2010/04/10-trigofunctions.png"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra ****<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Tutorial 10 – Vectors and Tessellation ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the strategy that we have learned in the Vector and Translation tutorial to tile a plane with regular octagons and squares. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">new ////<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">point //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> polygon //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> vector between two points //,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">translate object by vector //and//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> regular polygon //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/11-trigofunctions3.png?w=289&h=196 height="196"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 11 – Sliders and Graphs of Trigonometric Functions **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the slider to investigate the effects of the parameters//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">a, b, c // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">d // in the graph of the sine function//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;"> f(x) = a sin(bx -c) + d //. We will also explore the cosine and tangent functions of the same form. We will learn how to use check boxes to show and hide the graphs. The tools that we will use in this tutorial are //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider // and //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">check box // //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">to show/hide objects //. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/12-pictures1.png?w=200&h=152 height="152"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 12 – Pictures and Angle Measures ** <span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will learn how to insert text and picture in GeoGebra. We will use the protractor image to measure the angle formed by two segments. The tools that we will use in this tutorial are line through two points, segment between two points, angle, and semicircle through two points. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/13-latex.png?w=208&h=173 height="173"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 13– How to Use Latex in GeoGebra **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will learn how to embed Latex in GeoGebra worksheets. Latex is a typesetting program capable of constructing complicated mathematical formulas. It is widely used by mathematicians in creating scientific documents. It can also be embedded in websites and is integrated in many mathematics programs. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/14circle-area-approximation2.png?w=210&h=191 height="191"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 14 – Circle Area Approximation by Inscribed Polygons **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/15-circumscribe.png?w=202&h=158 height="158"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 15 – Tangents, Circles and Circumscribed Polygons **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/16-sliderssequence.png?w=208&h=85 height="85"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 16 – Slider, Sequence and Segment Division **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to learn how to use the slider control and the sequence command to divide a segment with an arbitrary length into n equal partitions. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra18-11.png?w=210&h=210 height="210"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 17 -Tangent and the Meaning of Derivative **
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra181.png?w=240&h=186 height="186"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 18 – Area Under a Curve and the Riemann Sums **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to compare the area of a plane under a curve f(x) = x<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 bounded by the x-axis and the line x =1 with the sum of the areas of rectangular partitions under the same boundaries. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra192.png?w=214&h=159 height="159"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 19 – Introduction to Spreadsheet **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Record to Spreadsheet tool // to record the coordinates of a moving point along the graph of a particular function. We will graph the function f(x) = x<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2, construct point **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">P // ** with coordinates//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">(a,f(a)) // , where //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">a // is a value from a slider. We will record the coordinates of the traces of **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">P // ** . ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra201.png?w=220&h=162 height="162"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 20 –Spreadsheet, Slider and Curves of Best Fit **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will use the spreadsheet window to input coordinates of points that will be plotted in the coordinate plane. We will use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Best Fit Line // tool to construct a line of best fit of the plotted points. Finally, we will also use the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Fitpoly // command and the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">slider // tool to construct polynomial (with varying degrees) curves of best fit. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra211.png?w=217&h=183 height="183"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 21 – Spreadsheet and Similarity **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we will construct a constant number //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k //, in the form of a slider, and see what happens if we multiply the coordinates (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ), (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ) and (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ) of the vertices of our triangle by //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">k. //We will investigate if there is a relationship between the original triangle and the triangle formed whose vertices have coordinates (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">1 ), (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">2 ) and (//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">kx //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ,//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ky //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">3 ). ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra22.png?w=225&h=139 height="139" align="center"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 22 – Spreadsheet, Vectors, and Matrices **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to explore the relationship between the product of two 2 x 2 matrices. We will set the entries of the factor matrices to integers, and limit the second matrix entries to values of -1, 0, and 1. We will also observe the relationship between their graphical interpretations, known as vectors. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra23.png?w=213&h=151 height="151"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 23– Spreadsheet, Bar Chart and Histogram **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to use the spreadsheet to perform basic data representation. We will plot a frequency table of grouped data and perform basic computations using the spreadsheet window. After the data is completed, we will construct a histogram. ||
 * <  ||< **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Tutorial 24– Box and Whiskers ** ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra251.png?w=215&h=157 height="157"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 25– The Rolling Circle **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to use GeoGebra in constructing a rolling circle. This way, we would be able to relate the diameter of the circle to its circumference. Moreover, this activity will reinforce the relationship between the angle and radian measure. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra26.png?w=212&h=143 height="143"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 26– Constructing a Cycloid **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">This tutorial is very similar to the Tutorial 25. In this tutorial, we are going to use GeoGebra to construct a cycloid.A cycloid is the curve defined by the path of a point on the edge of circular wheel as the wheel rolls along a straight line. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra27.png?w=200&h=171 height="171"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 27– Animation and Epicycloids **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to rotate a circle about the center of another circle tangent to it using the animation feature of GeoGebra. Along the rotating circle, we will also rotate a point on its circumference about its center (see red point in the diagram). The path of this point is called the epicycloid. ||
 * <  ||< **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">GeoGebra Tutorial 28– Animation and Hypocycloids ** ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra291.png?w=201&h=156 height="156"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 29– Animation, Loci and Radian Measure **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to introduce the concept of radian. We are going to rotate radius //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">AB’ //about point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A, // the center of the circle. As the point rotates, point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C // goes back and forth from //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">A // to //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B’ //at the same speed as that of //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C //. The path of point //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">C //traces forms petals. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra303.png?w=158&h=174 height="174"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 30 – Loci, Roses and Reflections **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to reflect a point on a circle about the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">x // -axis and about the //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">y // -axis to form rectangle **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ABCD // **. We will construct a segment passing through point**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B // ** where one of the endpoints on the center and with length equal to the area of a circle. As we move the point **<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B // ** along the the circle, the trace of the end point of the segment (not on the circle’s center) will form a 4-petal rose. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/geogebra301.png?w=208&h=189 height="189"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 31 – Paper Folding Simulation **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to use GeoGebra to simulate paper folding. We will represent a rectangular piece of paper with corners //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">ABCD ** // and drag the upper right corner (vertex //<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">**<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">B ** //) anywhere inside the rectangle. We will use the Point in region tool of GeoGebra 4.0 Beta Release (or New Point tool in 3.2) to construct the figure. ||
 * < [[image:http://math4allages.files.wordpress.com/2010/04/piecewise-i1.png?w=210&h=157 height="157"]] ||< **<span style="color: #2970a6; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial 32 – Graphing Piecewise Functions **<span style="margin-bottom: 10px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">In this tutorial, we are going to use the//<span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">function // command of GeoGebra to graph piecewise function[[image:http://s0.wp.com/latex.php?latex=f%28x%29+%3D+%5Cbegin%7Bcases%7D+1-x%2C+x+%5Cleq+1+%5C%5Cx%5E2%2C+x+%3E+1+%5Cend%7Bcases%7D&bg=ffffff&fg=000000&s=0 caption="f(x) = begin{cases} 1-x, x leq 1 x^2, x > 1 end{cases}"]].
 * 1) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 1 – Exporting a GeoGebra File to a Dynamic HTML
 * 2) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 2 – Embedding a GeoGebra Applet in Blogger/Blogspot
 * 3) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 3 – Embedding a GeoGebra in a Wiki
 * 4) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">[|GeoGebra Advanced Tutorial 4 – Constructing Customized Tools 1]
 * 5) <span style="list-style-position: inside; margin-bottom: 0px; margin-bottom: 0px; margin-left: 0px; margin-left: 0px; margin-right: 0px; margin-right: 0px; margin-top: 0px; margin-top: 0px; padding-bottom: 0px; padding-bottom: 10px; padding-left: 0px; padding-left: 20px; padding-right: 0px; padding-right: 0px; padding-top: 0px; padding-top: 0px;">GeoGebra Advanced Tutorial 5 - Constructing Customized Tools 2
 * 6) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 6 – Customizing the GeoGebra Toolbar
 * 7) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 7 – Embedding Form Controls and Javascript
 * 8) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Advanced Tutorial 8 – Random Numbers and Condition to Show
 * 1) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial: Graphs and Sliders Part 2
 * 2) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Tutorial: Graphing Functions using GeoGebra
 * 3) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Can we graph Inequalities in GeoGebra?
 * 4) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">New GeoGebra Tutorials
 * 5) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Video Tutorial 1 – Constructing an Equilateral Triangle
 * 6) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">GeoGebra Video Tutorial 2 – Constructing a Square
 * 7) <span style="color: #2970a6; list-style-position: inside; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px; text-decoration: none;">Introduction to GeoGebra Prim Beta