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 others. 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.

GEOGEBRA STEP-BY-STEP TUTORIAL SERIES LIST OF POSTS

GeoGebra Tutorial Series (For Beginners and Intermediate Users) GeoGebra Tutorial 17 -Tangent and the Meaning of Derivative In this tutorial, we are going to construct point A on a function, and construct a line tangent to the function and passing through A. We are also going to plot a point whose x-coordinate is is the x-coordinate of point A and the 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.

GeoGebra Tutorial 1 Midpoints and Quadrilaterals

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 new point, segment between two points, midpoint or center, and polygon, distance tool and angle tool.

GeoGebra Tutorial 2 – Constructing an Equilateral Triangle

In this tutorial, we will mimic 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 new point, polygon, circle with center through point.

GeoGebra Tutorial 3 – Constructing a Square

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 new point, circle with center through point, segment between two points, perpendicular line and parallel line.

GeoGebra Tutorial 4 – Graphs and Sliders

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 m and b to the graph of the function y = m x + b. In this tutorial, you will learn the advantages of GeoGebra over others. The tool use in this tutorial is the slider.

GeoGebra Tutorial 5 – Discovering the Pythorean Theorem

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 perpendicular line, segment between two points, and regular polygon.

GeoGebra Tutorial 6 – Parameterization of Area and Length of a Rectangle

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 new point, perpendicular line, parallel line, and polygon.

GeoGebra Tutorial 7 – Sliders, Rotation and the Angle Sum Theorem

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 line through two points, midpoint or center, polygon, slider, and rotate object around a point by angle.

GeoGebra Tutorial 8 – Tracing Graphs of Trigonometric Functions

In this tutorial, we will trace paths of points formed by coordinates of the distance d traveled by a point along the circumference of a circle. We will graph (d,x) and (d,y) where x and y are the x and y-coordinates of the points . The tools that we will use in this construction are new point, circle with center through point, and circular arc with center through two points.

GeoGebra Tutorial 9– Vector and Translation

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 new point, polygon, vector between two points, translate object by vector.

GeoGebra Tutorial 10 – Vectors and Tessellation

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 new point, polygon, vector between two points, translate object by vector and regular polygon.

GeoGebra Tutorial 11 – Sliders and Graphs of Trigonometric Functions

In this tutorial, we will use the slider to investigate the effects of the parameters a, b, c and d in the graph of the sine function 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 slider and check box to show/hide objects.

GeoGebra Tutorial 12 – Pictures and Angle Measures

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.

GeoGebra Tutorial 13– How to Use Latex in GeoGebra

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.

GeoGebra Tutorial 14 – Circle Area Approximation by Inscribed Polygons

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.

GeoGebra torial 15 – Tangents, Circles and Circumscribed Polygons

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.

GeoGebra Tutorial 16 – Slider, Sequence and Segment Division

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.

GeoGebra Tutorial 17 -Tangent and the Meaning of Derivative

In this tutorial, we are going to construct point A on a function, and construct a line tangent to the function and passing through A. We are also going to plot a point whose x-coordinate is is the x-coordinate of point A and the 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.

Geogebra 17
GeoGebra Tutorial 18 – Area Under a Curve and the Riemann Sums

In this tutorial, we are going to compare the area of a plane under a curve f(x) = x2 bounded by the x-axis and the line x =1 with the sum of the areas of rectangular partitions under the same boundaries.

GeoGebra Tutorial 19 – Basic Spreadsheet Recording

Spreadsheet programs have the ability to perform mathematical computations using their cell addresses. Recently, GeoGebra integrated a spreadsheet in its graphical user interface, and that is what we are going to discuss in this tutorial.

Tutorial 20
Tutorial 20 – Spreadsheet , Slider and Curves of Best Fit
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 Best Fit Line tool to construct a line of best fit of the plotted points. Finally, we will also use the Fitpoly command and the slider tool to construct polynomial (with varying degrees) curves of best fit.
Tutorial 21
Tutorial 21 Spreadsheet and Similarity
In this tutorial, we will construct a constant number k, in the form of a slider, and see what happens if we multiply the coordinates (x1,y1), (x2,y2) and (x3,y3) of the vertices of our triangle by k. We will investigate if there is a relationship between the original triangle and the triangle formed whose vertices have coordinates (kx1,ky1), (kx2,ky2) and (kx3,ky3).
Tutorial 22
Tutorial 22 Spreadsheet, Matrices and Vectors
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.
Tutorial 23
Tutorial 23Spreadsheet and Histogram 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.


Tutorial 24– Box and Whiskers
Tutorial 25
Tutorial 25– The Rolling Circle

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.

Tutorial 26
Tutorial 26– Constructing a Cycloid

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.


Tutorial 27 – The Compass Tool and SSS Congruence

Tutorial 28 – Perpendicular Bisectors and the Circumcenters

Tutorial 29 – Angle Bisectors and Incircles
Tutorial 30
Tutorial 30 – Loci, Roses and Reflections

In this tutorial, we are going to reflect a point on a circle about the x -axis and about the y -axis to form rectangle ABCD . We will construct a segment passing through pointB where one of the endpoints on the center and with length equal to the area of a circle. As we move the point 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.

Tutorial 30
Tutorial 31 – Paper Folding Simulation

In this tutorial, we are going to use GeoGebra to simulate paper folding. We will represent a rectangular piece of paper with corners ABCD and drag the upper right corner (vertex 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.


Tutorial 32 – Perpendicular Bisectors and the Circumcenters

Tutorial 33 – Angle Bisectors and Incircles

Tutorial 34 – Treasure Hunt and Circle through Three Points




Last modified: Tuesday, 7 December 2010, 05:15 PM
Skip Navigation

Navigation