GeoGebra is an interactive mathematics software for learning and teaching mathematics and science from primary school up to university level. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions.
All of them can be changed dynamically afterwards.
Teachers and students can use GeoGebra to make conjectures and to understand how to prove geometric theorems.
Its creator, Markus Hohenwarter, started the project in 2001 at the University of Salzburg.
GeoGebra is available on multiple platforms with its desktop applications for Windows, Mac OS and Linux, with its tablet apps for Android, iPad and Windows, and with its web application based on HTML5 technology.
OFFICIAL WEB: https://www.geogebra.org
SESSION 1:
Download the software, install and "play" freely !!
1. DOWNLOAD :
OPTION 1 https://www.geogebra.org/download
OPTION 2
2. INSTALLATION : click the software you have downloaded and follow the instructions.
3. Open the software and start creating objects.
SESSION 2:
You can start learning how to use the program by following the tutorials and the manual included in the following link :
https://wiki.geogebra.org/en/Main_Page
1. Practise the " Basic Parallelogram Construction example "
2. Practise the " Regular Hexagon"
SESSION 3:
1. Practise the " Circumcircle of a Triangle Construction example "
2. Save the file and upload it into the active "pou".
3. Practise the " Basic Parallelepiped Construction example "
SESSION 4:
There are lots of examples in Youtube.
Watch the video and do the same.
SESSION 5:
a) Introduce the following functions: y=x / y=2x / y=5x / y= 10x / y=-x / y=-5x
The number before x is called slope (pendent). Which effect does the slope do??
b) Introduce the following functions: y=2x / y=2x+1 / y=2x+5 / y= 2x+20 / y=2x-5
The number after x is called y-intercept (ordenada a l'orígen). Which is its effect?
c) Introduce lines through the following points: (0,5) / (2,4) / (-2,4) / (5,12) / (-4,-8) /(-4,6)
d) Introduce the following functions: y=x^2 / y=x^2+3 / y=x^2-8 / y=-x^2 / y=-x^2-5
What conclusion do you come to with this quadratic functions ?
SESSION 6: TRIANGLE CENTERS / EULER LINE
CENTERS OF A TRIANGLE:
The CENTROID (BARICENTRE) of a triangle is the common intersection of the three medians (MITJANES).
A median of a triangle is the segment from a vertex to the midpoint of the opposite side.
The ORTHOCENTER (ORTOCENTRE) of a triangle is the common intersection of the three altitudes (ALTURES).
An altitude is a perpendicular segment from a vertex to the opposite side.
The CIRCUMCENTER (CIRCUMCENTRE) of a triangle is the point in the plane equidistant from the three vertices of the triangle. It is the common intersection ot the three perpendicular bisectors (MEDIATRIUS).
A perpendicular bisector is the perpendicular segment that passes through the midpoint of a side.
Also, it is the center of the CIRCUMCIRCLE(the circumscribed circle)(CIRCUMFERÈNCIA CIRCUMSCRITA) of the triangle.
Also, it is the center of the CIRCUMCIRCLE(the circumscribed circle)(CIRCUMFERÈNCIA CIRCUMSCRITA) of the triangle.
The INCENTER (INCENTRE) of a triangle is the point on the interior of the triangle that is equidistant from the three sides, so it is the common intersection ot the three bisectors (BISECTRIUS).
A bisector is a segment that divides an angle in two equal halves.
Also, it is the center of the INCIRCLE(the inscribed circle)/(CIRCUMFERÈNCIA INSCRITA) of the triangle.
SESSION 7: 3d-graphics / area and volume calculation
1. Create a polygon. For example a triangle.
2. Activate the 3d-graphics window (view menu).
3. Extrude to prism by selecting the polygon in the 3d-graphics window. For example 4 units in altitude.
4. Rename the triangle as A and the prism as B.
5. You can calculate the area and the volume of your objects by using the tools in the main tool palette. But the labels you get are very close to the objects.
6. If you want to improve this labels, you can calculate the area and the volume in the input box.
Area[ <Polygon> ] Change Polygon by A
Volume[ <Solid> ] Change Solid by B
And then you can drag and leave them in the place you want in the 2d and 3d windows.
7. You can also create a text using the values you have calculated or the objects you have created.
8. Create a prism and show its area and volume in different ways.
Send the file to the platform.
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