TIC 2n ESO: de setembre 2025

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

CLICK HERE TO DOWNLOAD THE EULER LINE GEOGEBRA'S FILE

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.

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.

Scratch is an educational programming language and multimedia authoring tool that can be used by students, scholars, teachers, and parents for a range of educational and entertainment constructivist projects from math and science projects and others.

Simple games can be made with it. Playing with the existing projects available on the Scratch website, or modifying and testing any modification without saving it requires no online registration.

Version 3 of Scratch is currently available online and as a desktop software.

The first version of Scratch was developed in 2003 by the Lifelong Kindergarten group, led by Mitchel Resnick, at the MIT Media Lab.

WEB SCRATCH ( MIT) (http://scratch.mit.edu/)

SESSION 1

1. Watch the Introduction.

2. Download the Scratch 3 Offline Editor

3. Explore the Scratch web.

SESSION 2

1. Open Scratch Desktop

2. Listen to the explanation:
tutorial- "Comença" and tutorial-"Crea animacions que parlin"

3. Create...

4. Send to the school platform (pou session 2).

SESSION 3

In the scratch website you can search for lots of examples in order to improve your level and take ideas.

https://scratch.mit.edu/starter_projects/

1. Try and understand the next file Teens at the Castle.sb2 to produce a story with different backgrounds.

2. Listen to the explanation: tutorial- "Crea una història"

3. Create a story

4. Send to the school platform (pou session 3).

SESSION 4

Try to understand what the following program does:

Position:
X Horizontal position. From -240 (left) to 240 (right).
Y Vertical position. From -180 (down) to 180 (up).
Center point x=0 y=0

Direction:
0º Up
90ºRight
180º Down
270º Left

Complete the program. The cat must walk around all the edges.
Send the file to the platform (pou session 4).

SESSION 5

Today we've got three sprites:

We want the hippo catching the cat. When the cat is hunted, it turns to a ghost.

Look at the three sprites code:

Do you know to which sprites these codes belong to?

Try them. Improve the program. After this, send the file to the platform (pou session 5).

SESSION 6 : Variables and control structures.

A variable is like a "box" where you keep data like numbers to control the program and other important issues. When you control a program with a variable you have to initiate it, change it and control the last value.

Control structures help you to monitor the program's behaviour.
For example: if-then-else ; repeat-until, forever, ...

This is a example of a program controlled by a variable (a). It uses the controlling structure: repeat until.

After the teacher's explanation, try this program.

Improve it with another sprite. It must be controled by another variable (b). Use the if-then and forever structures instead of repeat-until.

Send the file to the platform (pou session 6).

SESSION 7

Watch the video and try to do the same game.

Work in groups of 2 or 3 people.

If you want to increase your mark, improve the game by adding music, and counting how many times you have touched the ground, ...
Send the file to the platform (pou session 7).

Hints: