# GeoGebra

GeoGebra is free and multi-platform dynamic mathematics software for learning and teaching. It has received several educational software awards in Europe and the USA.

• #### Ellipse

There are three points on the ellipse that can be moved and changed. Watch what happens to the ellipse and its properties. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 13
• #### Conics Test

This is a short test that contains ten graphs. They are made visible one at a time with the use of a slider. You can also show the answers. You can also change the equation of a graph by moving it or editing the equation, the answers will also change. It is designed as a consolidation activity to build speed of recognition of graphs and their equation. It has been used for Year 13 Calculus but could also be edited to be used in Year 12 circles or non-linear graphs. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Year Level: Year 13
• #### Expanding Boxes

Using area, this applet provides a visual proof of:
x² + (a + b)x + ab
= (x + a)(x + b)
= x(x + b) + a(x + b)
= b(x+a) + x(x+a)
The sliders change the values of x, a and b. There is an explaination that can be hidden. Setting b to zero allows the teacher to start with x(x + a) = x² + ax and develop the concept. This will work for teachers who already teach this way, the applet just makes it easier. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### 3D Box

This applet can be used to illustrate how to get the maximum volume open cuboid from a piece of paper. Watch what happens to the volume as the measurements change. This applet was supplied by Priscilla Allan, Pakuranga College.
• #### Transformations

This applet shows rotation, reflection, translation and enlargement. Just move the slider to see the different transformations. Each transformation is interactive, in that you can chance the angle of rotation, the mirror line position, the translation vector, the scale factor and centre of enlargement. You can also change the object and see the image change with it. If used in the classroom "right click - show axis" at some point and get students to draw on the white board the expected transformation prior to checking their answer with the chosen transformation. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 9
• #### The Juggling Clown

At the end of the year a good exercise is to creating some "Geo-Art" Try this after junior exams or even as a afternoon activity using creativity, problem solving and geometrical transformations. A lot of learning can take place even though the students are seemingly having fun creating art. This applet was supplied by Priscilla Allan, Pakuranga College.
• #### Silly Tangents

Another example of art that can be created by GeoGebra. Although it may seem to be a silly exercise to have students creating art the actual mathematics learning, awareness of geometry and graph awareness that takes place will surprise most teachers. One such exercise is to have students demonstrate their art to the class but then explain the mathematics that they have learnt. This applet was supplied by Priscilla Allan, Pakuranga College.