# 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.

• #### Angles on a Straight Line

Visual proof that angles on a straight line add to 180 degrees. Note that you can push "stop" at the bottom left of the screen and manually change the angle with the slider. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 9
• #### Vertical Angles

This GeoGebra applet shows the properties of vertically opposite angles. There are two lines and the angles are give. The lines can be moved from any point and students observe what happens to the angles. A visual demonstration such as this is easier, quicker and more interesting for students than a static picture on the board. Year / Level: Year 9

This applet has a grid and a line with two points on it. It is designed to make it easier for a teacher to teach the concept of a gradient. There is a skier on the line, and positive and negative gradients can be linked to the skier going up or down the hill. The gradient of the line, rise and run, can be shown or hidden on demand. This feature helps students consolidate their learning with the applet, after the initial lesson. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 9+

This applet extends the work covered in the Gradient Starter file. The skier is now on hills, allowing the teacher to encourage students to observe positive, negative and zero gradients in relation to curve. It can be used with Year 10 and Year 11 students, but it is also very good for introducing differentiation at Year 12 or 13. This applet requires the user to move the sliders, not the actual point. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Sketching a Gradient Function

One of the requirements of the NCEA Level 2 Calculus paper is to be able to determine what is happening to the gradient of a graph. It can also be relevant to distance - time graphs and what is happening to the velocity at various points or even to the acceleration. The GeoGebra applet illustrates graphs and their gradients. Year / Level: Year 12+

This applet is an example of a distance v time graph where the gradient of the line represents the speed. There are 3 lines, with different gradients. I have included this one in the list because the axis have different units, and once you know what Geogebra can do, finding out how to do it is easy. When you teach with this applet make the point that the gradient calculation requires looking at the values on the x and y axis, not just counting squares. It should therefore follow as a teaching tool after the other gradient applets. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 10+
• #### Linear Graphs

This applet shows the line in the form y = mx + c with m and c being able to be changed by the sliders. There is a point on the line which can be moved and traced to the spreadsheet view. The key teaching idea is to see the connection between the line, equation and table of points. The line can be hidden and the point moved and traced to see that the line is made up of lots of points. Note: It is important that the user understands to refresh views to get rid of unwanted trace. The refresh view button is on the top left of the graph window. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 9+
• #### Linear Line Test

A quick 10 question Graphs Test where students write down the equation of the graphs shown. This is easy to change and create more tests instantly. A slider is used to show one graph at a time. There is then an option to show all the answers. This applet was supplied by Priscilla Allan, Pakuranga College. Year / Level: Year 11
• #### Simultaneous (Linear) Equations

This GeoGebra applet shows two lines on a set of axes. You can change the gradient and y intercept and y intercept. You can have the equation written as y = mx + c or in the form ax + by + c = 0. The sliders allow you to change the a, b and c variables.
• #### Simultaneous Equations 1

This GeoGebra applet was designed to help students studying for the NCEA Level 1 CAT (Common Assessment Task). The sliders allow you to change up to 4 of the variables. With each of the options the answer and working can be shown. Year / Level: Year 10+