Teaching resources
You may not be a teacher, but it helps if your software is pedagogic.
We usually consider maths as separate from our daily lives. This is despite the fact that most big decisions are made based on calculations – we just don’t notice. With this disconnect, mathematics education is of utmost importance. The packages in this collection are to teach mathematics in many ways, some more than others.
Geogebra is centred around education. As mentioned earlier, the manual runs in the client. With a plethora of resources on the website, you can start teaching very easily. If you are a professional, they have paid services also.
GNU Octave is more centred around getting results for problems. Many professors have written their thesis by finding insights with Octave. Exporting to LATEX and other formats is well supported, using the programming language included. With that said, several universities use Octave as the main software for teaching several disciplines.
Engauge Digitizer is not for teaching, but it is useful for finding data from graphs in pictures. Genius has, with the default install, a remarkable amount of known algorithms and mathematical proofs. They are available in the examples, and just running these will demonstrate the principles. You cannot easily add comments to the results or calculations. Since exporting is so well supported it does work well to create documents though. It also has its own programming language which is useful for students to learn from.
Inside the packages for Scilab are many demonstrations for the most diverse range of subjects. Integrating clarifying text to show your point is also well supported. You can add buttons and sliders using its programming language.