GeoGebra

In mathematics, one drag beats a hundred explanations. How the parabola changes as parameter a grows, why a triangle's three medians always meet at one point, what the derivative really has to do with the slope of a tangent — GeoGebra's answer is to let you drag the figure and watch the formula change with it. Understanding tends to arrive in that moment.

Its coverage is broader than most people expect: plane and analytic geometry, function plotting, calculus (derivatives, integrals, limits), probability and statistics, matrices, 3D solids, and a dedicated spreadsheet view. That spans most of secondary school through early undergraduate work.

Practical strengths: the desktop version is fully offline — install it, disconnect, and it keeps working, with no ads and no sign-up nagging. The web version opens instantly for a quick calculation or classroom projection. And the official materials library holds hundreds of thousands of interactive activities built by other people, searchable by keyword, which saves teachers a great deal of preparation time.

The licensing needs stating plainly, since it differs from most tools on this site: GeoGebra is free for students, teachers and personal non-commercial use, but it is not free software. Some components are open source; the product as a whole is not, and commercial use — embedding it in a paid course or a commercial product — requires a separate license. That is why it carries no open-source badge.

If you need a fully open alternative, look at Maxima, SageMath or similar. But for "usable immediately, broad coverage, materials already made", GeoGebra remains the most practical choice in this space.