Education is crucial to society. Great opener eh? I'm making this post mostly for educators, but it can also work well for a computer at home to help the kids learn. I've tried these myself and had a first grade teacher and high school chemistry teacher look at them as well. These are all packages found in the Ubuntu and Debian repositories. There are a lot of high school packages, so I have my top picks in each lesson area. The package name is listed in parentheses next to the name. I've only tested this in Debian derivatives, but it could work in any distro capable of utilizing .deb packages.
Elementary School Applications
Childsplay - (childsplay) This is a well-intentioned suite of educational software, but with poor documentation and instructions. It's a translation from French, thus causing the English documentation to be lacking. Worth trying, the learning is done through game-like programs. For more games install the plugins (childsplay-plugins). These games are mainly meant for 4th grade and lower. It should work in KDE, Gnome, and XFCE.
Kanagram - (kanagram) This is an excellent anagram game, fun puzzles for all ages. I would recommend it for grades 3 and up, it's a bit much for first and second graders, since it requires a little larger vocabulary and pattern recognition skills. This would be good for older people as well to keep their mind sharp. It works in KDE or XFCE.
Ktouch - (ktouch) This is a typing tutor, and can actually be used for all ages, though I recommend it for kids, possibly even before school age, though hand size may be a factor. It has dynamically updated typing speeds and variable levels of difficulty. It's well written and I wish it had been around in 1988, I might be able to type correctly now. It will work in KDE or XFCE.
Kbruch - (kbruch) One of the things found to be a common problem among students is the ability to manipulate fractions. In Indiana they're taught in 3rd grade, so I recommend using this program for 3rd grade and above, though starting it earlier would be beneficial. This is a fraction teaching and practice program that allows you to manipulate fractions in various ways. It works in KDE and XFCE.
KGeography - (kgeography) A very good geography program with built in quizzing abilities. It has countries by continent and regions of countries as well. Worth a look for all grade levels actually. Works in KDE and XFCE.
Khangman - (khangman) A word game based on hangman, where you guess letters to get the word, and only 10 wrong guesses allowed. It has 4 difficulty settings. I would recommend it for grades 2 and up. Works in KDE and XFCE.
Linux Letters and Numbers - (lletters) A letter and number learning application, and very simple. I recommend it for Kindergarten and below. It should work in Gnome and XFCE, but I haven't tried it in KDE.
Little Wizard - (littlewizard) An insanely cool intro to programming and logic meant for Elementary kids. It uses drag and drop modules so all the work can be done without a keyboard. It takes a bit to learn and I recommend reading the documentation and specializing it to your students style of learning. I wish they had this when I was a kid, I started in BASIC in 1991, actually one of the first books I was reading. It works in Gnome and XFCE.
Gcompris - (gcompris) This is a suite for ages 2-10 meant to teach basic skills to kids. It's a nice unified environment, but I'm not a big fan. I recommend trying it out and seeing how it works for your needs. It works in Gnome or XFCE.
Gnome Chemistry Utils - (gcu-bin) This is a package containing a 3D modeler, a chemical calculator, and a digital periodic table. Works in Gnome and XFCE.
Kalzium - (kalzium) A KDE/XFCE periodic table chock full of pictures, atomic data, structures, spectra, and other information on each element. Works in KDE and XFCE.
GNU Solfege - (solfege) An ear training program meant to help musicians and such. For Gnome and XFCE.
Kayali - (kayali) Still in beta, but a good algebraic evaluator. Worth a look. For Gnome and XFCE.
Stellarium - (stellarium) An absolutely amazing program. Gives realistic sky views in real time, from any location on earth. Great for anyone. Somehow still in beta too. It's actually for Linux, Mac, and Windows.
Celestia - (celestia-glut) A universal space simulator that allows you to fly through space. Also allows plugins to add more abilities.
Oregano - (oregano) An electrical circuit designer. Takes a bit to learn, but lots of uses for upper level physics or pre-engineering. Works in Gnome and XFCE.
PCB Designer - (pcb) Ok, admittedly this may be a bit above high school level, but good for those interested in physics and electronics. It works in Gnome and XFCE.
Kverbos - (kverbos) A Spanish verb-learning program designed for KDE and XFCE.
Klettres - (klettres) An alphabet learning program for Czech, Danish, Dutch, English, French, Italian, and Slovak. Designed for KDE and XFCE.
KLatin - (klatin) A Latin learning and revision program for KDE and XFCE.
Kiten - (kiten) A Japanese learning and revision program similar to KLatin. Also for KDE and XFCE.
Keduca - (keduca) An exam writing and recording program designed for networks. Students take the teacher-made exams on the computer. In my opinion there are better FOSS options out there, but this is it in the repository. Works in KDE and XFCE.
For all these programs and more you can go through the Add/Remove utility in Ubuntu, and find even more options not mentioned here.