Quick Graph: This full featured graphing calculator app is highly rated by visitors to the iTunes store. It allows you to plot 2D and 3D equations with ease, and up to three equations can be visualized simultaneously. You can pinch to zoom in on your graph, drag to move or rotate it, and shake to reset your view. There is also a library of the most commonly used equations. Finally, unlike some apps on this list, Quick Graph is not a free version of a paid app. Quick Graph is a free standalone app that has all the features you need without paying for any more. A must for advanced Math classes, and another easy pick for one of the top 10 iPod Touch apps for Math teachers.
Touch Calc: This useful scientific calculator app means that your iPod Touch can serve double duties in the classroom. It offers all the basic calculator functions like addition and subtraction, but also includes a scientific mode, a statistical mode, and a bit/integer mode. Colored keys are added to help you distinguish between the different functions, and preferences can be set for each mode. All in all, this is a powerful and useful free app to have.
TanZen Lite: Help your students foster a shape awareness with this neat tangram app. This is another award-winning game that students will love to take time out to play. Choose one of the 45 puzzles, and try to fit all seven shapes in the shaded area to complete the level. Puzzles range in difficulty from easy to hard, and a full tutorial is included for new users. Hints can be turned on or off, and an advanced mode is available for master puzzlers to try the same puzzles in a whole new light. Soothing zen music is played in the background to all puzzles, but that too can be turned off if needed.
Units: Sometimes you find free iPod Touch apps and games that just have a universal usefulness. Units is one such app. This handy utility is a unit of measurement converter. You can convert area, currency, energy, temperature, time, length, weight, speed, and pressure quickly and easily. Just choose the category you want, and input the data you want to convert. Simple, but effective.
Math Drills Lite: More drills, but these are drills with a difference. Solutions to the problems are revealed with a variety of on-screen manipulatives like number lines, the nine times tables on your fingers, or wooden blocks. There are also problems with missing operation signs, or greater than and less than signs, so it could be a useful way to introduce students to basic algebra problems. An on-screen graphic keeps track of the number of right and wrong answers.