Geoboard is a very basic app that simulates stretching bands around pegs. In the app, you can choose from two board sizes, depending on how complex your shapes will be.
Shapes can be created using one of the 8 band colours, which are simply dragged onto the board to the desired peg. You can also fill a completed shape with colour so that it’s easier to see and understand.
One of the big problems with Geoboard is the inability to save your board. This means you have to resort to saving a screenshot (power button and home button pressed simultaneously), but even then you can only view it — not edit it later.
If you do save your progress as a screenshot, you could take things further by importing it into another app. You could then add extra information such as annotations to help explain things further.
In addition to the free iPad app, you can also find a free web browser version on the Math Learning Center website.