This program was inspired by the No Matter What Shape Your Fractions are In site developed by Cynthia Lanius and was developed specifically to complement it. At the end of this page there are links to her pages with exercises that can be worked on and solved using this program.
The shapes are the standard pattern blocks used in many classrooms today and they are:
This program can be used to familiarize oneself with the different shapes, their relations, and their proportions. By rotating them, one can also get a good feel for their symmetry. But the real purpose behind the program is to use it as a tool to learn and practice fractions.
Let's illustrate this with an example. Lets assume that the hexagon represents a whole or one unit. In that case, a triangle represents one sixth (or 1/6), so it is very easy to show graphically that 3 * (1/6) = 1/2 (i.e. that three triangles occupy the same space as half a hexagon). You can do this by dragging out three triangles and one hexagon and laying down the triangles right next to the hexagon or even on top of it as the following figures show:
Of course, you can make any shape or combination of shapes represent one unit; even more, you can have any combination of shapes represent any number of units. The possibilities would be endless.
A more challenging example would be the following. Lets assume in this case that a hexagon and a rhombus together represent 1 and 1/3 units. You could ask, what does one rhombus represent? What does a triangle represent? What does the hexagon represent?
The ability to do many of these exercises in a visual or graphical context is very helpful, especially for young minds, to get a good sense of the shapes, their proportions and the mathematics behind them. The use of tools like this to solve a variety of problems will make the person mathematically stronger in his or her: