In my training, I was shown how to do the geometrical form of multiplication (see math album 1 on albums page.) A couple of months ago I had some students who were struggling with division using the Stamp Game. They were not struggling because they didn’t understand it. They just didn’t like using the materials – they thought it slowed them down. Yet, they were unable to do long division purely in the abstract. If these were 2nd graders, I would have simply insisted that they continue with the stamp game. However, these are students brand new to the Montessori setting in 4th grade. So I worked through the Stamp Game with them making sure they understood each step, querying them at the right moments. Once I was sure they understood the logic behind it, I introduced them to the Geometrical Form of Long Division. Maybe this is already out there, but I have not seen it. I created the following lesson using graph paper, green, blue, & red pencils.
For, if it is true to say that in essence the tragic hero is intent upon claiming his whole due as a personality, and if this struggle must be total and without reservation, then it automatically demonstrates the indestructible will of man to achieve his humanity. The possibility of victory must be there in tragedy. Where pathos rules, where pathos is finally derived, a character has fought a battle he could not possibly have won. The pathetic is achieved when the protagonist is, by virtue of his witlessness, his insensitivity or the very air he gives off, incapable of grappling with a much superior force. Pathos truly is the mode for the pessimist. But tragedy requires a nicer balance between what is possible and what is impossible. And it is curious, although edifying, that the plays we revere, century after century, are the tragedies. In them, and in them alone, lies the belief--optimistic, if you will, in the perfectibility of man. It is time, I think, that we who are without kings, took up this bright thread of our history and followed it to the only place it can possible lead in our time--the heart and spirit of the average man.