What is Cassius's determination/motivation for assassinating Julius Caesar? In class, we are doing a Julius Caesar treason trial to determine...

Do not overlook one of the strongest and most insidious of motivators in human nature:  ENVY.  Caesar himself senses this dangerous quality of Cassius as he and Marc Antony and the "train" enter the streets of Rome:

Let me have men about me that are fat,/Sleek-headed men, and such as sleep a-nights,/Yond cassius has a lean and hungry look;/He thinks too much:  such men are dangerous....Ge us a great observer, and he looks/Quite through the deeds [sees through their motives]of men....Seldom he smiles, and smiles in such a sort/As if he mocked himself, and scorned his spirit/That could be moved to smile at anything./Such men as he be never at heart's ease/Whiles they behold a greater than themselves,/And therefore are they very dangerous. (I,ii,192-210)

That Cassius is envious of Caesar's power is evident in his words.  He speaks to Brutus of being ignored by him, showing his desire for attention and affection:

Brutus, I do observe you now of late;/I have not from your eyes that gentleness/And show of love as I was wont to have....(I,ii,32-34)

In what is known as "the seduction scene" of Brutus by Cassius, Cassius offers no concrete evidence of Caesar's tyranny or ambitions except for describing Caesar as a Colossus, but even in this description, the envious nature of Cassius is evidenced in such words as "we petty men."

Why, man, he doth bestride the narrow world/Like a Colossus, and we petty men/Walk under his huge legs and peep about/To find ourselves dishonorable graves (I,ii,135-137)

Cassius tells Brutus how he, who "was born free as Caesar" I,ii,97) had to save Caesar, who became weak, from drowning; yet, this same Caesar

Is now become a god, and Cassius is/A wretched creature, and must bend his body/If Caesar carelessly but nod on him. (I,ii,116-117)

In his envy of Caesar's power, Cassius manipulates his brother-in-law, "seduces" him by means of flattery and an appeal to Brutus's sense of honor and republican ideals because he knows that the Romans respect Brutus who will be more able to effect a change of power. In his famous remark to Brutus, he all but says "why not me?":

Men at some time are masters of their fates:/The fault, dear Brutus, is not in our stars,/But in ourselves, that we are underlings./Brutus (and me!) and Caesar: what should be in that "Caesar"? (I,ii,139-141)

(When you have Cassius in court, you could question him about his words:  Isn't it true, Cassius, that on ----you said, ----?  Did you not remark to Brutus that -------?  Make Brutus testify, too, if you can in order to have Brutus verify what Cassius has said.)