In our basic math class, we spend a fair amount of time at the beginning with the idea that the equals sign isn’t just that thing that comes before the answer. In the spirit of starting with a fairly simple abstraction, we use the analogy that a person can be called different names, but still be exactly the same person (no, we don’t get into the difference between equivalent and equals,
I’m seeing that concept or lack thereof is behind much of the confusion with simplifying radicals. When are we changing values, and when aren’t we? Hmmmm……
(And now back to my regularly scheduled endeavors — I’m combing through ALEKS so I can have my visual/concrete explanations at the ready next semester, for the folks in the modules who will need that [up ’til now, people in modules didn’t have to do ALEKS], creating more practice of the basic skills for the pre-pre-algebra folks for these final days of the semester, and trying to apply the same principles to my JAVA class and going for fluency in the basics.)
Resource Room Dot Net Blog 
Posted on November 18, 2013
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