This nine year old can already count, so all I'm doing is giving him new stuff to count. That stuff has names, like "x to the third" and "x squared" and "x", you can also teach kids who are just learning the names of numbers these too: it's just more vocabulary. Mostly I find that the teachers themselves are the ones who have a bias against counting "x to the thirds" due to their own ill experiences with math, but really, to little kids it's just counting.
Little kids actually enjoy algebra because it's like learning with puzzles...the teacher can add more or less meaning as needed, depending on age and skill level.
This little snippet may look impressive but if you watch the whole thing which is on the "advanced" algebra page you can see it was easy and fun and it was a natural progression. The child even made up the problem himself.
It will be a while before we move into negative expressions and we still have to play around quite a bit before we start setting these equal to zero and solving them and then move on to graphing them. One step at a time.
Also for homework you could take that last problem we did and draw it so that one side is x2 + 2x + 1 and the other is 3x + 2. You'll get the same thing just in a different shaped rectangle. There's often more than one way to factor third and fourth degree problems.
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