Factoring Positive 3rd Degree Polynomials

Factoring 3rd degree polynomials can be intimidating not to mention frustrating if all you have to go by is some rules in a textbook, but when you can see it it's EASY. This student is autistic and we just made a game of it once we had done a few examples and were familiar with the names of the pieces. Refer to the concepts page and use the 3 period lesson to make sure we know the names of the symbols and and what the symbols represent. The use of color markers helps but isn't necessary.

"Whoa! That's big," she exclaimed upon seeing the symbols.

Just count the sides and you're done.
"Well, that's EASY!" She laughs and writes it down. We do a few not pictured here and then she has a chance to make one up of her own. Of course she makes a big one:

The picture and the symbols are fast and easy to write. Much faster than drawing it, which is the point.

Now we make a trickier one with some square x²'s...

But of course that easy too because she can SEE it. Factoring polynomials is a snap, and kind of fun and builds the child's math confidence and self esteem.

Then we start making a game of it. I draw a picture give her the symbols and she has to make a drawing that matches mine. We have fun and a few laffs as she tries to figure it out...in no time she gets the hang of it. "My mind is warmed up now." I made some for her so it's only fair that she gets to make some for me.  This helps her with mastery and makes the game more fun.

So she reads me her drawing next:

I start out like this because of all the clues in the terms.

Factoring polynomials: pretty easy once you are used to it and have had some practice. One hour does not a pro make. Also it gets more complicated when the terms get negative, so lets get comfortable with the basic concepts and stay positive. Children under 5 can also do this! All we do is count.

Then the rest just falls together. A better explanation is given in the screencast below, because for some of you it can't be this easy so you need more than just pictures.

Then we move on to a little problem solving with hero zero and no fun get back to one...

Then a few problems with fractions which she says are harder and not as much fun as the algebra!!!

After a few problems she remembers what to do and why we have to make them SAME kind before we can add them. Again it's just rectangles and counting.

And there it is done.

Here is the screencast:


Here is a much better explanation of factoring by grouping on YouTube. The one on the sccreencast is verbal only and lame...the YouTube vid is an actual lesson with a 15 year old cheerleader who is freaking out because of all the symbols...

Find me on Facebook and be sure to dig around at the house of math and on this blog for more. There is and will be a lot more on this on the Advanced Algebra Page which is password protected; how to do negative expressions for example is well covered as are many other topics.. Passwords now cost 3 bucks for a month, and 12 for a year pass. And soon they will cost more than that.