# Why Factor Polynomials?

A4A project of the combined team consisting of teachers from Gladstone and Mid Peninsula Schools.  Gladstone teachers - Beth Deacon, Deanna Liberty, Bruce Murray, Robin Schwartz, Jeannie Woelffer.  Ryan Lyle represented Mid Penisula.

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Could you explain a little more about the diamond and box method, especially with a not equal to1?
I do "box method" for FOIL and am interested in this. Thanks!
You probably would be best off if you contacted one of the following teachers directly - Robin Schwartz - rschwart@gladstone.k12.mi.us or Ryan Lyle - rlyle@dsisd.k12.mi.us.
Can you post up an answer key for this, I am interested in how this works. Thanks
I'll ask the authors - or you can contact them directly, Robin Schwartz - rschwart@gladstone.k12.mi.us or Ryan Lyle - rlyle@dsisd.k12.mi.us.
There is a really nice PowerPoint on this method at

http://taselm.fullerton.edu/cluster%20page/los%20amigos%20cluster/l....

I also have a a worksheet that explains it - shamelessly stolen from both this powerpoint, and from Gladstone teacher Beth Deacon via one of her students. I have attached it here - hope you find it helpful.
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This is great. It is a nice way to combine the x which I already use and algebra tiles
I think the problem a lot of us have (had) with understanding this is that the box and the "diamond" or "x" (by "x" I am not referring to the variable)are both part of the process... first you put the numbers in the "x" as described and then you use the numbers created there to fill in the "box" ... from there figure out what the factors have to be.

With algebra tiles, many of have conditioned ourselves to look at the factors to create the area of the box... still a lot of guessing and checking. The "x" part creates a road map for the area, which we use to find the factors... interesting... fun... thanks for sharing!
I recently came across something similar to this which included a 'bottoms up' method for factoring ax^2 + bx + c. It can be seen here http://coxmath.blogspot.com/2010/03/bottom-up.html.

Also, a graphic organizer for when students should use which factoring method can be seen here http://coxmath.blogspot.com/2010/03/identify-your-opponent.html

Thanks to David Cox for the good ideas.

I usually teach ax^2 + bx + c factoring using grouping, which works well the day we do it but seems hard for the kids to remember. I look forward to trying a few new things that hopefully have better sticking power.
WOW --this is really nice. Thank you ... great post.
Here is another blog post and worksheets scaffolding the many nuances of factoring. Enjoy.

http://www.ateacher.org/blog/?p=714

This lesson uses the diamond method to factor quadratics.  It has a nice document with a lot of good problems that are ready to use.  I have been experimenting with the diamond method after attending a workshop last year.  I have found that it provides structure that the students can always fall back on if they have difficulty factoring.  I try to give a variety of options for students to use when factoring and encourage them to look for shortcuts (we call it guess and check).  It also has some problems that connect factoring to algebra tiles. If you are getting ready to cover factoring in your algebra class I would recommend taking a look at this document.

This lesson has a lot of nice problems using the box and diamond method for factoring that ties it in with algebra tiles.  In my classes I use a modification of the box and diamond method and have had pretty good success in getting my students to learn how to factor and retain what they have learned.  This is a definate consideration if you are teaching a unit on factoring.