X-box Factoring with Color

I tried using the area model this year for factoring GCFs and ax^2 + bx + c in addition to already using it for completing the square.

I felt like there were so many steps that color would be helpful in 'seeing' what we were doing.

I love using concept attainment when I can so I start with students noticing three things that all the 'yes' column problems have in common that the 'no' column problems don't.


From there, we went through an example and wrote down the steps in color {which of course took longer than it should have}. I did the rest of my examples in color and let them decide if they wanted to use color or not.

I was finding the gcf of each row and then dividing to find the top of each column. It took weeks until a student pointed out to me just find the gcf of the rows AND columns.

Overall, I haven't been a huge fan of the box method. I felt like students got mixed up with where to put the numbers and how to find the answers. They're never going to see an X and a box on any other math problems. If I don't put it there for them, they don't know to do it. 

I think I'm going back to my old method of slide divide bottoms up.

Factoring is the bane of my existence so in an attempt to be proactive, I'm going to do factoring Friday's with three problems per week for EVERY course, Algebra I and on up. Hopefully doing 3 problems a week for years in a row will finally give them a solid foundation for Algebra II.


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  1. I've taught the box method many years, so I'm really comfortable with it. One thing that I've found is that it makes more sense to them if I use the box for multiplying 2 binomials before we ever get to factoring. I tell them we're using the grid to organize our distributive property. I'd never heard of "slide, divide, bottoms up." It's very intriguing! I may try it! Thanks for your generosity in your blog. Very helpful to me as I'm going back into the classroom after 4 years in another position.

  2. I echo the above comment. I have been using the box method for two years now and I love it, but I use it for everything. Like above, I use it for multiplying polynomials of all sizes (rather than FOIL) so it makes for a natural transition to factoring. I also don't use the X thing any more. I just teach them to find the two numbers that will make the diagonal boxes have the same cross product while still having the correct sum. I was like you in that it took a student pointing out that we could find the GCF of the columns rather than dividing. ;) This method also makes for a nice transition to long division with boxes.

    Another tip that makes using the color go faster (because I do each step in a different color too) is that I write the step out and then we do that same step for EVERY SINGLE EXAMPLE while we have that pen/marker already out before we go on to the next step on any of them. Then we switch colors and we do that step in that new color on EVERY SINGLE EXAMPLE before going on to the next one. Less switching colors means less lost time.

    Don't give up on the box method yet!!!

    1. I also use the boxes to teach factoring by grouping BEFORE I teach factoring quadratics.

    2. I did the same thing you mentioned with one color at a time.

      I also used it for multiplying but that's what I mean by getting confused. Are we writing numbers inside and factoring or writing them outside and multiplying? They couldn't seem to remember the difference.

      I have not been won over.

    3. I admit that some of my students struggle with inside or outside, but to me it's more apparent what the logic/math is for the boxes than with the (super cool) "slide, divide, bottoms up" method. I'm still mulling all this over too...

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