Using the Box (Area) Method to Create Coherence and Connections

Anna Hester

Saturday 4:00-4:30

The box method builds on the area model and creates coherence between operations.

Check out @gfletchy's multiplication video for background

Move from one arbitrary method (FOIL) to methods that connect and build (area model, box method).

Factoring Progression

GCF --> Difference of 2 Squares -->; Trinomials

Thanks for this blog it's perfect. I love this method now that I have seen it explained. I always thought it took too much time but I'm starting to see somethings that take more time might make for a deeper conceptual understanding. Nice to see all the different ways you can use it all in one blog post.

ReplyDeleteI love how it makes things seem coherent. I was also thinking about using color to introduce the strategy- like color the terms in the problem and in the diagonals to show what the like terms should add up to.

DeleteI used this for the first time this year, and absolutely loved it. One thing I figured out along the way is that when factoring trinomials and trying to figure out what two terms need to go in the middle two boxes, the cross products should be the same. So in the picture above, the product of the two empty boxes needs to be the same as the product of three x squared and 8 and then just have the sum of the middle term. I know that sounds simple but it took me forever to realize it. And my students had an easier time remembering to make the cross products the same. Plus checking the cross products was an easy way to determine if four terms could be factored by grouping. Sorry to be redundant if you already knew that, but I was weeks into the boxes before I figured out that small detail and it was very helpful.

ReplyDeleteI should clarify that I found the cross product detail more helpful than saying "Multiply the first and third coefficents. Then find two numbers who have that same product and make those same two numbers have the sum of the middle term."

DeleteIf you see at the top where I drew a line connecting the 3 and 8 and then drew an X under it- that's how I teach factoring trinomials. "X-factor": multiple the first and third on top, the middle term on bottom, and then find the left and right sides of the x which multiply to 24 and add to -10.

DeleteYep! That's how I used to do it. :) My kids always spent more time trying to remember what went where in the X than understanding the whole process. Figuring out the cross products in the boxes helped me eliminate that step. We just did it mentally. Kind of like...hey we have four boxes and three terms. How are we going to split up the middle term so that the cross products are the same?

DeleteIn either case, I hope you love the boxes as much as I do! Happy Factoring!