Archive for the ‘polynomial factoring’ Category

Rectangle with GCF

Students and I worked on factoring a trinomial that had a common factor.  Notice that the common factor need not come out of the product first as is often demonstrated.  In the top example, you see that the common factor means that there are two duplicate rectangles to be considered.  In the bottom left, we showed that there are at least two correct ways to factor correctly.  In the bottom right, we see a student who factored out the 2 at the start. 

three related

Two students and I used our skills to factor three polynomials using tiles and grids.  Notice that the rectangles are the same “shape” for all three. For more information and practice on the is method, see the video below.



In the last week before winter break, it is tempting to let the curriculum go a little, to kick back and enjoy my students without my mathematical lens. NOT! For me, there is much more pleasure in going deeper into curriculum. If there is something to let go of, it is the “schoolishness” of some math that we do.  In the video below, I was able to revel in one of my favorite topics: factoring polynomials.  This method, based on thinking of products as area and factors as dimensions, was taught to me by Dr. Tom Kieren, an exceptional scholar and educator.

I would like to see this kind of factoring in all our high school classrooms.  It demonstrates three features of a well chosen algorithm:  transparency, error resistance, and memorability.