Factoring a > 1......is there really any easy way to teach this??? I rank it with long division....a necessary topic to teach in Algebra 2, but no real easy way to teach it. :)
In previous years, I taught the guess and check method. That is the same way I was taught in high school and it works. But teaching it is so painful. Some students get it right away....others never get it. In the past, once I taught factor by grouping, I would go back and reteach factoring a > 1 using factor by grouping and would seem to get a few more students factoring this way.
This year I decided to try something different and I taught my students the box method using a factor T. I gave this graphic organizer to them to get them started. I provided a link to dropbox below if you would like to download it for free.
In this method students multiply the "a" and "c" parts of the trinomial,
find the factors, and look for the pair that makes the "b". Then they
place the terms in the box, using this design:
They then find the GCF of each row/column and voila....they have two binomials! It is easy enough to do and most of the students understood it. I picked this method because it works every time but as I didn't teach the guess and check method first, my students did not appreciate the efficiency of this method. It also makes finding a prime trinomial easier as well.
Here is an example I wrote out....I tried to write it out in steps but I did not write out explanations...on a student paper you would only need a box and a factor T.
My reflection: Next time I will teach guess and check first as it is still the method I prefer first and then teach the box method as an alternate. I'm also not sold on whether it is better than teaching to factor using the grouping method. Which way do you prefer?
Get the file HERE for the factor box.