Polynomial Division - Box Method

After finishing up polynomial long division and synthetic division I wanted to give this polynomial box division method a try.  I was intrigued by this method after I saw Sarah Hagan's post about it on her blog.  It wasn't a method I was familiar with, so I had to first spend some time figuring it out.  Love it!  I really thought this method would be so much easier than long division because it eliminates all the potential sign errors when subtracting in long division.

I was hoping to teach the method and practice one day, then do Sarah's box division activity on the second day.  Unfortunately we just didn't have that extra day for the activity, so we were just going to chug through it in one day.  The day before I spent quite a bit of time working through some problems myself as I didn't want to fumble over my words during the lesson and confuse the kids.  Some of them were already confused enough with all the factoring and division we had been doing.  Then sometime during the middle of the night I woke up thinking about the lesson and decided to change it up.  I decided I wasn't going to teach them this method at all, I was going to see if they could figure it out on their own.

So this is how it went...

When they walked into class I had two polynomial multiplication problems for their warm up and I asked them to do it with the box method.

When they were finished with these two problems I asked them to take the problem given and their answer and turn it into a division problem.  Then I asked them to look at an empty box and tell me where would did the divisor come from, the dividend, and the quotient for the division problem.  We diagrammed the empty box together on the white board.

After this I short discussion, I put up the following seven problems on the board and told them to use the box and see if they could figure out how to do the division problem with a box method.  That was it, all the direction I gave them.

I told them when they think they had the quotient figured out, they then needed it factor it and look for the solution in the scrambled answers in yellow.

After a few initial complaints about me not helping them, they all got busy thinking and discussing.  Talk turned to patterns and how to find each term and it was awesome!

By problem 7 they were all pros at using this method and when I polled them at the end of class on their preferred method for solving, almost all of my students thought this one was easier to figure out.  I guess we shall see on the test tomorrow.