Factoring trinomials with a leading coefficient >1

I don't know why this has turned out to be so difficult this year for the kids to understand.  I have been teaching this for 15 years and it seems that there was always a way to get them to grasp the concept.  First of all , they have seen it in algebra 1, 2 years ago.  I have tried the old trial and error dry erase sheets that I posted on afa earlier.  I have tried the logical approach to the understanding of the FOIL frontwards and backwards.  I have tried the box method that seems to be the new fad these days.  Every method I go through with them causes them to just shut down and refuse to do it.  All I hear is that it is too difficult and they just don't want to put in the effort to understand it.  If I had a dollar for every complaint about it I would be rich.  I remember back in the 90's we used to put it into a factor by grouping problem to solve these type.


In our district we have come to the conclusion over the years that the trial and error method was the best for the kids to go with.  We developed dry erase sheets for this.  They have been very effective over the years.  This year the kids just don't want to put in the effort to do this method.  They want the easy answer method and there just isn't one. (Instant gratification, the new reality)


I have tied it to solving equations to give them a basis for factoring.  I just keep running into massive dissension.  What I am interested in is what are other schools doing with this concept?  Are you running into the same problems?  What method are you using?  Is there a good video out there that might be more entertaining than me or what?  I am really seeing the lack of work ethic coming out on this activity. 


I would really like to hear some feedback on this one.  It is really driving me up the wall.

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Comment by Jerome Krakowiak on January 21, 2011 at 10:36am
Is factoring a quadratic polynomial with a lead coefficient of 1 different than factoring a quadratic polynomial with a lead coefficient greater than 1?
Comment by Sean Karsten on January 15, 2011 at 3:34pm

Here is a link to a discussion we had about almost this very same issue on this site.


I now use the "Bottoms-Up" method and it works quite well for me, as long as I am able to refer back to it enough that students remember it.  They seem quite comfortable with dividing by 'a' at the end because they multiplied by it at the very beginning.  It hearkens back to basic algebra and solving equations.  I hope this helps.  Feel free to post any other questions you have.

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