To factor a trinomial into its two factors, look at the coefficients of the three terms and take the following steps:
1) Determine the different factors of the third coefficient. Pay attention to whether the third coefficient is positive or negative. Remember that your factors could also be positive or negative.
2) Choose the two factors that add up to the middle coefficient.
3) Split the first term into its individual factors. For instance, if the first term is x2, put one x in the first binomial and the other x into the second.
4) Put one of the factors that was determined in step two into the first binomial and the second factor into the second binomial.
Paraphrasing these steps for factoring really helped me to streamline the process in my own mind. Since I have never taught factoring, I had not thought ever about how this process could be taught to middle school students. I hope that I now have a better handle on how to make factoring clearer.
Having my students complete an exercise like this could be useful for any process that I am teaching my students. I firmly believe that you never truly understand something until you can put it in your own words. I would probably have them do this exercise as closure at the end of class or as part of a review. Doing so would allow me to really know if the students understand the material for that day.
Andy,
Great point – anytime you can explain a concept you have a much better chance of internalizing it. Having students discuss and rephrase a process, skill, or concept means it is stored in a place that is more easily accessed.
Judy
Andy,
Putting this into my own words was very difficult. Your sentences are brief and to the point. I can follow your steps, but I think that is because I understand the process. Having your students put the steps in their own words would certainly solidify the concept for them. This would only be after many, many examples and concrete models, such as the area of a rectangle.
Tom