## Thursday, November 15, 2012

### Two Methods to Teach Prime Factorization

As we are all discovering, the new Common Core Standards for Math stress the importance of teaching students a variety of strategies for a particular skill.  It is then up to the student to choose which strategy they feel most comfortable using.

I have used two different strategies to teach prime factorization in my classroom.  The ‘tree method’ works from the top down and focuses on factors.  The ‘birthday cake method’ works from the bottom up and focuses on division.

The tree method is most widely taught and used.  It is the way you and your parents will be most familiar with.   I have found, however, that the ‘birthday cake method’, while not as widely used, seems to be the method my students prefer and have the most success with.

We, the teacher, have a choice to make.  Do we choose to teach just one and not the other?  Which one?  Or, do we introduce our students to both?  Each teacher needs to decide what is best for the students in their classroom.  Regardless of what you decide, I have created a packet that will provide you with the necessary resources.

Included in this packet are two matchbook foldables--one for each method, a minibook for each method and a two-sided practice page for each method.  Detailed answer keys for practice pages and both mini-books are included as well.

 Birthday Cake Method Resources

 Birthday Cake Method Matchbook Foldable (cover).
 Birthday Cake Method Matchbook Foldable (inside).
 Birthday Cake Method Matchbook Foldable (assembled & folded).

There is also a mini-book foldable for each method.  For information on how to fold a mini-book, I would highly recommend viewing the following video.  Unfortunately, I can not adequately show the process with pictures so viewing the video is very necessary.

 Unassembled mini-book page (mini-book with answers included).
 Assembled mini book.
 2-sided practice page (detailed answer key included).
 All materials described above are available for the 'tree method' as well.
This product is available at my TpT Store and my Teacher's Notebook Shop.  Happy Factoring :)

1. This is the best idea about integer factorization, written here is to let more people know and participate.
A New Way of the integer factorization
1+2+3+4+……+k=Ny,(k<N/2),"k" and "y" are unknown integer,"N" is known Large integer.
True gold fears fire, you can test 1+2+3+...+k=Ny(k<N/2).
How do I know "k" and "y"?
"P" is a factor of "N",GCD(k,N)=P.

Two Special Presentation:
N=5287
1+2+3+...k=Ny
Using the dichotomy
1+2+3+...k=Nrm
"r" are parameter(1;1.25;1.5;1.75;2;2.25;2.5;2.75;3;3.25;3.5;3.75)
"m" is Square
(K^2+k)/(2*4)=5287*1.75 k=271.5629(Error)
(K^2+k)/(2*16)=5287*1.75 k=543.6252(Error)
(K^2+k)/(2*64)=5287*1.75 k=1087.7500(Error)
(K^2+k)/(2*256)=5287*1.75 k=2176(OK)
K=2176,y=448
GCD(2176,5287)=17
5287=17*311

N=13717421
1+2+3+...+k=13717421y
K=4689099,y=801450
GCD(4689099,13717421)=3803
13717421=3803*3607

The idea may be a more simple way faster than Fermat's factorization method(x^2-N=y^2)!
True gold fears fire, you can test 1+2+3+...+k=Ny(k<N/2).
More details of the process in my G+ and BLOG.

Email:wanfu.sun@gmail.com

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1. I have nominated you for the Liebster Award.
Hop over to my blog to see!
I'm interested in looking into the birthday cake method!

2. I am having issues sending you to the page! :-)