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 foldablesone for each method, a minibook for each
method and a twosided practice page for each method. Detailed answer
keys for practice pages and both minibooks 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 minibook foldable for each method. For information on
how to fold a minibook, 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 minibook page (minibook with answers included). 

Assembled mini book. 

2sided practice page (detailed answer key included). 

All materials described above are available for the 'tree method' as well. 


This is the best idea about integer factorization, written here is to let more people know and participate.
ReplyDeleteA 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^2N=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.
My G+ :https://plus.google.com/u/0/108286853661218386235/posts
My BLOG:http://hi.baidu.com/s_wanfu/item/00cd4d3c5a2fd089f5e4ad0a
Email:wanfu.sun@gmail.com
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I'm interested in looking into the birthday cake method!
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