We learned how to find the Greatest Common Factor [GCF(a,b)] of a given set of number and also the different methods we can use to find them. Maybe one of them will help you out. They are :
-Listing Factors
-Linear(Cuisinaire Rods)
-Prime Factorization
When listing factors it is easiest to use the curtain method to list out your factors. When using the curtain method you list the factors from outside to inside like shown below. It is highlighted in purple.
The next step you circle the like factors & identify the largest common factor.
Therefore the GCF(18,56)=2
The Linear also known as the Cuisenaire Method is where you use small block units that are called cars and create trains with them they are each different sizes and colors and each are assigned a number. 
When presented with a problem like find the GCF(5,10), you can take a orange(10) car and line it up with a yellow(5) car and continue lining them up side by side until they even out and in this case 2 yellow cars even out with 1 orange car .Prime Factorization is where we use the factors of a number to find the greatest common factor.
I find it easiest to draw out a factor tree first and find the factors that way.
I love the prime factorization tree method because i think it is the easiest. All you have to do is break the number down by factors until you cant break it down any further. It is a very simple method to teach and to learn and it clearly shows you the answer. Its quick and easy.
ReplyDeleteI really like that visual you found of the "curtains closing" method (the V shape keeps it more organized than listing the numbers in a line.) Maybe I'll try that next time. I do like using the factor tree method the best; it's a sure-fire way to break it down completely and then multiply the common factors of (a,b).
ReplyDeleteI think the "curtains closing" method is a perfect way to explain to children how to find all the factors of a number, and I also think it's very cool that you found a picture to clearly demonstrate the concept. Having the word "greatest" in GCF can definatley be confusing because you think the number would be the largest number, not the smallest. But understanding the idea behind what you're trying to accomplish is the goal for learning about both GCF and LCM.
ReplyDeleteThe GCF and LCM was just not clicking for me for some reason. Then I came across how it looked like it was set up like an equation:
ReplyDelete30=2*3*5
42=2*3* *7
2*3 =6
That's when it clicked for me. It just goes to show why we need more than one way to look at it.
I loved using the Cuisinaire Rod method! I am very familiar with closing the curtains method and prime factorization, which i also think is a very easy concept. Although I have never used the cuisinaire before! I enjoyed using them because it taught me a different way to find the GCF and LCM. I am a visual learner, and i like to do things hands on just like a lot of students do, so this is a great way understand how to find the GCF and LCM if the other two methods are not being understood by the student!!
ReplyDeleteGreat blog! The blog link was very helpful. Another thing that helped me was your pictures connected with your explanations.
ReplyDelete-Margaret
Amanda,
ReplyDeleteWow you have alot of information here.
Your models/graphics are great.
30= 2 * 3 * 5
42= 2 * 3 * 7
----------------
2 * 3 =6
GCF(30,42)=6
I had trouble with this concept but working with it and using models like yours made it easier.
Your mathcats.com link is a good one, there's a lot of good information and explainations tosimplify the learning process.