GCF and LCM

I don't know about you guys but I was always confused about which was which with the Greatest Common Factor and Least Common Multiple. My lead teacher showed me a trick to determine these. You factor out a number all three have as a factor. That goes on the left. The number underneath is what is left. You keep doing this until there are no more common factors. The GCF is found by multiplying the left hand numbers. The LCM is found by multiplying the GCF by the left over numbers. Voila! It is actually pretty cool. I taught it to the other teacher I worked with and she asked me to teach it to the class, she liked it so much.

Remedial Math Programs

I work with kids that do not even have basic math skills when they come to us at the beginning of the year. I mean, they can't add without counting on their fingers. Forget about multiplication. Do any of you have experience teaching these types of students? We use a computer-based program that is student specific and it seems to be working although I don't think there is alot of data yet. Let me know if you have any experience with these types of students. Any suggestions are welcome! Most of them hate math and think they are never going to get it. I think they just weren't given the skills needed.

Alternate Method for Teaching Factoring Polynomials and Multiplying Binomials

Back in the dark ages when I was learned how to factor and multiply binomials it was basically a trial and error method. I learned a new way to do this from my lead teacher. It is SO much easier. I wanted to share it with you and see what you think.
Example #1. You draw a box with 4 spaces in it. On the top you put one of the binomials, on the side the other. Multiply x times x and you put that in the first box. x times -4 goes in the upper right corner, etc. until all the boxes have something. Then you add the boxes. This method can be used for multiplying polynomials too. There are just more boxes, one for each term. You add like terms and come out with the answer.
Example #2. Factoring. First multiply the coefficient a and c (in this example a=2, c=-12). Draw an x. The top of the x has this total, the bottom of the x has the coefficient b. Then find the factors of the top number (in this case -24) that add to the bottom number (5). Draw the box, place the first number in the upper left box, the last number in the lower right box and the two other numbers in either of the boxes left. Then factor out what you can going across and down to get the two factors. Let me know what you think!