Today we continued to review problems from the Chapter 4 -Generate Equivalent Expressions. We began by working on factoring. We worked with the expression 63y-42. Aiden was initially stuck on finding the GCF, but he had the great idea of writing out all of the factors of 63 and 42. By doing so, he noticed 21 was the largest factor they had in common. He factored to get 21(3y-2). I told Aiden that I didn't see the 21 as the GCF at first. My brain saw a "7" first. So I showed Aiden what would happen if that's what he saw first. We would get 7(9y-6). Then that should prompt us to see that 9 and 6 still have common factors, so the 7 that we factored out was actually NOT the Greatest common factor, it was a factor, just not the greatest. We practiced another problem that we could run into a similar situation with. 81x-54. Aiden saw that they both had 9 in commmon. He factored to get 9(9x-6). Then he saw that the 9 and 6 inside the parenthesis still had a common factor of 3. We discussed how to properly take out the 3. I showed Aiden that 9(9x-6)=9(3(3x-2)). Then by commutative property we could combine the 9 and 3 to get 27(3x-2). Next we reviewed what happens when the leading coefficient is negative. We considered the problem -12y-16. Aiden's initial factoring was 4(-3y-4). I explained to him how that is correct, I would never mark it wrong, but I will comment each time that it would be ideal to take out a negative leading coefficient. This is just a good habit to get into now, as when we see more advanced factoring types having the negative factored out will be easier to work with. This problem type led us to discuss the WHYS behind the rules of positives/negatives in multiplication/division. I am going to look up a good way to explain this to him for tomorrow.