Today Aiden and I worked on the Midtopic Review from the textbook. We already completed the first few, but since he has spent a few days with MAP testing, we reviewed them together. We reviewed the vocab words: coefficient, variable, and constant. Then we discussed the WHYS and HOWS of combining like terms. We saw a word problem that sparked the discussion of the differences between 2(3x) and 2(3+x). Aiden understands the distributive property in that 2(3+x) is equivalent to 6+2x. However, we were grappling with the idea that 2(3x)=6x. Aiden is curious why the 2 isn't applied to the 3 AND the x. We replaced x with 2 and showed how the two would not be equal in that case. I explained that 2(3x) actually means twice 3x so 3x+3x, which would result in 6x also. We wrote it out how 2(3x)=2(x+x+x)=(x+x+x)+(x+x+x). In all cases we could see that there is 6 total x's. I showed him that if we applied that 2 to both the 3 AND the x, there would be too many 2's. It would result in double what we want. Aiden followed along understanding the explanations. However, he is trying to understand that when you multiply 2(3x), the 3 is already being multiplied to the x, so once you multiply the 2 to the 3, it's ALSO affecting the x. We are going to resume with this concept tomorrow. Once Aiden understands WHY 2(3x)=6x, he'll be able to do the computations without question. He's on his way!