On my broken record mode (you know, those things that music used to come out of and were bigger than 12" diameter?): I'm loving teaching algebra 1 this year since it's so fun to show them all the cool stuff they'll see over and over again - FOILing, lines, exponents, quadratics...
But it's also daily unsettling because I don't know what they'll find difficult or what will need extra practice or how the best way to explain something will be. Today I told them we were going to do "big kid math" (they were going to start the FOIL process without me saying FOIL just yet). To build up to it I needed to teach them like terms and adding like terms of expressions such as (5x^2)(y^3) or (3xy^7), etc.
I racked my brain (okay I just googled "wracked"/"racked" ....) for a way to present this since I was tired of worksheets and notes. I decided to fold up a white paper to have 20 squares (4x5) and opened it up and put various monomials in each making sure that there were sets of 2 to 3 like terms usually. Then I did it with another piece of paper making sure to put some sort of bubbly border on each square (on one paper only). Then I copied (from 1 to 2) the papers onto various pretty colored papers. The kids then chose their color and cut out the 20 pieces (yay, less work for me) and they had the 2 sets of 20 monomials.
I chose a side (border or no border) and randomly picked a card for the overhead, say (7x^2)(y^6), and told them to find it and cull it from the herd. Then they were to find like terms in their cards (without explaining what like terms were). I wanted to see what they knew. I saw various mistakes as I walked around the room, and it was interesting. So I went up front again and said, "this is like making chocolate milk. You have 2 parts milk and 6 parts chocolate (refering to the exponents). You want to find similar "drinks", and those are like terms". That seemed to work with everyone, and we practiced some more.
Then I had them find a set of like terms, say the cards were 3xy^2, -5xy^2, and 8xy^2. I asked them to add them up to see what they'd get. Instead of 6xy^2, a lot of students got 6xy^6. I was expecting the mistake of (6x^3)(y^6), but I guess the "silent 1 power makes it stay 1!".
Anyhow then we built up the skills for that: 3x + 5x, 10x^2 + 8x^2, etc. They still had the silent 1 problem: 3x+5x = 8x, but 10x^2 + 8x^2 = 18x^4. Then what seemed to work for most (all?) kids was the EXCELLENT box again. Think of the variable parts as boxes filled with x or x^2 or such, and how many boxes do you have and when you add them what happens.
All in all, I think it went well. I also want to share an excellent resource for algebra worksheets. It's been a godsend for extra practice problems all neatly laid out.