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.

Awesome! Thanks for the worksheets link!

ReplyDeleteThat sounds like a great teaching exercise.

ReplyDeleteOn a side note, I now refuse to teach FOIL because the students don't grasp when to use it and when not to, this continues to calculus. I simply teach distribution all the way and they are fine (never hearing the word FOIL).

I've always felt math literate, and I thought that analogies like the chocolage milk one you mention seem like a dangerous way to teach the concepts. If I actually have 2 parts milk and 6 parts chocolate, then 1 part milk and 3 parts chocolate would be a similar drink, right? Obviously, the math doesn't hold up.

ReplyDeleteI haven't taught math, so maybe I'm paranoid, but I seem to remember a lot of my student peers doing OK in math until the analogy or trick that all their success was based on was pulled farther than it could stretch. At that point, they are too far along to spend time learning the original concepts, and they just have to limp through the rest of their math career.

Again, I'm probably paranoid, and I bet brief use of examples like that just to get the ball rolling probably works very well.