Happy 2013! So one of my new year's resolutions is to blog more so here I go!
Since today was the first day back, I had kids start class by writing new year's math resolutions which was a huge success. I was surprised at how honest they were about them!
Then I began my algebra unit with my classes. We talked about linear and nonlinear patterns and tomorrow we will be discussing simplifying expressions. My worksheet for this lesson is on my school computer, but I'm not going to have time to blog tomorrow night so I figured I would go ahead and write this tonight and I will add the and worksheet tomorrow :)
Last year, I found that my students really struggled with combining like terms. I couldn't get them to understand that x + x^2 couldn't be combined. So, I decided to reteach it and made it very concrete (some of the kids even complained that it was too kindergarten-y) but guess what...they had an epiphany and mastered combining like terms! This year, I decided to just start out with the revised lesson so here it is:
I started out by giving the students a worksheet that had the following expression on it:
2 cows + 3 pigs + 1 dog + 1 cow + 2 dogs + 5 cats + 1 pig
I asked the students to simplify the expression and they came up with 3 cows + 4 pigs + 3 dogs + 5 cats. I asked them why we couldn't combine anything further, and they told me that you can't combine dogs and cats; they are 2 different animals.
Then I did something they all loved. We did the same problem in Spanish. I speak Spanish and my kids find that very interesting, so I decided to take the opportunity to teach them a few words. They came to the conclusion that they changing the language didn't change the outcome. You still can't combine "perros" (dogs) and "gatos" (cats).
Once they seemed to be ok with words, I switched to colored squares. They then had to make expressions with the colored squares (1 yellow + 2 pink + 4 orange + 1 pink + 1 yellow + 1 pink + 2 green + 2 yellow). Once they laid all the squares out on their desk, they were instructed to simplify the expression by combining the like terms. Students came to the conclusion that the like terms in this example were the colors. They, very easily, came to the conclusion that the simplified expression was 4 yellow + 4 pink + 4 orange + 2 green. I asked them why we couldn't just say the simplified expression was 14 colored squares. They all were like "duh..because they aren't the same colors...you can't combine the pink with the green!"
Finally, we made the jump to variables. And here was the cool part (that I still remember to this day) one of my kids said the following "Wow, I know what we can do! Each variable, even ones with different exponents can be a different color! And that's why we can't combine them!" "Now I get why you made us go back to kindergarten! It's so easy!" While yes, eventually I will teach them WHY you can't combine x + x^2 mathematically so that they don't get to high school and college saying well they can't be combined because they are different colors and have people look at them like they are insane, but for the time being this lesson worked for my kids. Really well.
I think this year I am going to add a game to this lesson. I will have kids get into groups and will give them dice with variables written on them (y, 2x, 3y^2, etc.) One student will roll the dice and write down all terms. They will roll again and write down all of those terms. The other student will do the exact same process. Then they will simplify their expressions by adding the two rolls together. The first person to simplify their expression correctly gets a point. The first person to 5 points wins.
Again I will add the worksheet once I get to school tomorrow and will talk about how the lesson goes, but in the mean time, does anyone have any cool ideas for simplifying expressions??
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