Thursday, November 05, 2009

Algebra Algebra Algebra

Phew! That's what seems to be consuming my thoughts these days. I like teaching it for the 2nd year, and also I like that I know what's coming up on the horizon in the higher level math classes for the kids, so I can know what skills to focus on. For example, we just covered solving proportions, and I had some problems with the variable in the denominator. Well. The kids learned from 8th grade that you can just change the equation by taking the reciprocal of both sides and then solve.

So 12/5 = 7/x becomes 5/12 = x/7.

This is all well and good, and sometimes that's the simplest way to solve, but what if in algebra 2 or above you come across:

3x/(x+1) = (3x-2)/x.

Then "flipping" does not get you any closer to the answer.

Oh. Then someone mentioned "cross multiplying". Well, I didn't even want to go there because of all the misuse of that I've seen later on: OH! magically any time I see 2 fractions together involving variables whether or not there's an equal sign, I'm going to cross multiply without knowing why it works or even IF it works. Voila!

Anyway .... tons of algebra fun. I did have a discussion with my coworker, and she had this brilliant idea that I tried with solving absolute value equations ... but it can work with solving any equation. Write down the equation. On top of it, write numbers in circles in the order of operation of what would be done to x if you were to plug in a number. Then on the side I listed PEMDAS and the circled numbers in order and wrote in words what that was:
1. multiply by 3
2. subtract 4
3. take absolute value
4. add 10

Then under that sidebar, I wrote "to solve: undo in backwards order SADMEP"
4. subtract 10
3. 2 cases
2. add 4
1. divide by 3

Then the kids had a road map of what to do, and they didn't do weird things like get rid of stuff inside the absolute value symbols before taking care of them.

2 comments:

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  2. Anonymous12:16 AM

    Here I was doing a typical search for my calc class, and I came upon your blog. Over an hour later (after laughing, nodding, reading entries to my husband(also a teacher)), I'm finally leaving a comment...something I have never done. Don't even know if you'll get this, but I just wanted to let you that you have been cracking me up. I have been teaching for the past 13 years as well...it's just so refreshing to read anecdotes from someone who thinks much like I do...can't wait to share this with my friends!
    Love this post because I feel the SAME way about the use of "cross multiplying"...it's like blasphemy in my algebra class. I love what your coworker suggested and I have have been doing this with my students since starting at my new school 3 years ago. In fact, I first saw it introduced in the text we are using, Discovering Algebra...they call it the "undo table" which is taught after reviewing the order of operations. It's a great method for the students to figure out why they are solving an equation in a certain order.

    Thanks for providing all the ideas and resources...definitely adding your blog to my bookmarks...I admire that you take the time to reflect on your day and are willing to share it!

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