Re: Checking simplified algebraic expressions (the -3 test)

On May 3, 5:57 pm, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
> wrote:
> I tutor a lot of algebra and as you know there are three basic types
> of problems that algebra students are given. The ones that say
> "Solve", "Factor" and the ones that say "Simplify".
>
> Solve you check by plugging the answers back in.
>
> Factor you check by multiplying things back together.
>
> Simplify... Well neither my students nor I were ever taught a reliable
> and simple check for simplified expressions. Example "Simplify (x^2
> -1) / (x+1)" this becomes "x-1".
>
> The best check I have thought of I call the -3 check. You plug in the
> number -3 into the unsimplfied expression and the simplified
> expression and see if you get the same answer. This technique is not
> perfect. Sometime you will get the same answer even if the expressions
> are not equivalent such as -3x and x^2 and the test blows up for
> expressions like 1/(x+3). Still these problems come up seldomly.
>
> -3 is the smallest and easiest to use number that rarely gives a false
> check.
>
> 0 fails in multiplication x=2x
> 1 fails in exponentiation x=x^2
> 2 has some weird properties x+x = x*x = x^x
> 3 has a problem with abs(x) = x and some other minor ones
>
> -3 distinguishes all the above situations and is easier to computer
> than larger numbers.
>
> So, I want to get your opinion on this test and ask if you can think
> of anything better. I encourage my students to review their
> calculations but many times they will make the same mistake more than
> once if they don't know that their answer is wrong. Remember, in
> general I am teaching this to 8th and 9th graders. They are not very
> sophisticated or abtract thinkers yet and thier ability to keep track
> of multiple things is quite limited.

Larry says the right answer is 17. -3, hmmm.