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

On May 5, 12:42=A0pm, fflit...@[EMAIL PROTECTED]
 wrote:
> On May 3, 5:57 pm, "michalc...@[EMAIL PROTECTED]
" <michalc...@[EMAIL PROTECTED]
> wrote:
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> > 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.
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> > 0 fails in multiplication x=3D2x
> > 1 fails in exponentiation x=3Dx^2
> > 2 has some weird properties x+x =3D x*x =3D x^x
> > 3 has a problem with abs(x) =3D x and some other minor ones
>
> > -3 distinguishes all the above situations and is easier to computer
> > than larger numbers.
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> > 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.

I would have guessed 42.

> -3, hmmm.- Hide quoted text -
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