Q&A #4383

Absolute Value

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From: Marielouise (for Teacher2Teacher Service)
Date: Aug 02, 2000 at 14:14:08
Subject: Re: Absolute Value

Hi, Eva,

Rather than try to "reinvent the wheel"  I think that you can find your
answer in an answer given to a similar question last October, 1999.

I hope that it gives you some good ideas.

From Claudia:

>Does anyone have any suggestions of ways to teach Absolute Value in new,
>fun, or exciting ways?  My kids just don't get it!!!

Yes, I use two number lines. One I call and color the zero finder and the
other is just the other.  Consider  |x-4| ...  3  (any math verb will do,
=,<,>, etc)   Define absolute value as the DISTANCE of a number FROM ZERO.

Now... students can usually handle that 3 in the example is the
distance. That means that (x-4) must have to do with the "from zero". Set (x-
4) = 0. Solve for x. You get 4.  I place the ZERO FINDER number line above
the other number line where 0 "lines up with" the 4.  Sort of like

                -4  -3  -2  -1  0   1   2   3   4
                 0   1   2   3  4   5   6   7   8

Now I can walk 3 units to the right (positive 3) and still claim to have
traveled 3 units. If I do this on the Zero Finder, the 3 lines up with the
7. I can walk 3 units to the left (negative 3) and still claim to have
traveled 3 units. If I do this on the Zero Finder, -3 lines up with the 1.
So my TWO Numbers are 1 and 7.

Next... =  means I travel exactly 3 so my answers are 1 or 7
         < means I travel less than 3, so I walk in BETWEEN 1 and 7 which
means  1 < x < 7
         >  means that I travel more than 3 in either direction so I go past
7 and "go past 1"; going past 1 means moving toward zero on the number line.
So my answer is  x<1 or x > 7.

This avoids the usual contrived nature of the or/and stuff.

You can model with students too.

Eventually, I move toward the following...  |x+2| > 6

      Where do I start ???    @ -2   (because x+2=0 @ x = -2)

       What is my distance??? 6   I move RIGHT 6 +6  and then LEFT 6 -6

                       -6 <------|-------> +6
                        -8               +4
       Greater than means Walk more than 6  so answer is x<-8 or x > 4

  Hope this is clear and helps! My students love it!

Another thing to do is get a car sticker!  They love cars!!!  Use the
info about gas mileage and start by having them write an inequality about
how far they can go on a tank of gas. The sticker usually puts the size of
the tank info.  Then work into...write this as an absolute value. What is
the meaning of the number in the abs value?  |x - #| <  number 2  Lots of
questions and discussions which give abs value meaning...

 -Claudia, for the Teacher2Teacher service

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