Q&A #19028

Everyday Mathematics slide rule

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From: Steve R. (for Teacher2Teacher Service)
Date: Nov 12, 2007 at 13:57:49
Subject: Re: slide rule

Hi Yevgeniy -

The EM "slide rule" is really just a mechanical device to help kids visualize
overlapping number lines.  It's used for adding and subtracting integers and
also for fractions and works the same way in both cases.  I'll give you an
integer example.

First, understand that one of the methods EM teaches for adding and
subtracting integers is to "walk" along the number line.  The keys are that
addition means facing to the right and subtraction means facing to the left,
and a positive number means to walk forward (the direction you are facing)
while a negative number means to walk backwards (away from the direction you
are facing).  So, if we want to do 8 + (-3) we can imagine standing on a
number line at positive 8, facing to the right (since it's an addition
problem) and then moving backwards three spaces (since it's negative three)
thus finishing on positive 5.

To do -4 - (7) we would start by standing on -4, facing to the left (since
it's a subtraction problem) and walking forwards seven spaces (since it's
positive seven) thus finishing on -11.

You can see how this handles the "subtracting a negative" issue since in that
case you face left but walk backwards, moving you in the positive direction.

So the "slide rule" consists of two number lines, one of which remains still
(the holder) and the other of which moves (the slider).  The holder is
v-shaped and the slider sits inside it.  Both pieces have the numbers to the
left of 0 (ie, the negatives) shaded.  The holder actually displays those
numbers with a negative sign while the slider has the shading but does not
include the negative signs.

To use the slide rule to do the two problems above, here's what I'd do.

For 8 + (-3) I'd move the slider so that the 0 on that scale aligns with +8
on the holder.  That's the starting point and is the same as imagining that
I'm standing on 8.  Then, since I'm adding negative three, I'd imagine I'm
facing right and move backwards three, or three into the shaded zone.  Then
I'd look at the holder and see that I'm now lined up with positive five.
Note that the slider doesn't actually move in this part, I just count spaces
on the slider and then look at the holder to see where I am.

For -4 - (-7) I'd align the slider so its 0 aligns with -4 on the holder.
Then I'd imagine facing left and backing up 7, so moving 7 into the unshaded
numbers.  Then I'd look down at the holder and see that I'm lined up with
positive three.

The fraction slide rule works the same way - imagine two rulers aligning with
each other, with both calibrated to sixteenths.  It only works for halves,
quarters, eighths, and sixteenths.

So yes, this is based on a linear scale and is really just a way to help kids
physically visualize that "walking the number line" approach by using the
slider to set the starting point and measure the steps, then viewing the
holder to see where you finish up.

Does this make sense and help?

 -Steve R., for the T2T service

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