Conference rusure::math

166.0. "first grade arithmetic" by REX::POWERS () Tue Oct 16 1984 12:53

I have a daughter in first grade.  Yesterday she brought home a work sheet
that involved the use of color rods.  Color rods are a teaching tool
for elementary arithmetic.  Rods run in integral lengths, each length
being differently colored;  they are used in combination to demonstrate
numerical relationships.  I was impressed by a number of points.
Color rods are a sneaky way of getting algebra into the first grade
curriculum.  The kids are doing subtraction (the point of the exercise
in question) without knowing it.  My daughter got all twleve problems right.

My wife and I were also intrigued to see if we could figure out 
the lenght-to-color code from what looked to be a set of simultaneous
equations, so we attacked the problem straightaway.

The problem statements:
	1) What is the length-to-color code?
	2) Is your solution unique?
	3) How many of the twelve problems could my daughter have gotten
		wrong (whether I knew it or not) and still have provided
		enough information for a solution?
(We solved the first two;  I'm not sure how to address the third.)

The twelve equations:
	d - g = g
	r - w = w
	y - r = g
	n - w = k
	o - y = y
	k - p = g
	e - r = k
	y - w = p
	o - d = p
	n - p = p
	g - r = w
	k - d = w

(If the letters confuse you, the naming system takes the last letter of the
color name where duplicate first letters exist, so k is black, e is blue,
and n is brown; d is dark something.)

Use whatever assumptions you think you need given the environment,
that being one to teach first grade arithmetic.

- tom]

The numbers 1-10 are represented by W,R,G,P,Y,D,K,N,E,O. The solution is
unique. I didn't use equation 12 to get the solution, so it appears to be
redundant. - Lynn Yarbrough

By glancing at the solution given, it appears one could have also solved
the problem with a good memory. I used those colored sticks as an intro
to mathematics when I too was a toddler.....

wim

the unit rod is a cube.  the unit on the set my kid used was one cm.
early intro to metric system.  the rods can be used for multiplication,
division, area, volume, conversion of units, and more.
they are also fun to play with, so the kids are less likely to be
intimidated by math.  most teachers do not realize all that the
rods can be used for.
the rods are available for home use and are not expensive.
but beware.  spilling the box makes a lot of rods to pick up.