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Solving nonroutine problems with multiple approaches is one of the goals promoted by the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). I present two problems that seem to fit the bill, since my seventh-grade students worked on them in various ways.

Mathematical games are a popular element in any teacher's repertoire of motivational activities. This game promotes learning and fun at the same time by combining two unlikely allies: a deck of ordinary playing cards and a calculator. The material presented here uses a simple fourfunction calculator with a square-root key. With minor adjustments, the more powerful scientific models can be used.

IN OUR EARNEST DESIRE TO EDUCATE OUR students about the great importance and significance of the number p by celebrating with special mathematical activities on March 14, we just may be teaching a concept that we had not intended or that we are overlooking altogether. I am referring here to the fundamental concept of the place-value structure of our decimal number system.

If you are interested in a novel approach to number patterns, an experience in following an algorithmic procedure different from the usual one, some practice in systematic search techniques, and something that provides students with significant amounts of practice with the basic facts—all this in one activity—we would urge you to consider number bracelets.

I can “second the motion” that the motivational effect of palindromes, as described by Nichol io “Addition through Palindromes” in the December 1978 issue is indeed great. And the instructional spio-offs not touched upon by the author provide many opportunjties for further learning.

L/iscovery can be an important process in elementary mathematics education. The unit described here encourages self-discovery and allows the student to occasionally make a discovery that is new even to the teacher. All that the unit requires is a pencil, some paper, a creative imagination, and a "Let's see what would happen if . . ." attitude toward the problem. It is based on the concept of the digit sums of numbers, specifically of sets of numbers that have a pattern linking them together. The topic of digit sums (or digital roots) is an old one, sometimes referred to as "casting out nines," that is experiencing a revival in many textbooks. The topic is simple enough for elementary school children to handle with ease (this article is based upon experiences with fourth-grade children), yet it is one that appears in advanced-level number theory. The ideas are more than mere curiosities.

Number games can provide elementary students with a good opportunity to test their observation skills for problem solving, and at the same time they will be practicing such drill skills as adding and subtracting. Here are five trivial number games guaranteed to provide hours of fascination and lots of hidden drill. The word trivial is used here with two meanings in mind. The games are trivial in the usual mathematical sense—namely, once the secret is known to both players, the game's winner is predetermined, based on the starting number and who begins play. The games arc nontrivial from the point of view that they are valuable teaching aids for motivating student thinking.