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Equations: The Game of Creative Mathematics, by Layman E. Allen. $6.50, WFF'N
PROOF, 1490-SM South Blvd., Ann Arbor, MI 48104.

Instructional Math Play (IMP Kits: Simulations of Computer Assisted Instruction
Programs, by Layman E. Allen and Jon K. Ross. $1.00 per kit, $15.00 for set of
21.

WFF'N PROOF.

On-Words: The Game of Word Structures, By Layman E. Allen, Frederick L. Goodman,
Doris J. Humphrey, and Joan K. Ross, $6.50, WFF 'N PROOF.

It is both convenient and natural to review these two games, and the associated
instructional-simulation aids, as a single publication because they are, besides
being designed by the same person or persons, very closely related in purpose,
playing equipment, rules, and interest for the players.

EQUATIONS is played by two or more persons (or, as the IMP kits indicate, by a
person and a computer program) with the objective of finding ways of expressing
equations in simple arithmetic operations. One player defines a goal (one side
of the equation) by selection of some of the numbers and operators provided by a
roll of a dozen or more special dice. The players then try to come as close as
possible to supplying a left-hand side, without actually doing so, by selecting
one die at a time from the remaining dice. Getting too close to a solution, or
preventing all
solutions (by eliminating crucial dice from play) loses the game; successfully
challenging an errant opponent wins.

The above description does not do full justice to the rules. Let me hasten to
add that the actual rules supplied, including variants for those who find the
standard rules too tame, covers forty (40) pages of printed text, so there is no
way that a review can do justice to the rules. In fact, the standard rules, once
understood, are not all that complex: rather, it is the presentation that is
complex. This is the major problem with what are basically very interesting
games: the statement of the rules is far too formal and complex.

The IMP kits contain a summary of the rules which is vastly easier to read and
comprehend, and I would strongly recommend that anyone who buys EQUATIONS get
some of the IMP kits as well. They provide solo practice as well as a clearer
understanding of the rules (in Kit No. 1 only.) Once the rules have been
assimilated, the game can be played by elementary school children (4th grade up)
and will be enjoyed by many, I believe. The games have considerable popularity
in some schools in which they are used.

My two boys (5th and 7th grades) found that they picked up new insights into
arithmetic in their first attempts to play. However, they do not seem to be
ready to
accept the game as part of their regular selection (they are currently hung up
on Cribbage.)

The play of ON-WORDS is similar: the goal is the length of a word, which is to
be made up from a selection of the remaining cubes, which have letters on them.
The
general structure of the rules is identical, including, unfortunately, the
complexity of the explanation. I find the game interesting and challenging, but
an attempt to
introduce it to a group of word-game enthusiast friends was met with furrowed
eyebrows and eventual rejection. Maybe it's my poor powers of explanation, maybe
they are just not ready for a game of this sophistication, but we did not get
past the first game. It is a real pity that the author did not spend less time
making the rules rigorous in favor of making them clear and concise.

L. D. Yarbrough

Lexington, Mass.

"With regard to excellence, it is not enough to know, but we must try to have
and use it."

Aristotle

On-Sets (Game), by Layman E. Allen, Peter Kugel, and Martin F. Owens, $6.50,
WFF'N PROOF, 1490 South Blvd., Ann Arbor, Ml 48104.

Objectives:

After a student plays the game of ON-SETS he should know

1. what a set is.

2. the relationship between the names of a set and the number of things that are
in the named set. 

3. operations with sets such as union, intersection, complementation and
difference.

4. what is meant by the universal set and the null set.

Evaluation: 

There are many variations of the game; the simplest versions are for use in the
primary grades. The game increases in complexity and should be suitable for use
all the way up to the adult level. The instructions for the elementary versions
are easy to follow, and this game can be used to effectively introduce concepts
of set theory at an early age. The game is played by 2-3 children at any one
time and should not take more than approximately 5-10 minutes to complete. lt
is, therefore, suitable for use in a classroom where a short time filler is
needed to keep small
groups of students occupied. This game is highly recommended for use at this
level in the classroom.

The more advanced versions of this game are too complicated for general
classroom use. lt would be much simpler to explain set theory to the middle and
high school student than the mechanics of this game. The rewards involved in
playing the game do not warrant the time needed to explain the play of the game.

Ms. E. T. Rubin

Richmond, VA

* * *

Space Hop: A Game of the Planets by Helmut Wimmer. $12.95. Teaching Concepts,
Inc., 230 Park Ave., New York, NY 10017. 

"Space Hop is a valuable teaching tool in the form of a game which illustrates
the scientific facts of our Solar System, its sun, moons, planets, comets and
asteroids. One of a series of GAMES BY TEACHERS." (Publisher's description.)

This game is suggested as suitable for 9-to-adults, and that evaluation seems
accurate. My two boys, 10 and 12, enjoy it thoroughly and like to show it off to
their friends. The educational aspects are well planned and the competitive
elements are just enough to make the game fun without introducing too many
stress situations of the type likely to set siblings at each other's throats. ln
addition to
coming away from the game with reinforced facts about the solar system (What was
the first planet to be discovered by telescope? My mission is to go there...),
they will
subliminally pick up the concept of odd-even parity, and just may come away
bemused by the peculiar topology of the "outer space" defined by the rules.

I recommend the game for any group of "kids" with a scientific bent.

Lynn D. Yarbrough

Lexington, Mass.

* * *

BASIC in a Flash, by Earl Orf and Royce Helmbrecht. $1.50. The Math Group, Inc.,
5625 Girard Ave. South, Minneapolis, MN 55419.

"This set of cards is designed to help students learn the meaning of symbols,
commands, and statements used in the BASIC programming language. Terms are
printed in red on one side and definitions in black on the other side. Many
cards also contain examples showing how the term might be used. Blank cards are
included to add your own terms. Could be used as flash cards or as a reference
near the computer terminal." - Publisher's summary.

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