America's Favorite Card Games®  Academic Research
http://setgame.com/teacherscorner/academicresearch
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SET and Matrix Algebra
http://setgame.com/setandmatrixalgebra
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <p class="rtecenter"><strong>SET<sup>®</sup> AND MATRIX ALGEBRA</strong></p>
<p class="rtecenter"><strong>By Patricia J. Fogle, Ph.D., D.O.</strong></p>
<p> </p>
<p> The following two tables represent ways of aligning SET cards on a tictactoe type board to make a magic square of <em>SET</em>s.</p>
<p class="rtecenter"><img alt="" class="attr__format__media_original attr__typeof__foaf:Image img__fid__1555 img__view_mode__media_original mediaimage" src="http://setgametbsirate2fqpbmoxg3.devcloud.acquiasites.com/sites/default/files/magicsquaretictactoe.jpg" style="width:100%" /></p>
<p> In both tables three SET cards are selected that in themselves do not make a <em>SET</em>. These cards are arranged on the board so that two of the cards are in a line, and the third card is laid anywhere except the third position in that line. When the two cards in that line are known, the third card in that line can be determined by the rules of SET. That card now forms a relation with the other card on the board, and the third card in that line can now be determined. Subsequently the entire board can be filled in.</p>
<p> In Table A cards #4 and #7 define card #1. Then cards #1 and #2 define card #3. Cards #3 and #7 define card #5, and so on.</p>
<p> In table B cards #2 and #5 define #8. Cards #4 and #5 define #6. Now it does not appear that two cards are in a line. But this table also has a unique solution. Two methods are available to finish the puzzle: trial and error (until every row, column, and diagonal makes a <em>SET</em>), or using a concept from matrix algebra.</p>
<p>Click on attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/SET%20AND%20MATRIX%20ALGEBRA.pdf" type="application/pdf; length=65890">SET AND MATRIX ALGEBRA.pdf</a></span></div></div></div>
Fri, 24 Apr 2015 23:31:36 +0000
latkinson
1556 at http://setgame.com

SET and Statistics
http://setgame.com/setandstatistics
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <h2 class="rtecenter">SET<sup>®</sup> AND STATISTICS</h2>
<h2 class="rtecenter">By Patricia J. Fogle, Ph.D., D.O.</h2>
<hr /><p>The use of statistics pervades the world in which we live. It is used arguably to defend positions in basic and applied scientific research, and ultimately affects all aspects of our lives. It therefore is important to understand the rationale and meaning of these "numbers" that affect our lives.</p>
<p>An easy way for students to begin to grasp the value of numbers involves collection of data while playing the game <em>SET: The Family Game of Visual Perception</em>. SET lends itself to this task because patterns which are removed from the board during play can be neatly categorized according to characteristics listed in Table 1 below.</p>
<p>Click attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/SET%20AND%20STATISTICS.pdf" type="application/pdf; length=79955">SET AND STATISTICS.pdf</a></span></div></div></div>
Fri, 24 Apr 2015 23:27:57 +0000
latkinson
1551 at http://setgame.com

Investigations into the Card Game SET
http://setgame.com/investigationscardgameset
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <p class="rtecenter"><strong>THE MAXIMUM NUMBER OF SETS FOR N CARDS</strong></p>
<p class="rtecenter"><strong>AND</strong></p>
<p class="rtecenter"><strong>THE TOTAL NUMBER OF INTERNAL SETS FOR ALL PARTITIONS OF THE DECK</strong></p>
<hr /><p class="rtecenter"><strong>By Jim Vinci</strong></p>
<p class="rtecenter"><strong>June 30, 2009</strong></p>
<p class="rtecenter"><strong>Email address:<a href="mailto:mathisfun@wowway.com">mathisfun@wowway.com</a></strong></p>
<hr /><p><strong>Introduction</strong></p>
<p>I never thought that a purchase of a card game would lead to any kind of mathematical adventure. However, it is evident, from the abundance of related articles and papers written, that SET has sparked an enormous amount of interest from nonmathematicians and mathematicians alike. Clearly, SET is no ordinary card game!</p>
<p>My first investigation into the mathematics behind SET began with a December 19, 1998 letter, written to the creators of the game, and concerning the odds statistics presented in the game’s instructions. Being an actuary by profession and an individual with a passion for mathematics, I was immediately drawn to the question of how to calculate the probability of no Set (the special meaning of this will be defined later) being present in twelve cards. This problem naturally led to the more general question of how to determine the maximum number of cards that could be chosen without a Set existing. I soon recognized that this was an extremely complex problem for which computer assistance would be required to evaluate the seemingly endless possible variations. Famous math problems, like the Four Color Theorem, were solved by the use of the computer, so why not this one? After all, counting problems are well suited to computer modeling!</p>
<p>But I also continued to optimistically hold on to the notion that the problem of determining the largest number of cards without a Set, and the possible maximum number of Sets for a given number of cards, could be formulated in algebraic terms. However, because other individuals, included the creators of the game, had already provided solutions to the original SET problem, I decided that it probably wasn’t worth any more investment of time.</p>
<p>Recently, my interest in the SET problem was rekindled after reading Mr. David Van Brink’s highly inspiring article on the subject. In that article, he demonstrates that a deck of N = 47 cards must contain a Set. While reading this article, it became apparent that the concept of parity was fundamental to formulating an alternate approach that might uncover the mathematical patterns behind SET.</p>
<p>This paper will cover the following topics:</p>
<ol><li>For the benefit of those new to SET, a brief explanation of the rules of the game and how Sets are formed.</li>
<li>Development of a general formula for the total number of Sets that can occur when a deck of C<sup>P</sup> (P = number of properties in the deck, C = number of choices for each property) cards is partitioned into two piles, and Set counts are restricted to those that are found exclusively within each pile.</li>
<li>The thinking behind the clever visual solution for why any collection of 20 cards must contain a Set, including a discussion of the Setblocking strategy.</li>
<li>A proposed computer modeling method, referred to as the Consecutive Maximization Method, for use in identifying the largest possible Setless collection of cards from a P property deck.</li>
</ol><p>Click on the attachment below to read the full article.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/SETPROOF.pdf" type="application/pdf; length=501295">SETPROOF.pdf</a></span></div></div></div>
Fri, 24 Apr 2015 23:23:50 +0000
latkinson
1546 at http://setgame.com

Promoting Strategic Thinking with SET
http://setgame.com/promotingstrategicthinkingset
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <p class="rtecenter"><strong>Promoting Strategic Thinking Skills in MiddleSchool Students Using <em>Set: The Family Game of Visual Perception<sup>®</sup></em></strong></p>
<hr /><p class="rtecenter"><strong>Sylvia Sykes<br />
Holy Names University, Oakland, CA</strong></p>
<hr /><p>Games are a natural expression of children’s playfulness and energy. Excitement, joy, and involvement motivate them to continue to play until they have mastered the game. Strategy games, in particular, address development of mental acuity and intellectual maturity essential to academic success. Consequently, educators, particularly in the primary and elementary grades, may incorporate subjectspecific games into classroom practices to support cognitive and academic development. For example, math bingo, math specific board and card games, and interactive educational software may reinforce knowledge of mathematical operations (Falco, 2001). Crossword puzzles and word searches increase and strengthen vocabulary in both language arts and science. Riddles introduce metaphors, similes, analogies, and descriptive language as well as assessing reading comprehension (Zipke, 2007). However, as children enter the middle and upper grades, game usage declines as classroom teachers shift from teaching learning strategies to instructing in content (Joseph, 2006). This study asks the question: What are the effects, if any, of a curriculum using <em>Set: A Family Game of Visual Perception<sup>®</sup></em> (Copyright ©1988, 1991 Cannei, LLC) on strategic thinking skills of middle school students?</p>
<p><em>Metacognitive Awareness and Strategic Thinking</em></p>
<p>Many of educators hold the misperception that direct instruction in teaching strategic thinking stops at the end of elementary school (Joseph, 2006). As a result, less proficient students may fall behind because they are struggling to grasp unfamiliar material without indepth comprehension (Day, 1994; Vaidya, 1999). Teachers may rely upon a more traditional teaching model that follows the pattern of giving an assignment with the expectation that the student will produce the work. The teacher then evaluates the product and assigns a grade. A student may rely upon rote memorization and fact regurgitation rather than developing a deeper and more substantive understanding of the subject (Day, 1994). In short, the student becomes a passive participant in her education because she does not understand how or why she learns (Joseph, 2006).</p>
<p>Click on the attachment below to read the full article.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/PROMOTING%20STRATEGIC%20THINKING%20IN%20MID%20SCH%20STUDENTS%20USING%20SET.pdf" type="application/pdf; length=377228">PROMOTING STRATEGIC THINKING IN MID SCH STUDENTS USING SET.pdf</a></span></div></div></div>
Fri, 24 Apr 2015 22:36:07 +0000
latkinson
1536 at http://setgame.com

Developing Mathematical Reasoning using Attribute Games
http://setgame.com/developingmathematicalreasoningusingattributegames
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <p class="rtecenter"><strong>By Anne Larson Quinn, Ph.D., Associate Professor, Edinboro University, <a href="mailto:Quinna@edinboro.edu">Quinna@edinboro.edu</a><br />
Frederick Weening, Ph.D., Assistant Professor, Edinboro University, <a href="mailto:Fweening@edinboro.edu">Fweening@edinboro.edu</a><br />
Robert M. Koca, Jr., Ph.D.</strong></p>
<p>Reproduced with permission from the <strong><em>Mathematics Teacher</em></strong>, copyright 1999 by the NCTM.</p>
<p>The game of SET<sup>®</sup> has proven to be a very popular game at our college mathematics club meetings. Since we've started playing, the membership has grown every month. In fact, one of our members brought her six year old son to a meeting, and he now looks forward to playing SET<sup>®</sup> with us every month. As a result of playing the game in our club and thinking about the results, we created and solved a variety of mathematical questions. For example, we wondered about possible strategies for winning and conjectured about phenomena that happened when playing. These questions involve a wide variety of traditional mathematical topics, such as the multiplication principle, combinations and permutations, divisibility, modular arithmetic, and mathematical proof.</p>
<p>In addition to encouraging the posing and solving of these problems in our math club, we took the game and our questions into our classrooms to see what reasoning could be encouraged. We tested our original questions on several groups of junior high and high school students and on several hundred freshmen and sophomore college students who were not mathematics majors.</p>
<p>The purpose of this article is to show how games such as SET<sup>®</sup> can be used to develop mathematical reasoning by describing student investigative work that has resulted from playing the game. After giving a description of the game, we will pose and answer some of the questions that were solved by members of our club and by students ranging in academic level from ninth grade to college. We will also describe what teachers can do to facilitate the development of reasoning using this game. Although this article discusses problems that were generated from the game of SET<sup>®</sup>, any game that uses attributes can be used to stimulate logical thinking.</p>
<p>Click on the attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/DEVELOPING%20MATHEMATICAL%20REASONING.pdf" type="application/pdf; length=209214">DEVELOPING MATHEMATICAL REASONING.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 23:27:19 +0000
latkinson
1496 at http://setgame.com

SET Recognition as a Window to Perceptual and Cognitive Processes
http://setgame.com/setrecognitionwindowperceptualandcognitiveprocesses
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <h2 class="rtecenter"><strong>MICHAL JACOB AND SHAUL HOCHSTEIN</strong><br /><em>Hebrew University, Jerusalem, Israel</em></h2>
<p>The Set visual perception game is a fertile research platform that allows investigation of perception, with gradual processing culminating in a momentary recognition stage, in a context that can be endlessly repeated with novel displays. Performance of the Set game task is a playoff between perceptual and conceptual processes. The task is to detect (among the 12 displayed cards) a 3card set, defined as containing cards that are either all similar or all different along each of four dimensions with three possible values. We found preference and reduced response times (RTs) for perceiving set similarity (rather than span) and for including cards sharing the most abundant value in the display, suggesting that these are searched preferentially (perhaps by mutual enhancement). RT decreases with number of sets in the display according to a horse race model, implying independence of simultaneous searches. Central cards are included slightly more often, but set card proximity seems irrelevant. A supplementary experiment determining dimensional salience showed consistent but individual preferences, yet these seemed not to affect set identification. Training induced gradual improvement, which generalized to a new version of the game, suggesting highlevel learning. We conclude that elements of perception such as similarity detection are basic for finding sets in this task, as in other realworld perceptual and cognitive tasks, suggesting the presence of basic similarityperceiving mechanisms. The findings confirm the conclusion that conceptual processes are affected by perception.</p>
<p>Please click attachment below to read full article.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/SET%20AS%20A%20WINDOW%20TO%20PERCEPTUAL%20AND%20COGNITIVE%20PROCESSES.pdf" type="application/pdf; length=227538">SET AS A WINDOW TO PERCEPTUAL AND COGNITIVE PROCESSES.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 21:57:19 +0000
latkinson
1491 at http://setgame.com

The Joy of SET
http://setgame.com/joyset
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <p class="rtecenter"><strong>Author: Miriam Melnick, Bard College at Simon’s Rock</strong></p>
<ol><li>Introduction to the game by constructing the deck in a series of algorithmic steps.</li>
<li>Discussion of how to play game and how to expand it from the standard 4 dimensions into n dimensions.</li>
<li>Model of mathematical nature of SET using strings of 0's, 1's and 2's.</li>
<li>Investigation of circumstances under which there are no matches visible.</li>
</ol><p class="rtecenter">"Pure mathematics is the world’s best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly."  Richard Trudeau, <em>Dots and Lines.</em></p>
<p><strong>1 Introduction</strong></p>
<p>In the game of SET, players race to collect sets of 3 matching cards. Sometimes, they get stuck and the players claim there are no matches on the table. Is this true? Are there circumstances in which there are no matches visible? What conditions must be satisfied for this to occur? In this paper, we develop algebraic, geometric, and computational frameworks to answer these questions.</p>
<p>It is always important to have precise definitions for our terms. You are likely familiar with the common mathematical concept of a "set" as a collection of objects surrounded by curly brackets. Throughout this paper, we will use the following terminology to describe SET:</p>
<p><strong>set </strong> An unordered collection of objects. The traditional mathematical notion of a set. Denoted with curly brackets.</p>
<p><strong>SET</strong> A card game played with a special ndimensional deck.</p>
<p><strong>match</strong><sup>1</sup> A set of three SET cards that conform to the SET rule as described below. Denoted using square brackets.</p>
<p>We introduce the game of SET by constructing the deck in a series of algorithmic steps (see Section 2.3). From there we will discuss how to play the game of SET and how to expand it from the standard 4 dimensions into n dimensions (see Section 2.5). Then we discuss the mathematical nature of SET and how we can model it using strings of 0’s, 1’s, and 2’s (see Section 3). We will investigate the circumstances under which there are no matches visible (see Section 3.4). We will model ndimensional SET using the vector space Zn3 and discuss its algebraic structures (see Section 4). Then we will model ndimensional SET using the projective affine space AG(n, 3) and discuss the geometric consequences (see Section 5). Finally, we will examine how many cards can be dealt and still have no match. We will approach this problem primarily from a computational direction (see Section 6).</p>
<p>Please click on the attachment below to read the rest of the article.</p>
<p> </p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/THE%20JOY%20OF%20SET.pdf" type="application/pdf; length=331691">THE JOY OF SET.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 21:20:34 +0000
latkinson
1486 at http://setgame.com

Cognitive Modeling with SET
http://setgame.com/cognitivemodelingset
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <h2 class="rtecenter">How to Construct a Believable Opponent using Cognitive Modeling in the Game of Set</h2>
<p class="rtecenter"><strong>Niels A. Taatgen (<a href="mailto:niels@ai.rug.nl">niels@ai.rug.nl</a>)<br />
Marcia van Oploo (<a href="mailto:marcia@ai.rug.nl">marcia@ai.rug.nl</a>)<br />
Jos Braaksma (<a href="mailto:j.braaksma@ai.rug.nl">j.braaksma@ai.rug.nl</a>)<br />
Jelle Niemantsverdriet (<a href="mailto:jelle@niemantsverdriet.nl">jelle@niemantsverdriet.nl</a>)</strong></p>
<p class="rtecenter">Department of Artificial Intelligence, Grote Kruisstraat 2/1<br />
9712 TS Groningen, Netherlands</p>
<p><strong>Abstract</strong></p>
<p>An interesting domain of application for Cognitive Modeling is the construction of computer opponents in games. We present a model of the game of Set. The model is sensitive to the difficulty of the situation in the game, and can explain the difference between beginners and experts. Furthermore, the model is used in a computer game in which players can play Set against various versions of the model.</p>
<p><strong>Introduction</strong></p>
<p>In computer games, the human player often faces one or more computer opponents. In order to make the game enjoyable, these computer opponents have to be intelligent, otherwise they wouldn’t be much of a challenge. The classical example of playing a game against the computer is chess, and the focus of designing a computer chess player has always been to have a player that plays as good as possible. In fact, since Deep Blue beat Kasparov the interest in computer chess seems to have diminished, but maybe the recent rematch against Kramnik will change matters. Nevertheless, human chess players complain that computer chess programs are no fun to play against. A possible reason for this is that computer chess programs have long left the approach of mimicking human chess players, but instead focused on bruteforce techniques.</p>
<p>This leads us to the idea that a computer opponent becomes more interesting and enjoyable to play against as it behaves more like a person. In this paper we will explore this idea and demonstrate how cognitive modeling can help to produce more interesting computer opponents. The basic idea is relatively simple: study how people (preferably at different levels of skill) behave in the game you want a computer opponent of, make a cognitive model of this behavior that closely matches human behavior, and incorporate this in a computer program.</p>
<p>The game we will use is the game of Set. Set is a card game that is quite trivial to play perfect for a computer program, so the challenge is to model an opponent that is interesting to play against. Another interesting aspect of Set is that it combines several aspects of cognition: perception, information processing, strategy, learning and time pressure. We will describe an experiment and several possible models of playing Set, and incorporate those in a program that can one can play against.</p>
<p>Click on the attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/COGNITIVE%20MODELING%20WITH%20SET.pdf" type="application/pdf; length=996547">COGNITIVE MODELING WITH SET.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 20:42:46 +0000
latkinson
1481 at http://setgame.com

Mathematical Fun & Challenges in the Game of SET
http://setgame.com/mathematicalfunchallengesgameset
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <h1 class="rtecenter">MATHEMATICAL FUN & CHALLENGES IN THE GAME OF SET<sup>®</sup></h1>
<p class="rtecenter"><strong>By Phyllis Chinn, Ph.D. Professor of Mathematics<br />Dale Oliver, Ph.D. Professor of Mathematics<br />Department of Mathematics<br />Humboldt State University<br />Arcata, CA 95521</strong></p>
<p><strong><em>The Game of SET</em></strong></p>
<p>In 1988 Marsha Falco copyrighted a new game called SET. This game proves to be an excellent extension for activities involving organizing objects by attribute. In addition to reinforcing the ideas of sameness and distinctness, the SET game, and variations on it, provide an interesting and challenging context for exploring ideas in discrete mathematics. Even though the NCTM's 1989 Curriculum and Evaluation Standards for School Mathematics includes discrete mathematics as a standard for grades 912, the activities suggested here are strongly supported by the K4 and 58 standards involving mathematics as problem solving, communication, and reasoning.</p>
<p>Click on the attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/Mathematical%20Fun%20%26%20Challenges%20in%20the%20game%20of%20SET.pdf" type="application/pdf; length=59241">Mathematical Fun & Challenges in the game of SET.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 20:27:26 +0000
latkinson
1476 at http://setgame.com

Mathematical Proof of Magic Squares
http://setgame.com/mathematicalproofmagicsquares
<div class="section field fieldnamebody fieldtypetextwithsummary fieldlabelhidden"><div class="fielditems"><div class="fielditem odd" property="content:encoded"> <h3 class="rtecenter">By Llewellyn Falco</h3>
<p>What you see here is a magic square, much like the addition and subtraction squares you may have used as a child.</p>
<p>These magic squares are even more talented, as they all follow the rules of the card game SET®. To learn how to make one with ease, read on.</p>
<p>SET® cards contain four properties: color, shape, number of objects, and shading. The rules state for each property, they must all be equal, or all different. For example, if we look at the top row of the square, we see three different colors, three different shapes, three different numbers, and three different types of shading within the objects. Need more examples? Any line on the magic square yields a set.</p>
<p>Click on the attachment below to read the full paper.</p>
</div></div></div><div class="section field fieldnamefieldtcattachment fieldtypefile fieldlabelhidden"><div class="fielditems"><div class="fielditem odd"><span class="file"><img class="fileicon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/applicationpdf.png" /> <a href="http://setgame.com/sites/default/files/teacherscorner/MAGIC_SQUARES_PROOF.pdf" type="application/pdf; length=314331">MAGIC_SQUARES_PROOF.pdf</a></span></div></div></div>
Thu, 23 Apr 2015 19:37:55 +0000
latkinson
1436 at http://setgame.com