XACTIKA Skill Connections

XACTIKA is an original card game, with three ways to play. Students can PLAY TO WIN: take the most tricks, high score wins. Or they can PLAY TO LOSE: take the fewest tricks, low score wins. Or PLAY TO BID, where the student must win exactly the number of tricks he/she bid (hence the name XACTIKA).

The three ways to play all teach critical thinking, math skills, and social and personal skills; however each way to play emphasizes different skills:

• When students PLAY TO WIN, they must understand how to play each card so it has the highest probability of winning.
• When they PLAY TO LOSE, students must understand the inverse of the rule and play each card so it has the highest probability of losing.
• When students PLAY TO BID, XACTIKA challenges and builds their ability to estimate the outcome of a series of processes. Each student must evaluate the probability of being in a position to take other players’ cards that are laid down each round, based on the cards in his or her hand. The game is designed such that cards that appear to be likely to take a trick initially may become less likely to take a trick as cards are played and those cards that do not initially appear likely to take a trick, may now be viable to do so. Developing the ability to correctly bid their hands involves analytical reasoning and following the evolution of the play develops patterning skills. Students must recognize the value of their hand, not just from having the highest point cards in one of the four suits on each card, but also from an understanding of the chances that opponents may or may not have cards of similar value.

Developing Mathematical Reasoning using Attribute Games

By Anne Larson Quinn, Ph.D., Associate Professor, Edinboro University, Quinna@edinboro.edu
Frederick Weening, Ph.D., Assistant Professor, Edinboro University, Fweening@edinboro.edu
Robert M. Koca, Jr., Ph.D.

Reproduced with permission from the Mathematics Teacher, copyright 1999 by the NCTM.

The game of SET^® 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^® 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.

MATHEMATICAL FUN & CHALLENGES IN THE GAME OF SET^®

By Phyllis Chinn, Ph.D. Professor of Mathematics
Dale Oliver, Ph.D. Professor of Mathematics
Department of Mathematics
Humboldt State University
Arcata, CA 95521

The Game of SET

SET Up

This version of the game is 1/2 luck and 1/2 skill for 2 or more players. SETs are made according to the rules of classic SET.

Object:  To play a card from your hand that does not make a SET with the cards already played on the table. 

Download Printable Instructions Here

XACTIKA Graphing Skills

You can use XACTIKA to teach students how to create bell curves and bar graphs.  Once your students have created their graphs, they can use the visual aids to learn about statistics and probabilities and to better understand how using statistics and probabilities affects their strategy when playing the game. 

End Game SET

Object
To determine the attributes of the missing card.

The Play
At the beginning of the game, remove one card from the deck and place it face down to the side. 

Now play the game according to the standard rules of SET.  When no more SETs can be found, you can determine the attributes of the missing card.

Download Printable Instructions Here

Mathematical Proof of Magic Squares

By Llewellyn Falco

What you see here is a magic square, much like the addition and subtraction squares you may have used as a child.

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.

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.