Teaching Chess in the 21st Century Strategies and

Chess Chess Detect ive Press

Illustrations Illustrations by Kevin Hempstead

Teaching Chess in the 21st Centur  Ce ntury y Strategies and Connections to a Standards-Based  World  Copyright © 2005 by Todd Bardwick. Printed and bound in the United States of America. All rights reserved. No part of this book shall be reproduced in any form or by any electronic or mechanical means including information storage and retrieval systems without permission in writing from the publisher, except by a reviewer, who may quote brief passages in a review. Included in these reserved rights are publishing on the Internet or in annotated databases. Published by Chess Detective Press, 1 Red Fox Lane, Englewood, Colorado 80111. 303-770-6696. First Edition. Second printing: 2010

www.ColoradoMasterChess.com

ISBN: 978-0-9761962-0-4 Library Library of Congress Control Number: Number: 2004097331 200409733 1 Library of Congress Cataloging-in-Publication Data available upon r equest equest

DEDICATION This book is dedicated to chess students everywhere with the sincerest wish that chess will enrich their life in whatever endeavors endeavors they they choose to pursue. Most of all, it is dedicated to you, the teacher or parent, who will share these principles and stories to enhance your student’s lives by teaching them how to play chess in a fun and educational way.

FOREWORD Beginning in 2003, Todd Bardwick was invited into the second and third grade classrooms of different elementary schools in Denver’s prestigious Cherry Creek School District to teach chess to the children with the ten-lesson course laid out in Teaching Chess in the 21st  Century as  Century as part of their math curriculum. Here are some reviews by the teachers whose classrooms hosted the chess pilot classes.

CHESS CHESS PILOT PILOT CLASS CLASS - 200 20 0 3 Having Todd in our classroom was an educational and fun time. I was really amazed at how quickly some of the children understood the lessons taught. About a third of the class had some previous experience playing chess and it was great to see them apply the strategies Todd taught them. While the class learned names of the chess pieces and how they moved on the board, what was more interesting to watch was how their level of concentration increased as they played. Many children talked with both Todd and I about how chess helped them with their math skills. They learned new strategies, such as castling, and could not wait every day to “play chess.” It was a wonderful experience to watch the children with limited chess knowledge. They never gave up and learned a little more every day so that by the end of Todd’s stay with us, they felt so much more comfortable in playing chess. It was remarkable to see those illegal moves made in the beginning turn around into legal moves mo ves by the the end. I can’t thank Todd enough for spending time in our classroom and teaching my third graders his passion. He planted a seed, nurtured it with so much love and knowledge,

and now, many of my children cannot wait to go on and learn more about chess. Thanks so much, Todd. You did a stupendous job. Debbie Lesko 2nd and 3rd grade teacher Highline Community School

CHESS CHESS PILOT PILOT CLASS CLASS - 200 20 0 4 Colorado Chess Master Todd Bardwick’s chess course is a mathematical success! From the moment he stepped into my classroom the students were enthusiastically engaged. Todd successfully entwines stories from his experiences as a chess master, tales of historically famous chess contests, and the practical application of classic strategic chess moves to provide an environment that promotes energetic student participation. From basic knowledge of the game such as chess piece point values and legal moves to the complexities of classic openings and tactics that successfully lead to the final objective of checkmate, checkmate, Todd Bardwick’s chess pilot has it all. Not only does this program teach students the joy of playing chess, but it also includes comprehensive math strategies that are directly tied to current school achievement standards. Exposure to x,y coordinates, mathematic computation, and strategic measures of worth are but a part of what this progr pro gr am addresses fro m a mathemat mathematic ic perspective. perspective. For thousands of year s, the the world’s wor ld’s greate gr eatest st intellects intellects have participated in this game of strategic forethought and tactical intrigue. For parents and teachers this is an opportunity to expose their children to a game that promotes the development of such intellectual thought processing skills as analytical decision-making and prudent forethought. This is what a few of my students had to say:

“I’m so glad Mr. Todd showed me how to be good at chess.” “Chess is the best!” “I didn’t know that chess made you think so much, this is cool!” “I want to be a chess master when I grow up.”

Chad Gerity 2nd grade teacher Holly Ridge Elementary School

Contents PREFACE INTRODUCTION

CHESS BASICS: - LESSON 1 Count the material exemplar

OPENINGS: - LESSON 2 Find the best opening move exemplar

SCOREKEEPING: - LESSON 3 Scorekeeping exemplar

BASIC CHECKMATES: - LESSON 4 Explain the checkmate exemplar

BASIC TACTICS: - LESSON 5 Queen pins and forks exemplar

DRAWS: - LESSON 6 Explain the types of draws exemplar

FREE STUFF!: - LESSON 7 Find the free stuff exemplar

PAWN STRUCTURE: - LESSON 8 Describe the pawns exemplar

SQUARE OF THE PAWN: - LESSON 9 Square of the pawn exemplar

CHECKMATE PATTERNS: - LESSON 10 Find the checkmates exemplar

Teacher Tips for Chess Play Time

REPRODUCIBLES

APPENDIX A - CHESS AND MATHEMATICAL STANDARDS

APPENDIX B - FUN CHESS GAMES FOR THE CLASS APPENDIX C - ADDITIONAL EXEMPLARS

GLOSSARY ABOUT THE AUTHOR 

PREFACE Chess is a fun application of mathematics and logic that also develops social skills and sportsmanship in young children. It has been referred to for decades as the ultimate game of strategy and mental challenge. Whereas teachers across the country don’t need too much convincing that the mental strategy of chess can benefit a child’s cognitive development, incorporating the game into a classroo m math setting rar ely happens. One stumbling block that prevents most teachers from even considering teaching chess is the teacher’s limited knowledge of the game itself. How can a novice chess-playing teacher feel comfortable spending time teaching such a complex g ame they know so little about? Teaching Chess in the 21st   Century  is an easy, fun book that breaks chess down to a simple format that anyone can understand. For those seeking additional chess knowledge, there are many well-written beginner chess books available on the market. It only takes a little time and effort to learn more, and as the teacher’s knowledge of the game increases, confidence in the subject matter will follow. Another fear that teachers may have is that chess may be a technical, dry subject matter. Stories and analogies are presented in these lessons that are entertaining for the children. As I run into parents of students that have taken my classes in years past, they tell me that their children still remember these entertaining chess stories. It is quite an honor to be one of the teachers whose stories and analogies a child never forgets! One of the main purposes of this book is to help teachers teach math more effectively, using chess as a vehicle. Educators are constantly looking for effective ways to improve efficiency. With recent educational trends towards greater accountability, chess is fun way to improve student

understanding of the core subjects of mathematics and language arts. Teaching Chess in the 21 st  Century lets you draw from my thousands of hours of experience teaching chess to children at all levels. The ten basic lessons in this book are tried and true tested methods that I have refined over the years to make the game easy and fun to lear n in an intro ductor y chess pro gr am. What about the mathematical justification for teaching chess in the classroo m? This is broken down in Appendix A. Because of a need fo r a more standard way to teach math consistently from school to school, most school districts nationwide are incorporating requirements put forth by the National Council of Teachers of Mathematics (NCTM). In Appendix A, I give a sample 2 nd grade math alignment and show where chess concepts overlap these standards. Finally, I explain in detail how chess dovetails into each of the NCTM standards. You may not be surprised to find out that chess overlaps about half of these national standards for second grade math curriculums! Because chess is such a wonderful teaching vehicle and is an interactive game that keeps the students’ attention, there is absolutely no doubt in my mind that the teacher can effectively teach these math principles to children in a fun way that they can understand in half to a quarter of the time a teacher currently spends in the classroom teaching and reinforcing the exact same principles. Appendix B contains four fun games that involve the whole class and can be incorporated to enhance the student’s chess learning experience. An exemplar is presented at the end of each lesson. The teacher can photocopy the Task page at the end of each exemplar to give the students to test concepts learned in the lesson. Appendix C contains additional exemplars. Chess clubs in elementary schools have been popping up throughout the country over the last decade. Unfortunately, many volunteer parents don’t know what to do and feel inadequate in their own chess knowledge. They want to do

more than just watch the children play, but what will they teach? Teaching Chess in the 21st   Century  is the solution. Follow the lesson plan and be sure to see the Teacher Tips for Chess Play Time after Lesson 10 to learn how to deal with the most frequently occurring challenges that will come up while the students are playing and the proper way to deal with these situations. Please pass along your success stories about how this book has helped you teach chess successfully to your students. Finally, I would like to thank all the people who contributed to helping make Teaching Chess in the 21st  Century a success. First, to my students over the years who helped to develop the stories presented here and for giving me the opportunity to gain experience as to how to effectively present a chess curr iculum to children. For proofreading and commenting on the book from a variety of chess and non-chess backgrounds, I would like to thank my father, Alan Bardwick, an Expert strength chess player and retired business professor at the Community College of Aurora; Gary Bagstad, a Class A/B strength chess player and Hill Middle School Teacher (Denver Public School District); Debbie Lesko, a 3 rd  Grade teacher at Highline Community School; and Carol O’Donnell, my mother. I would like to thank Debbie Lesko and Chad Gerity for the oppor tunity to pilot this chess prog ram in their classroo ms and for their assessments of the pilot classes presented in the Foreword. Special thanks to Shannon Lesko for her expertise in copy editing the book and fixing all my omitted double modifiers! I wish to thank Robert Fair, for many years the Cherry Creek School District K-12 District Math Coordinator, for his help and wise counsel in combining the sample 2nd gr ade math alignment with the National Council of Teachers of Mathematics Standards. Thanks also to Leslie Chislett, the Coordinator for Gifted Talented & Accelerated Learning for the Cherry Creek School

District, for her advice and ideas for the educational side of the book. I greatly appreciate the time and effort from Gordon Pierce for his advice and consultation in educating me about the details of the publishing industry. Finally, I would like to thank the artist, Kevin Hempstead, for the clever and entertaining illustrations that he created for the book. Best wishes in your chess endeavors, Todd Bardwick National Chess Master

INTRODUCTION Played by adults and children for centuries as a fun and entertaining way to challenge the mind, chess is one of the most popular games in the world. Benjamin Franklin wrote in 1779 that the game of chess “is not merely an idle amusement (since) life is a kind of chess, in which we have often points to gain, and competitors or adversaries to contend with, and in which there is a vast variety of good and evil events that are in some degree the effects of prudence or the want of it.” Franklin suggests that playing chess develops foresight, circumspection, perseverance, and sportsmanship. Godfrey Harold Hardy, a prominent British mathematician famous for his achievements in number theory, once said, “A chess problem is an exercise in pure mathematics.” The lessons presented here not only can be used as a text for math teachers, but can also be applied by practically anyone who wants to learn the basics of the royal game. Today, educator s and parents have discovered that chess is a wonderful way to teach young children mathematical concepts and important thinking skills that they can use their entire life. Chess also has connections to standards in the fields of language arts (reading, writing, oral presentation), social studies (geography – longitude and latitude, mapping), and science (graphing and critical thinking skills). Here are some other benefits of learning chess: Improves cognitive skills (including concentration, pattern recognition, decision making, algebraic and geometric thinking, problem-solving, spatial reasoning, and critical thinking) Improves self-confidence and self-worth Increases attention span Increases memory capacity

Encourages understanding of choice and consequences for problem- solving…helps students realize that they are responsible for their actions and must accept the consequences of those actions Offers a logical pattern and critical-thinking system Provides competition, fostering interest and pro moting mental alertness Offers a variety of quality analytical problems from which to choose Teaches good sportsmanship Improves communication through written and oral presentation skills Creates a learning environment organized around games, which is one of the most motivational tools in a teacher’s repertoire to encourage problem-solving and spend time quietly immersed in log ical thinking Many studies (see www.uschess.org) show that chess helps children with cognitive development and increases math and verbal test scores. Educators have also noted that chess helps to raise self-esteem. Major universities around the country recognize that top chess players make exceptional students and are offering everything fro m partial to full four-year scholar ships for high school scholastic chess state champions. The growing list of prominent colleges offering chess scholarships includes the University of Texas at Dallas, University of MarylandBaltimore County, Louisiana State University, Ole Miss, University of New Mexico, Mississippi State University, University of Connecticut, Mor ehead State University, Jackson State Univer sity, and Texas A&M. This book is specifically designed for teachers who wish to incorporate chess into their math curriculum. The teacher will find that chess is an effective teaching tool because it is a fun game for students to learn. The success of any teacher is greatly determined by their ability to get inside the student’s head and relate to the student, at the student’s level. Of course,

teachers who take the time to improve their own chess games will be more comfortable and effective relating chess skills to their students. Ten basic chess lessons are presented in this book. At the end of each lesson, there is an exemplar that covers the material presented in the lesson. Additional exemplars that overlap chess with other mathematical concepts can be found in Appendix C. The exemplars are geared for students who are typically fourth grade and older. Younger students, who are good chess players, are capable of solving many of the exemplars, but expect their solutions to be in a simpler format than the older students. Exemplars can be solved individually or in groups, orally or written. You may wish to revisit these ten beginner chess lessons at some later date as a refresher course, since chess topics register at different times for different students. In Appendix A, the chess curriculum presented in this book is compared to a sample second-grade math alignment and is correlated to the National Council of Teachers of Mathematics Standards. Students of any grade level, from kindergarten age on up, can benefit greatly from playing chess. Included throughout the book are analogies and stories that my students have helped to develop over the years. Using stories and analogies to teach chess concepts is an effective teaching tool because they hold the student’s attention and keep the class exciting. The thinking process learned in chess has strong correlations to the world of sports. “It is like a chess game” is a favorite cliché of commentators when describing the coach’s strategy in sporting events. I have interviewed several players from the Denver Broncos for my chess column in the  Rocky Mountain News who were both eager to say that chess helped their thinking processes and understanding of football strategies during their profession football careers. Around 80% of my students who also play soccer are the

mid fielder on their team, the thinker who sets up the plays. I often teach parallels between chess and sports strategies to my students (for example, the two-on-one concept and a breakdown of how to think during the game). Years ago, the mother of a child I once taught told me that the boy’s tennis coach was so impressed by the way he mentally worked out his tennis strategy that he compared it to a chess game. Ironically, at that same meeting, she told the tennis coach that she had to cancel the next tennis lesson because her son was attending chess camp that week! Scott Treibly, tennis coach to the Association of Tennis Professionals and Women’s Tennis Association, says, “Tennis is like a moving chess board. There are pieces on either side of the net which position for victory. You have to anticipate two and three moves in advance in order to win. I advise my students to play chess to sharpen their strategic skills in tennis.” It is well known that World Boxing Champion Lennox Lewis uses chess as a training tool to help him mentally prepare for boxing matches. Medical studies have shown that the breathing patterns of chess masters during a game are quite similar to those of a boxer during a fight because of the related punch, counterpunch, and strategy of both games. Chess also lays a solid foundation for the student’s realworld business success later in life. Time-management skills, in particular, are developed through chess. The chess player has a limited amount of time to complete the game and must budget this time carefully by picking the correct points in the game to spend his thinking time. In life, and in the classroom when taking tests, the student needs to learn how to prior itize his time efficiently. A chess problem also forces the student to look at both sides of a situation. This is a breakthrough concept for most young children who are mainly focused on themselves. In chess, a young student learns that his opponent’s moves and pieces are just as important as his own. Debating skills, where the debater must consider both sides of an argument, are

developed through chess. Cause and effect taught in history and mapping taught in geography are also good examples of academic connections to chess. Both time-management skills and the ability to assess a problem from different perspectives are critical for attorneys, businessmen, and salesmen. From a pure calculation perspective, chess can help develop logical and critical-thinking skills needed for engineering, which I can personally attest to as a civil engineer. Chess has been described as both a science and an art for m. The different ways that a chess position can be evaluated are analogous to different interpretations of literature or history. A chess game is like solving a puzzle in that different patterns must be considered. Specific calculations are required and the environment has to be modified in order to solve the problem. Evaluating chess strategies teach different ways to look at life and solve life’s problems. Good sportsmanship and etiquette, like shaking hands after the game, is also reinfor ced through chess. Children who learn chess in kindergarten or first grade will be introduced to these math concepts at an earlier age. Many of these younger children have no problem understanding basic chess concepts. When these chess concepts are taught to older students, they become reinfor cement exercises, not introductor y concepts. You will definitely observe a positive correlation between the better math students and the better chess players in the class. Most good math students will pick up chess quickly. But chess is also an effective teaching tool for the students who have difficulty with math, because it teaches math concepts in the context of a game, making it more fun and interesting. Some additional chess topics beyond the scope of this book that the teacher can incorporate into their curriculum are zugszwang, outflanking, the overworked piece, creating passed pawns, outside passed pawns, pawn arrows, space advantages, and castling strategies.

Teacher tips for common situations that surface while the children are playing are given in the Teacher Tips for Chess Play Time section. This curriculum has been successfully piloted in second and third grade classrooms in Colorado’s Cherry Creek School District. If you want to learn more about the game and hire a coach in your local chess community, see www.ColoradoMasterChess.com for qualities you should look for in a chess coach. In 2006, I published Chess Workbook for Children which is a companion book to Teaching Chess in the 21 st  Century. Both books can stand alone or be used together as a set to give a complete introduction to chess.

CHESS BASICS LESSON 1

“The chess-board is the world; the pieces are the phenomena of the universe; the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance.”

Thomas Henry Huxley (1825-1895) English biologist

This lesson introduces terminology, piece movements, and chess basics. Parts of this lesson may be review for some of the children who already know how to play chess. The teacher will discover that some of the students may not have learned the rules correctly. Topics to cover in Lesson 1: Piece names and abbreviations Names of the squares Define ranks and files Piece movements and values Guidelines for exchanging pieces Check Checkmate "Touch move" and "touch take" rules

Setting up the board

Piece names and abbreviations Introduce each chess piece to the class, spell it for them, and give them the piece’s symbol. Note that for a pawn, the capital letter P is omitted and a __ (blank) is used as a default. N is the symbol for knight because K is taken for the king. Pawn

Knight

Bishop

Rook

Queen

King

Names of the squares This is where the teacher introduces concept of the coordinate plane to describe location. Typically this is a 3 rd grade curriculum subject. Don’t worry though, it is an easy concept for most 1st graders. Ask the children, “How many squares are there on a chessboard?” You may get a wide range of answers. For older students, show them that 8 x 8 = 64; for younger students, count out all 64 squares. Ask the class, “How many squares are white?” and “How many squares are black?” Of course, the answer to both of these questions is half of them or 32 (this is a good place to introduce or reinfor ce the concept of one-half). Then tell the students that all of the squares have a name… and that chess square naming is similar to the game Battleship, which many of them may have played and will relate to. Point out that lower-case letters are always used when designating a square. Give a couple examples, and then move the king ar ound to different squares and go around the room asking them to call out the cor rect square.

The White king is on a2, the White knight is on g 7, the White pawn is on f3 , the Black queen is on e1, and the Black bishop is on b7.

Define ranks and files White’s pieces always start on the side of the board on rows 1 and 2. Black’s pieces line up symmetrically with the White pieces on the other side of the board on rows 8 and 7. The coordinate plane numbering system in chess is called algebraic notation. In chess language, r anks ar e rows and files are columns. Ranks are numbered from each player’s perspective, starting with the 1st  rank closest to the player. Note that White’s ranks correspond to the algebraic notation numbering system and Black’s ranks are reversed, or upside down. The 8 th rank is defined as the rank fur thest away from the player. In other words, on the previous diagram, the White king on a2 is on White’s 2nd rank and Black’s 7th rank. Columns are referred to as files, identified by a letter from a to h, with the a-file located on White’s left-hand side. The Black queen in the previous diagram on is on the e-file.

Piece movements and values Show the class how each piece moves. A player cannot capture his own pieces. Examining a piece’s head gives a clue as to how it moves.

Pawn Pawns are the only piece that cannot retreat. Each player begins the game with eight pawns. White’s pawns are lined up on the row corresponding with 2; Black’s pawns start on the ro w cor responding with 7. The pawn is the only piece that captures differently than it moves. Pawns capture one square forwards in a diagonal direction. In medieval times, the pawn was a foot soldier, holding a shield in front of him, for protection. The soldier would stab at his adversary diagonally out to the front, not directly forwards because his shield would be blocking the sword. In the diagram below, the pawns can capture an opponent’s piece if that piece is on a squar e marked by a black star. If a pawn is on its starting square, it can move one square forward or two squares forward, assuming no piece is blocking its path. Once a pawn has made its first move, it can then only move one square forward at a time, unless it is capturing a piece, in a forward, diagonal direction. The goal of every pawn is to get to the eighth rank (and score a touchdown), where it promotes on that square to a

queen, rook, bishop, or knight. This is the first of three special chess rules where a piece makes an unusual move (the other two special moves are castling (Lesson 2) and en passant  (Lesson 8). The queen is usually selected as the promotion piece because she is the most powerful. Note that pawns typically promote in the endgame because this is the phase of the game where the opponent has the fewest pieces available for defense. The greatest number of queens possible in a game for either player is nine, since each player starts with one queen and could possibly promote all eight pawns. I tell the students that the greatest number of queens that I have ever had is two, since the object of the game is checkmate the king, not to promote all your pawns. Since the pawns have the lowest value of any piece, we will arbitrarily assign a value of one to the pawn. To keep things simple, the values of the other pieces are whole number multiples of the pawn’s value.

 Knight  The knight loo ks like a hor se and is the only piece that can  jump over other pieces. Knights move in a capital L shape, two squares horizontally or vertically in one direction and then one square perpendicular to the left or right. Note that the knight moves from a white square to a black square and visa versa. Point out that the knight can eventually move to every square on the board, but it is a slow-moving piece. A knight in the center of the board moves in a circular pattern. Knights capture by landing on an o pponent’s piece, not by  jumping over it. The analogy that I use is if a hor se jumps over your head, you are okay. If a horse lands on your head, you are not okay! Because knights are slow-moving pieces, they like to be located in the center of the board so that they can move to any part of the board quickly. A knight on the edge of the board takes several moves to get to the other side of the board. There is an old chess rhyme, “A knight on the rim is dim.” The rim is the outer edge of the board where the slow-moving knight is restricted, and dim meaning bad. A knight is wor th three pawns.

 Bishop The bishop has a pointed or diagonal-shaped head that looks like a miter or the hat worn by a bishop. The bishop moves diagonally and cannot jump over pieces like a knight can. Note that a bishop is a fast-moving, long-range piece, but is limited to only one color, or 32 squares. At the start of the game, each player gets a white-square and a dark-square bishop. Bishops and knights are referred to as minor pieces. Comparing the two, the knight has the advantage o f being able to touch each of the 64 squares, but he is slo w. The bishop can touch only 3 2 squares, but he is fast. On a chess board that is 8 squares by 8 squares, these powers balance each other out, making both bishops and knights worth about the same. Most

of the students have seen the type of scale that can be balanced out by putting an equal weight on each side. Bishops are equal to knights in strength, and are also worth three pawns .

 Rook Rooks move horizontally (left and right) and vertically (forwards and backwards) in the direction of the cutout portion of the top of the castle on their head. Rooks are fastmoving, long-range pieces that can move to all 64 squares. Rooks, like bishops, cannot jump. Comparing a rook and a knight, both can move to any of the 64 squares, but the rook is fast and the knight is slow.

Therefore, the rook is more valuable than the knight. Comparing a rook to a bishop, both are fast. The rook can move to any of the 64 squares, while the bishop is r estricted to 32 squares. Again, the rook has the advantage. The rook is worth five pawns.

Queen The queen moves horizontally and vertically like a rook, and diagonally like a bishop. She is both pieces all rolled into one. I tell the students that the queen has a pretty crown that points out in all directions (a clue as to how she moves) and is worth nine pawns.

This is why 99% of the time when a pawn is promoted, it is promo ted to a queen. The other 1% of the time, the knight is typically chosen because a knight moves differently than a queen, which may pro ve useful in particular instances. If your queen has been captured, you can place the captured queen back on the board on the square where the pawn promotes. When the original queen is still on the board, and a pawn promotes to give a player a second queen, either flip a captured rook upside down or borrow a queen from another chess set and place it on the promotion square to represent the newly pro moted queen. A pawn placed on its side or two pawns crisscrossed on their side (so they don’t roll around) can also r epresent the promoted queen. Queens and rooks are refer red to as major pieces.

 King The king can only move one square at time in any direction. You can only have one king (unlike checkers) and he is worth infinity. I tell the students that he is valuable, because he is carrying all the gold of the kingdom, and he is slow, because gold is heavy! The other player wants to capture the king and take away his go ld.

Guidelines for exchanging pieces Using this basic point valuation (pawn = 1, knight = bishop = 3, roo k = 5, and queen = 9), I will tell the students that we now have a scale to help us determine which pieces we are willing to trade for each other. I ask the class, “Would you trade a rook for a bishop and a knight?” Yes, because 5 < 3 + 3 = 6. “How about two rooks for a queen?” No, because 10 > 9. “Would you trade a bisho p for three pawns?” Maybe, since they are both worth three. This scale can be used by the teacher to demonstrate many of the math requirements in the Number Relationships part of the curriculum. A player is said to have a material advantage

in chess when he has mor e points (pawns) than his opponent.

Check Check is the term used to describe the situation when a king is attacked by an opposing piece. By the rules of chess, when a player attacks the king and puts him in check, the opponent MUST make a move to escape the check, as he cannot lose his king. There are three possible ways to escape check: capture the checking piece, interpose (or block) the check with one of your pieces, or move the king to a square that isn’t attacked. It is not required to announce “Check,” although most students will choose to do so.

Checkmate Checkmate is when the king is placed in check, and there is no way to escape the check by moving the king to a safe square, interposing a piece, or capturing the piece that checks the king. The object of the game is to put your opponent’s king in checkmate.

In this position, Black is checkmated. The students will later be asked to demonstrate checkmate, which is analogous to proof problem in geometry class. Proof: The White queen

is attacking the Black king, putting him in check. The king cannot move safely to e8, e7, g8, or g7 because the White queen also attacks these squares. The Black king cannot capture the White queen because the White knight protects her. Therefore, since the Black king is in check and has no way to escape check, he is checkmated. Note that the students are not allowed to capture the king if he moves into check or if he doesn’t move to a safe square when he is attacked. In either of these cases, the player made an illegal move and must undo this move and make a legal move to get out of check. Capturing the king of a player who made an illegal move is not checkmate and not the end of the game. Even though you point this out to the class, the majority of the students will capture kings when they play each other. When this happens, explain to them again that they can’t capture the king, and ask what the last move was. Back up the game and have the student who made the illegal move chose a different move that is legal and doesn’t result in leaving his king exposed and in check.

“Touch move” and “touch take” rules “Touch move” means that if you touch a piece, you have to move it (if you can legally). “Touch take” means that if you touch an opponent’s piece, you must take it (again only if the piece can be leg ally captured). A move is completed when you take your hand off the piece. These rules are all strictly enforced in chess tournaments and are good to introduce the student to right at the start of their chess careers. Tell students that it is best to think with their head, not their fingers! Tell students who seem to have a need to touch all the pieces to sit on their hands or put them in their pockets. If one of the pieces is not centered on the square, the player whose move it is can say, “I adjust,” and then center the piece on the square. The player must say, “I adjust,” before touching the piece to negate the touch move rule. Some students will touch a piece, realize that it was a mistake, and

then say, “I adjust,” with the hope to undo the touch move rule. Because the piece was touched first, it must be moved. I relate the touch move and touch take rules to table manners at dinner. I ask the children if their parents allow them touch all the pieces of bread on a plate at the dinner table. No. They have to eat the piece they touch. I call this “touch eat!”

Setting up the board The board is set up the same way for every game, with a White square in the lower right hand cor ner o f the boar d. The White pieces always start on the side of the board with the 1 and 2, the Black pieces on the side with 8 and 7. On the back rank, the pieces are lined up with the tallest (king and queen) in the center and decrease in height to the shortest (rooks) in the corners. In determining which center square the king and queen start on, most players learn that the queen starts on her own color; the White queen on a light square (d1) and the Black queen on a dark square (d8). One of my older students once suggested another way to remember where the king and queen start. The symbol for queen is Q and queens start on the d-file. DQ (or dQ) is the abbreviation for Dairy Queen! The king always starts on the e-file, and kings are males. An easy way to remember this is e-mail! Here is the starting position for the game. White always moves first. Whereas moving first is an advantage at the master level, for beginners there really isn’t much advantage to playing White.

This lesson covers a lot of ground for students who are new to chess and are second grade or younger. There will be

questions from some of the children about how the pieces move and what they are worth for the first several lessons. Most of the children will have these basics figured out after a couple playing sessions. Help them out during chess playing time and in subsequent lessons to reinforce these basic concepts. For the novice teacher, let me clear up any confusion that may exist in regards to r eferr ing to squares or pieces as White and Black. Many chessboar ds and pieces are not actually white and black, but a lighter and a darker color. The lighter color ed squares and pieces are referred to as “White” and the darker color ed squares and pieces are refer red to as “Black.”

Count the material exemplar Task Students are given a group of White and Black pieces in the “Count the material” exemplar task (end of this chapter). Have them add up the piece values to determine whether White or Black is ahead and calculate by how many pawns the advantage is. Ask the student to verify the solution using another method of calculation (regrouping or cancellation method).

Context This task allows the student to identify what each piece is worth in value and demonstrate addition and subtraction skills, regrouping, and associative and commutative properties of addition. The object of this exercise, from a chess perspective, is to calculate the difference between piece values remaining on the board in o rder to determine who is ahead in material in the game and by how much.

Task purpose This task gives the student the opportunity to demonstrate different ways to use addition and subtraction, regrouping, and the associative and commutative properties of addition and subtraction to arrive at the correct solution.

Student task Students will try to ar rive at the solution that Black is ahead by three pawns (which equals a bishop or a knight). To verify the solution, the student may simplify the math by canceling out like pieces for each side or regroup the pieces (easiest to do in groups of ten).

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. Critical-thinking skills are used to arrive at the correct solution using different methodologies where the concept of adding up piece values can be taught with any other subject where the students are required to add or subtract

different quantities. A money example, where making change is required, is a goo d real-life interdisciplinary link.

Teaching tips Students learn what the pieces are worth and why in Lesson 1, along with piece movements. Piece values will be reinforced in later lessons as students are asked to share their ideas and evaluate positions. Since the students will play against each other the last half hour of each session, the teacher should ask the children individually during their games, “How many points do you have?” This gives the students who don’t understand the concept as quickly individual help with piece values. As the students are playing, the teacher can help students individually by sho wing how to cancel out like pieces (associative property) and regrouping by tens. This concept should be easily mastered by all of the students by the end of the course. The teacher can create similar exemplars with different piece combinations.

Concepts to be assessed and skills to be developed Addition Subtraction Regrouping Commutative and Associative Pro perties (used by cancellation of like pieces) Problem-solving skills Reasoning and decision-making Critical thinking Number sense Communication

Suggested materials

The students will be given a copy of the task, “Count the material,” that shows the following figurine chess pieces on it.

Solution White has 24. Black has 27. Black is ahead 3 pawns (which equals a knight or bishop). The basic solution  is to add up all the Black pieces (27 pawns) and add up the White pieces (24 pawns) and calculate the difference (3 pawns). 27 (3+1+1+1+1+3+3+5+5+1+3) - 24 (9+3+1+1+5+3+1+1) = 3

Cancellation solution: Cancel out like pieces for White and Black (same idea as commutative and associative properties), leaving…

Black is ahead 3+5+1+3 – 9 = 3 or (3+5+1) + 3 – 9 = 3

Regrouping solution: simplify the math)

Regrouping into gr oups of ten (to

or White: 10 + 10 + 4 Black: 10 + 10 + 7 Canceling out the gr oups of 10, 7 – 4 = 3 pawn advantage for Black

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t remember what each piece is worth. No logical solution is given.

Apprentice Student remembers what each piece is worth, but the math doesn’t add up to the correct solution or the math addition is correct, but the piece values are incorrect.

Practitioner The practitioner understands the problem and explains correctly how he arrived at the correct answer using one of the solutions.

Expert The expert understands the problem and explains clearly how he arrived at the correct answer using two or more of the given solution methods. The solution is correctly verified by using another methodolog y.

Count the material Task Add up the value of the pieces below and determine if White or Black is ahead and by how many pawns. Check your solution by using a different method of calculation. Clearly explain your solution for each method used.

OPENINGS LESSON 2

“But the enemy has the move, and he is about to open his full game. And pawns are as likely to see as much of it as any. Sharpen your blade!”

J. R. R. Tolkien (1892-1973) Oxford professor, author of The Lord of the Rings

The Openings lesson should immediately follow the Chess Basics lesson because the students will play the opening moves in every game during their chess play time. By following this lesson order, you won’t be reinforcing the bad habit of opening on the edge of the board that some of the children will develop by moving the rook pawns first. The opening is typically the first eight to ten moves of the game. The tendency in the opening for new chess players is to move the pawns on the edge of the board and bring the rooks out early. Beginning students tend to resist moving the center pawns (which opens up the king) because they are afraid of getting checkmated quickly. Once the student learns how and why to castle, which gets the king out of the center and develops the rook, the fear of moving pawns in the center tends to g oes away.  Developing a piece means moving the piece off its starting square to a better square, increasing its potential. In chess

terminology, pieces are refer red to as knights, bishops, rooks, and queens. Pawns are referred to as pawns, not pieces. In medieval times, pawns were commoners, not real people, in their class distinction. Once again, here is the starting position for the game.

White always moves first; after that, the two players alternate taking turns for the rest of the game. In master games, White wins more games than Black because of the advantage o f the first move. In chess tournaments, players tend to alternate playing White and Black. When the students play each other at the end of the lesson, often both players will want to play White. Instead of a coin flip to determine co lor s, take a White and Black pawn, mix them up behind your back, and with a pawn in each closed hand, put both hands out in fr ont of the children and have each of them pick a hand to determine their color. Explain the concept of probability and that they each have a 50-50 chance (same odds as a coin flip) of playing White. If they have time to play a second game, have them switch color s from the first game. The beginning student only needs to learn basic opening principles at this stage in their chess development. A common mistake made by inexperienced chess teachers is teaching specific opening variations or lines, which requires more

memorizing than learning.

The goal of this lesson is to teach three important opening concepts: Try to control the center  of the board (e4, e5, d4, and d5) with pawns and then support the pawns with the pieces. Develop pieces quickly and efficiently so that each piece can get to an active square in the least number of moves possible. Develop the knights and bishops first, and then the major pieces (queens and rooks). Try not to block the diagonals for the bishops with pawns. Move the roo ks to open files. Do not develop the queen too early. If she enters the game too quickly, an experienced player will develop his pieces while attacking the queen and force her to move again, wasting time. If the player isn’t looking at his opponent’s threats, the queen usually gets captured quickly. Often when a beginning student brings the queen out early to capture a piece, on the next move, he retreats the queen back to her home square. This is not always the best chess move, but the student who retreats the queen back to her home square shows that he is paying attention to the lesson and r ealizes the danger of bringing the queen out early. This practice is fine for beginning students. Castle early  to safeguard the king by getting him out of the center of the board. The time to centralize the king is in the endgame, because he is a strong fighting piece with little opportunity to get checkmated when there are only a few pieces left on the board. Castling also develops a rook by bringing it to the center of the board. Try not to push pawns forward in front of a castled king because this opens space in front of him, making him more vulnerable to attack. These pawns cannot move backwards later to defend the key squares in fro nt of the king.

Castling Castling is the second special move and is the only time that two pieces (king and rook) can be moved in one turn. A player can castle only once per game. In order to castle kingside, the king knight and king bishop must move first so that the squares between the king and rook are open. When castling, you must touch the king first (because of the “touch move” rule…since moving the rook first would be a complete legal rook move) and move it to the g-file (g 1 for White and g8 for Black) and then, with the same hand, pick up the rook and put it on the f-file (f1 for White and f8 for Black). The king always moves two squares when castling. Castling kingside is scored 0-0. In order to castle queenside, the queen, queen bishop, and queen knight, must first be moved off of their starting squares. To castle queenside, pick up the king and move it to the c-file (c1 for White and c8 for Black) and then, with the same hand, pick up the rook and put it on the d-file square (d1 for White and d8 for Black). Castling queenside is scored 0-0-0. The king moves two squares when castling on either side and the rook jumps over him. Some students will incorrectly think that the king and rook switch squares. Besides having all the pieces cleared out so that the king can “see” the rook, it is also a requirement that the king has not previously moved in the game  and that the rook that he is castling with also has not previously moved. You ar e also not allowed to castle to escape check, through check, or into check . The diagrams below show a position before castling, with both sides castled kingside, and both players castled queenside. In a real game, each player has the choice of which side to castle on, or to not castle at all.

Before castling

Both players castled kingside

Both players castled queenside

Opening Presents story for chess openings I made up a story that is fun and easy for the students to remember that effectively teaches the basic opening concepts. The childr en will remember the story, be entertained by it, and ask to hear it over and over. Teachers who are experienced chess players may have their o wn style in teaching the opening principles. The moves I chose are not the main line of any opening that a master would play, but are desig ned to teach the basic principles. I will give detailed explanations of each move for the novice chess teacher.

First, I ask the students, “What happens on Christmas morning?” The usual answer is that they open presents. That’s right. There are presents for the entire family. In chess, you are in charge of the White family or the Black family. Every time a piece moves, the piece opens a present and is happy. Next, we must identify the family members. The king is their dad, the queen is their mom, the knights and bishops are their brothers and sisters around their age, the rooks (a little more valuable and older) are their teenage brothers and sisters, and the pawns are the babies. A big family! Who opens their presents first? They usually say that the children around their age do. That is correct. What pieces are they? The students are the bishops and the knights. The goal of the opening is to have a happy family! Is it a good idea to make a lot of king moves? No…that is like the dad opening his presents first, while everyone else watches. How about queen moves? No. That is like the mom opening her presents first, while the children their age watch. What about pawns? In real life, babies will open presents, if they can get their hands on them…but babies are too young to know what presents are…so the pawns won’t be unhappy if the children their age (the knights and bishops) go first. The rooks (teenager s) usually let the younger children go first. The children (knights and bishops) around the age of the

students in the class usually go first. Well, the knights can open a present on the first move, because they can jump. What about the bishops? Bishops can’t move on the first move of the game, because the pawns block them. There are babies on their presents. What do you have to do first, if there is a baby on the present? Move the baby! I also point out that there are four children (two knights and two bishops) that want to open presents. Remember the goal is to create as much happiness as you can in the family. What would happen if one of the knights or bishops made a lot of moves or opened a lot of presents at the start of the game? The brothers and sisters would be unhappy. Therefore, you want to take turns, so all the children ar e happy.

Sample Game

(You may want to see Lesson 3,

Scorekeeping.) 1.e4 e5 (controlling the center with pawns)

Now we want to develop (open a present with) the knight on g1. The choices are 2.Nh3, 2.Nf3, and 2.Ne2. I ask them which one they think is best. 2.Nh3 Remember the old chess rhyme? ”A knight on the rim is dim.” The rim of the board is the outer edge. Because

knights are slow-moving pieces, they want to be in the center of the board where most of the action is and they can get to any part of the board quickly. A knight on h3 would have a long journey to the queenside. 2.Ne2 This attacks the d4 center square. But let’s think of everyone’s happiness. The bishop on f1 was happy when the baby (pawn) on e2 moved off his pr esent. Now his brother, the knight, jumped onto his present and made him sad again. A good strategy is to avoid blocking the bishops, especially with pawns, so that they can develop to active squares. 2.Nf3 The best knight move because it develops toward the center, attacking d4 and the pawn on e5. 2.Nf3 also doesn’t block the bishop on f1.

2.Nf3 Now I point out to the students that after your opponent makes his move, always ask yourself, “What is he threatening?” Figure out what he is trying to do to you before you try to figure out what to do to him. Remember, his pieces are as important as yours. (Chess helps children realize that they are not the center of the world. In the beginning, many children won’t pay attention to what their opponent is doing and lose a lot of their pieces because they didn’t take the time to see which ones are under attack.) Black should notice that his pawn on e5 is attacked by White’s knight. The pawn needs to be protected. Can this be achieved while opening a present with a child their age? Yes, by either 2…Nc6 or 2…Bd6. Which move is better? The problem with 2…Bd6 is that the bishop blocks the d7 pawn (a center pawn), which in turn blocks in the bishop on c8. Black plays… 2…Nc6 White asks himself, what is Black threatening? Nothing, he is protecting the pawn and developing the knight. Okay, let’s open a present with the bishop on f1. Ask the students which square they think is best. 3.Bc4 or 3.Bb5 are both main line chess openings. 3.Be2 is passive, 3.Bd3 blocks the d2 pawn, which in turn blocks the bishop on c1, and 3.Ba6

leaves the bishop vulnerable to capture by Black’s a6 pawn. For this example, let’s play…

3.Bc4 What does this threaten? The f7 pawn is now attacked, but is also pro tected by the Black king. The bisho p is worth 3 and pawn is worth 1, so taking on f7 would be a mistake for White because it gives up material. 3.Bc4 is a good move because it attacks one center square (d5) and develops the bishop. Say Black will now develop his f8 bishop. Ask the children where they think the bishop should go. 3…Be7 is passive, 3…Bd6 blocks the d7 pawn, 3…Ba3 loses the bishop (to the pawn or knight), 3…Bb4 is okay, but 3…Bc5 looks like the best move since it also attacks the d4 square (a center square). 3…Bc5

This attacks the f2 pawn, which is defended by the king. What should White play? Good moves are 4.Nc3 because it develops another piece, 4.d3 because it opens up the diagonal for the dark squared bishop, and 4.c3 since it threatens 5.d4, establishing a strong pawn center. I suggest to the class that castling is White’s best move because it is impo rtant to get the king out of the center of the board as soo n as possible.

4.0-0 Castling has the double benefit of getting the king to safety and it develops the rook. In the opening presents story, recall the rook is a teenage brother or sister. When you castle, not only does your dad (the king) get a present, but I ask the class what they think the best present for a teenager would be…a CAR!! (I have heard everything from a book to a cell phone to a girlfriend!) I tell them that a car is the best present for a teenager, and you only get a car by castling. Since you can only castle with one of the rooks, I tell them that castling on either side gives both teenagers a car, so they don’t have to fight over it.

I tell them that many years ago the children in one o f my kindergarten classes suggested that if you don’t castle, your teenagers get a worm! Of course, the car is a much better present than a worm. (As the children ar e playing, I ask the students who have castled what kind of car they would like … and the students who don’t castle what kind of worm they would like! Most of the children g et the point that castling is go od thing to do because they get a car.)

It is normally best to castle as early in the game as you can. A teenager can drive a car at sixteen or nineteen years old. Most children say that they would want a car when they are sixteen, the younger age. Some say nineteen, because they will be more responsible then! Castle early and get your car when you are as young as possible. Of course, they will feel this way when they are sixteen.

4…Nf6 This is a good move because it opens another present and prepares to castle or get a car. Black threatens the pawn on e4. So White opens a present and defends the pawn at the same time by playing… 5.Nc3 playing… 5…0-0

Black can now get a car for his teenagers by

This is a good time to point out that the position is symmetrical (usually one of the students notices that Black is copying White). Define symmetrical for them. Which of White’s children hasn’t opened his first present? The bishop on c1…but there is a baby on the present…so we must first move the baby. 6.d4 looks like a good move that controls the center, but the pawn would be attacked three times (pawn, knight, and bishop) and only defended once (knight and queen). This would lose the pawn. So White plays…

6.d3 Say that Black continues to copy White and plays… 6…d6 White’s best dark-squared bishop moves are 7.Bg5 or 7.Be3. Let’s say he plays…. 7.Be3 Attacking the bishop on c5. Have Black play… 7…Bxe3 Capturing White’s bishop. I tell the class that Black’s bishop grounds White’s bishop and takes away his present for Black’s children to play with. Usually at least one of the students refers to capturing as killing. It is a good idea to correct this terminology to capturing (the chess term) or grounding (the opening presents story term) for obvious reasons. So White grounds Black’s bishop by playing…

8.fxe3 Now Black can have his last child open a present by playing… 8…Bg4

All the younger children have opened their first present (and are happy). In master play, sometimes a minor piece moves two or three times before another minor piece makes its first move. There are exceptions to all chess principles, but this topic is beyond the scope of a beginning class. The goal at this level is to get the students to understand that it is important to get all the pieces developed and into the game. Now, after letting her children go first, White’s mom can open her first present. Both 9.Qd2 and 9.Qe2 are fine here. Say White plays…

9.Qd2 Black’s queen (mom) now opens her first present, so… 9…Qd7 The rooks in chess work best when they are in contact with each other and no other piece is between them. Rooks also like open files. (In this position the f-file is a halfopen file for White.) I ask the children if when they are

teenagers (rooks), do they think they would rather hang out with adults (king and queen), babies (pawns), children their age now (knights and bishops), or other teenagers (rooks). They usually say other teenagers. Rooks like to be together. Say the game continues…

10.Rad1 Rad8 Since both of the rooks can move to the d-file, you must designate which one moved when you record the scor e. In this case, both players mo ved the a-roo k.

We are now done with the opening and are into the middlegame. The opening goals are usually accomplished in the first ten moves or so of the game. Here we can say that White and Black both did a good job accomplishing their opening goals: control of the center, all the children (knights and bishops) opened at least one present, equal-valued children got grounded (the dark-squared bishops), the teenagers g ot cars (castled), not wor ms, the teenager s (r ooks) are connected, the queens (moms) didn’t come out early, and the pawns in fro nt of both castled kings haven’t moved and are providing protection for the kings.

Optional part to openings lesson: Scholar’s Mate I do want to mention one more thing that doesn’t need to be addressed, unless it comes up. Often, one or more of the students has been exposed to the Scholar’s Mate, or what children today call the “Four-Move Checkmate”. The Scholar’s Mate is not good chess because one side (usually White) brings the queen out early and tries to checkmate Black quickly on f7 with the aid of a bishop. If Black doesn’t see the threat (because he didn’t ask himself, “What is White threatening?”), the queen move (which is bad because the queen shouldn’t come out early because of the danger of being attacked and chased all over the board by the other player’s knights and bishops) works and the game ends with a quick checkmate. This gives immediate gratification to the player who mistakenly brought the queen out early and hoped that his opponent would miss the checkmate threat. You should ALWAYS assume the other player makes the best move. Here is a typical Scholar’s Mate pattern. A question mark after a move identifies it is a bad move (See Lesson 3 –  Scorekeeping).

1.e4 e5 2.Bc4 Nc6 3.Qf3? (or 3.Qh5? g6 4.Qf3)

Bringing out the queen early and threatening checkmate on f7. 3…Bc5?? 4.Qxf7 mate.  I point out that if Black only plays 3…Nf6 and then 4…0-0, White not only wasted a queen move and placed the queen on a square where she soon may be chased away (by maybe …Nc6-d4), but also took away the natural f3 developing square from his knight. Again, don’t bring this up unless one of the students does (and it will occur frequently). It is not a good idea to encourage immediate gratification by teaching bad chess principles.

Find the best opening move exemplar Task The student explains the relative strengths and weaknesses of five different possible opening moves for White that are suggested for the position on the “Find the best opening move” task page.

Context This task integrates piece movements with achieving the correct thought processes and principles to start off the game correctly.

Task purpose This task will show whether or not the student has developed a clear gr asp of chess opening principles.

Student task The student will consider five possible opening moves and explain why each is a go od o r bad move.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. Subjects where critical thinking skills are applied using the Scientific Method and a correct plan of action must be determined (debating would be a good

example; or a history lesson where the teacher analyzes different battle plans by gener als in war situations).

Teaching tips Openings principles are covered in Lesson 2. It is okay if students chose to phrase their answers in terms of the Opening Presents story.

Concepts to be assessed and skills to be developed Understanding o f opening pr inciples Problem-solving skills Reasoning and decision-making Critical thinking Communication Understanding of piece movements Use of coor dinate plane to describe locations

Suggested materials Give students a copy of the task, “Find the best opening move”.

Solution

5.Bd5 A bad move because the bishop has moved twice. 5.Nc3 A go od move because it develops another piece. 5.Qd2 A bad move because it blocks the bishop on c1 and brings the queen out early. 5.Na3 A bad move because it puts a knight on the rim o f the board, which limits its capabilities since it is a slow-moving piece. Knights should move toward the center of the board in the opening. 5.0-0 A good move because castling gets the king out of the center of the board where the action is and develops the rook.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand how the pieces move or the goals of the opening. No logical solution is given.

Apprentice The apprentice correctly identifies whether some of the moves are good or bad, but doesn’t come up with all of the correct reasons.

Practitioner The practitioner understands the problem, correctly selects the good and bad moves, and for the most part, explains his answers clearly.

.

Expert The expert clearly understands the problem, arrived at the correct solutions, and clearly explains why each of the moves are good or bad.

Find the best opening move Task In the position below, with White to move, explain why you think each of the suggested moves are g ood or bad.

5.Bd5 5.Nc3 5.Qd2 5.Na3 5.0-0

SCOREKEEPING LESSON 3

“The chess pieces are the block alphabet which shapes thoughts; and these thoughts, although making a visual design on the chess-board, express their beauty abstractly, like a  poem. …I have come to the personal conclusion that while all artists are not chess players, all chess players are artists.”

 Marcel Duchamp (1887-1968) French artist

Learning chess notation is essential for reading chess books and keeping score in tournament play. Most chess books published in the last fifteen years are written in what is called algebraic notation. The basics for scorekeeping were introduced in Lesson 1 and reinforced in Lesson 2. All you have to know to keep score is the symbol for each piece (K for king, Q for queen, R for rook, B for bishop, N for knight, and the absence of a letter or a blank for a pawn) and how to name the squares (a location designated by an ordered pair on the coo rdinate plane…a lower case a-h, then a number 1-8 ). Algebraic notation combines two concepts: the piece that moves and the square it moves to. In the pre-1990 era, most chess books were written in descriptive notation. Algebraic notation has pretty much replaced descr iptive notation because it is more universal and easier to understand. In descriptive notation, if on the first move, White moved the pawn in front

of his king two squares forward, it would be scored 1.P-K4. In algebraic notation, this move is scored 1.e4. Recall that castling kingside is designated 0-0, and castling queenside is 0-0-0 . Therefore, 0-0-0 for White would mean that the king moves from e1 to c1 and the queen’s rook moves from a1 to d1. To designate a capture, an x is placed between the piece making the capture and the square that the captured piece is resting on. Using an x for a capture can be optional since an opposing piece on the named square must be captured when landed upon. So if a White knight captures Black’s queen on her starting square, it would be scored either Nxd8 or Nd8. I recommend teaching the children to use an x for captures. A + sign is written after a move that puts the king in check.

In order for the author to explain the quality of a move, the following punctuation marks are used: !! is a brilliant move, ! is a good move, !? is a move deserving attention, ?! is a questionable move, ? is a mistake, and ?? is a blunder. Here are specific cases using the position below that will help clear up any potential confusion.

 Pawn captures: Say it is Black’s 32 nd  move and he captures the bishop with his g -pawn. It would be sco red, 32…gxh4  Promoting a pawn: It is White’s 45 th move and he promotes the pawn to a queen, while putting the Black king in check. This move would be scor ed, 45. a8=Q+ Two pieces of the same type move to a square in common to both of them: In this case the specific piece that is moving must be designated. First say on White’s 37 th move, he moves his rook on a1 to c1. (Note that the f1 rook can also move to c1). This move would be scored 37.Rac1 (as opposed to 37.Rfc1). For a second example, say it is Black’s 40 th  move and he moves the knight on c2 to d4. Since either knight can move to d4, the move should be written 40…N2d4. Note that 40….Ncd4 doesn’t tell which knight moved, since they are both on the c-file. Give the students a blank copy of the chess scor e sheet on the page befo re Appendix A. Then make the first 15 moves o f this fictitious g ame while each student records the moves. The

moves on their scor e sheet should correspond to the moves below. The final position on your chess demo board should match the following diagr ammed position.

1.c4 c5 2.Nf3 Nf6 3.d4 cxd4 4 .Nxd4 e6 5.g3 Bb4+ 6.Nc3 0-0 7.Bg2 Nc6 8.0-0 Qa5 9.Ndb5 a6 10.Nd6 Bxc3 11.bxc3 Qxc3 12.Bg5 Rb8 13.Qa4 b6 14.Rac1 Bb7?? 15.Rxc3

Scorekeeping exemplar Task The teacher will make the moves on the demonstration board from the famous game between Morphy vs. The Duke & The Count from 1858 as the students record the game on a blank score sheet.

Context This task is about writing chess moves on a score sheet by identifying the moving piece and the square it moves to. Moves should be written with good penmanship so that the student could r eplay the game at a later date.

Task purpose This task allows the students to demonstrate their knowledge of chess scorekeeping in algebraic notation.

Student task The student will write down the moves from the game, Mor phy vs. The Duke & The Count (from 1858 ), in algebraic notation.

Time required 30 minutes for students third grade or younger, 20 minutes for older children.

Interdisciplinary links

Students will use written- or oral-presentation skills to explain their solution. Good penmanship and distinguishing between capital and lower-case letters is important in chess scorekeeping. Geography, using latitude and longitude, to identify a location using a two-dimensional coordinate plane is a link.

Teaching tips The teacher can select any short game that they may prefer to use. The game that I selected is a short, classic game that should be interesting to the students. If they didn’t keep score back in 1858, we wouldn’t be able to enjoy it today! The teacher may make some comments about the moves of the game to explain what is happening. This exemplar requires direct teacher interaction as the teacher makes a move, and waits for the students to record it on their score sheet. The teacher may wish to, in a one-on-one setting, have the student play back the game from their score sheet on a chess board, with the goal of ending up with the final position given below. The good moves in the game below have an exclamation point after the move (point out the good moves to the children when moving the piece, as a clue for them to use an !). Paris, France – 1858; Paul Morphy–Duke of Brunswick & Count of Isouard

1.e4 e5 2.Nf3 d6 3.d4 Bg4 4.dxe5 Bxf3 5.Qxf3 dxe5 6.Bc4 Nf6 7.Qb3 Qe7 8.Nc3 c6 9.Bg5 b5 10.Nxb5! cxb5 11.Bxb5+ Nbd7 12.0-0-0 Rd8 13.Rxd7! Rxd7 14.Rd1 Qe6 15.Bxd7+ Nxd7 16.Qb8+! Nxb8 17.Rd8 mate This game shows that the goal of chess is to checkmate the opposing king, not to win the most material. Point out to the class that in the final position, Black is ahead by ten points (pawns)!

Final Position

Concepts to be assessed and skills to be developed Mapping skills Understanding r ecording a game in algebraic notation Understanding the symbols for each piece Use of coor dinate plane to describe locations Critical thinking Communication

Suggested materials Give students a copy of the scoresheet on the task page, “Scorekeeping”.

Solution

Rubrics and Benchmarks

Novice Student is confused by algebraic notation and doesn’t understand how it wor ks.

Apprentice Student gets some of the moves correct. Apprentice may not include the + sign for checks, may not have the moves in the proper column, may skip a move, may not make capital letters for the pieces or small letters for the squares, or may miss some of the moves altogether. The apprentice may also have trouble r eading his own handwriting.

Practitioner The practitioner understands algebraic notation and records most or all of the moves in the correct location on the score sheet. Practitioner pays special attention to the following moves: Black’s 11…Nbd7 (because both Black knights could move to d7) and White’s 12.0-0-0 (castling queenside). Penmanship is g ood.

.

Expert The expert clearly understands algebraic notation and recorded moves on the score sheet correctly. The expert correctly identified all of the tough moves (11…Nbd7 and 12.0-0-0) and got all of the punctuation correct. Penmanship is excellent.

Scorekeeping Task Write down the moves to the game presented by the teacher.

BASIC CHECKMATES LESSON 4

“I play chess about four hours a day in training camp. You have to decide what move to use, or what combination of  moves. I think less when I box because the reaction time is a lot quicker, but some people call me the chess boxer because they say I think too much in the ring.”

 Lennox Lewis Wor ld Heavyweight Boxing Champion

The object of chess is to checkmate the opponent’s king. This is achieved by attacking the king in a position where the opponent cannot escape the check by moving the king (no available flight squares), capturing the checking piece, or interposing one of his own pieces in the line between the king and the attacker. Young players have a tendency to check the king for the sake of checking. No tournament points are awarded for checks. An important distinction needs to be made here between checkmate and stalemate (a type of draw that will be r eviewed in Lesson 6). By the rules of chess, when it is your turn to move, you must make a move. You are also not allowed to move your king into check where he can be captured.

In the position above, explain to the class that White’s last move was Qf7 (from a7). Now Black must move. Black cannot move to g7 or h7 because the king would move into check from either the White queen or king. Black also cannot move to g8 because the queen attacks it. Since Black cannot move into check, he has no legal moves. Black has been stalemated by White and can claim a draw. A draw is chess terminology for a tie. Tell the students that instead of playing Qf7, White could have played four moves that would have checkmated the Black king. What are they? Qa8, Qb8, Qg7 and Qh7. Show the class why each of these moves r esults in mate. Again set up the position above, but this time add a Black pawn on a4. Unfortunately for Black, he now does have a legal pawn move and he must play …a3 and, in this case, cannot claim a stalemate. As the children play, occasionally one of the students will claim a stalemate because he has no legal king moves. Remember that a stalemate is when you have no legal moves with ANY of your pieces, not just when the king has no legal moves. Some students will move their king on a square next to their opponent’s king. This is illegal because they put their own king in check. To help them understand that the kings can never be next to each other, use an analogy of two magnets,

with the positive poles facing each other. When the magnets get close to each other they repel each other, just like the two kings in chess. Explain to the class why the following position is checkmate.

The Black king is in check because the White queen is attacking him. He cannot move to g8 because the White queen also attacks that square. The h7 square is attacked by both the White king and queen. The Black king cannot capture the White queen because the White king protects her. Therefore, the Black king is checkmated. Proving that a position is checkmate is analogous to what the students will be asked to do in geometry class with proofs.

Ask the students why these positions are checkmate.

Mating with a King and Queen vs. a King The student should learn the basic fundamental of how to checkmate the opposing king with his king and queen. This basic mating concept will occur frequently because one player will often end up with an extra queen due to a pr omo ted pawn. On what part of the board is it easiest to checkmate the king…center, edge, or corner? In order to checkmate the king, we must be put in check and have all his escape squares taken away. Consider these positions.

In order to checkmate the king in the fir st position with the king in the center, White must attack eight escape squares (marked by the black stars) as well as e4, for a total of nine squares. In the second position with the king on the edge of the board, White only has to eliminate five escape squares plus h5, for a total of six squares. In the third position with the king in the corner, White only has to eliminate three escape squares plus h8, for a total of four squares. It turns out the king can be checkmated both on the edge of the board or in a cor ner. Therefore, White’s objective is to use his king and queen to force the Black king to one of these locations. In order to do this, White uses his queen and king to form a “box” around the Black king, and then he must shrink the box. Always make sure that the opposing king has a legal move so that he will not be stalemated.

In this position, the edges o f the box (the way a queen moves) are marked with black stars below.

Note that I am only defining the outer r ectangular edges of the box, not the c1-h6 diagonal inside the box. A king and rook can also checkmate a lone king using the same procedure. While shrinking the box in this case, the king may have to protect the rook from the opposing king. The rook defines the box. The goal of the king and rook is the same as

the king and queen: continue to shrink the box until checkmate is possible. This exercise teaches the students how to extend patterns (by figuring out how to shrink the box) and force checkmate (a geometry proof).

White first plays 1.Qc4+. Defining a different box, by playing 1.Qf4, is another possible solution. The objective is to checkmate the king as quickly as possible. Here is the new, smaller box.

The Black king wants to stay near the center of the board, so he plays, 1…Ke5. I will give the moves, but not all the explanations on the way to forcing checkmate. There are other possible solutions than the one given below. This solution will force the Black king toward the h8 corner. Explain each step along the way to the class and identify the edges of the box after each move. 2.Kc3 Kf5 3.Qd4 (shrinking the box) 3… Ke6 4.Kd3 Kf5 5.Qe4+ Kf6 6.Ke3 Kg5 7.Kf3 Kf6 8.Kf4 Kf7 9.Qe5 Kg6 10.Qf5+ Kg7 11.Qe6 Kf8 The objective is to pin the opposing king against the edge of the board and then advance you own king to help set up the checkmate. White continues, 12.Qd7 Kg8 13.Kg5 Kf8 14.Kg6 Kg8 15.Qd8

mate (Point out that 15.Qc8, 15.Qe8, and 15.Qg7 are all also checkmate).

Queen and Rook Roller Mate Here is another important basic mating pattern for the students to lear n. If a player has a queen and a rook, his king is not needed to help force a checkmate since the queen and rook have the power to form a mating net on their own. Two queens or two rooks checkmate in a similar fashion. The idea is to shrink the box by alternating moves with the rook and queen. The box is marked with black stars.

1.Rc3+ Kd4 2.Qb4+ Kd5 3.Rc5+ Kd6 4.Qb6+ Kd7 5.Rc7+ Kd8 6.Qb8 mate Note that White could even blunder away the queen or rook and still have sufficient mating material to checkmate by shrinking the box and bringing in the king as shown in the previous shrinking the box example. A mating net is a chess term that describes attacking all of the squares adjacent to a king so that he cannot move. After the mating net is in place, checking the king often results in checkmate. Here are a couple other examples of checkmate positions:

Explain the checkmate exemplar Task The student is to analyze the position on the task page, “Explain the checkmate,” and explain why the Black king is checkmated.

Context This task demonstrates the student’s ability to explain why a position is a checkmate and to clearly communicate his reasoning.

Task purpose The students will demonstrate their understanding of a mating net by explaining why a position is checkmate. The students will express the solution in chess notation (using a coordinate plane to describe location). Explaining the checkmate solution is analogous to a geometry proof.

Student task The student will demonstrate the concept of checkmate by explaining that the Black king is in check and then show why the king cannot escape to any of the flight squares.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This type of critical and analytical thinking

applies to any subject where the student is required to articulate his position and then prove his case. The student is introduced to the concept of proofs, a skill required in geometry.

Teaching tips The checkmate concept is explained thoroughly in Lesson 4, “Basic Checkmates,” and taken a step further in Lesson 10, “Checkmate Patterns.” During each half hour playing session, the teacher can r einfor ce the checkmate concept.

Concepts to be assessed and skills to be developed Creates patterns (mating net concept) Use of coor dinate plane to describe location Problem-solving skills Consideration and assessment of different possible move combinations Reasoning and calculation Communication Knowledge of chess piece movements Critical thinking Predicting possible future outcomes of an event

Suggested materials Give the students a copy of the task, “Explain the checkmate”.

Solution

Recall the three ways to g et out of check: 1) move the king to a safe square, 2) capture the piece giving check, or 3) interpose a piece between the checking piece and the king (blocking the check). Interposing a piece does not work when escaping check fro m a knight or a pawn. The Black king is attacked and put in check by the White knight on f5. The White knight on f5 also attacks h6. This knight cannot be captured by any of the Black pieces. The Black king can’t escape to g8 or f7 because of the White bishop on b3. The White knight on g5 also covers f7 as well as h7. The pawn on h5 attacks g6. Therefore, Black is in checkmate because his king is in check and he has no flight squares to escape to.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand the checkmate concept.

Apprentice The apprentice more or less seems to understand the checkmate principle, but doesn’t consider all of the possible flight squares.

Practitioner The practitioner explains all of the reasons why the Black king is checkmated and understands the checkmate concept.

Expert The expert clearly explains all of the reasons why the Black king is in checkmate and gives the logic to back up his solution by identifying the mating net concept clearly and concisely. The expert may even obser ve that White’s last move was Nf5 mate.

Explain the checkmate Task White has checkmated Black in this position. Clearly explain the r eason why Black is checkmated.

BASIC TACTICS LESSON 5

“You sit at the board and suddenly your heart leaps. Your hand trembles to pick up the piece and move it. But what chess teaches you is that you must sit there calmly and think about  whether it’s really a good idea and whether there are other, better ideas.”

Stanley Kubrick (1928-1999) filmmaker, producer

Tactics are the individual battles between pieces that occur during all three phases of the game. In other words, tactics are shor t-term, immediate threats and attacks. The differ ent types of elementary tactics are: pins skewers forks discovered check discover ed attack double check double attack All of these types of tactics are forms of a double attack. Pins and forks are the most common. Combinations are a series of moves used to improve your position that include

some or all of these tactical themes. Combinations have a great range in degrees of complexity. For kindergarten or first-grade classes, the teacher may wish to stop after introducing pins, forks, and skewers. The last four types of tactics may be taught as a separ ate lesson.

Pins A pin is when a long-r ange piece (queen, rook, or bishop) attacks an opponent’s piece that shields a piece of equal or greater value. If the pinned piece moves, the piece behind it would then be vulnerable to attack. It is a metaphor for a real pin: a thin, long, pointed piece of metal that can poke through, say, different layers of fabric, in a straight line. In the diagrammed position below, the White bishop pins the Black knight to the Black king. When a piece is pinned to the king, it is called an absolute pin because the pinned piece absolutely cannot move, since the king would be placed in check. The bishop on d4 would also pin the knight to the king from any of the starred squares along the a1-h8 diagonal. In this case, the less valuable piece, the knight, is in front of the more valuable piece, the king.

Here are examples of pins with a rook:

Since the queen has the powers of both the rook and the bishop, she can pin on ranks, files, and diagonals. Once again, a pin would occur if the queen were placed on any of the starr ed squares.

In the next position, the White knight is pinned to the h1square. If the White knight were to move, Black would play ...Qh1 mate.

Skewers Skewers work the same way as pins, except now the more valuable piece is in front of the less valuable one. Skewers, also known as x-rays, are less common than pins. The less valuable hidden piece is usually ends up getting captured after the more valuable piece in front of it moves to safety. In the first position below, the bishop skewers the rook and the knight and, in the second position, the rook skewers the king and the queen.

Forks A fork is when a piece attacks two or more pieces that are vulnerable to capture simultaneously by the same attacker. (You may use the analogy of eating beans with a fork. The fork is used to stab more than one bean at a time.) Since the other player only gets one move, he has to choose which piece to save. All the pieces have the potential to fork. Here are examples of each type of White piece forking two Black pieces. The starred squares represent other places where the White piece could also fork the Black pieces.

Discovered Check Discovered check occurs when a player moves a piece that shields the opposing king from check by one of the longrange pieces. It is kind of like playing peek-a-boo. When you move your hands from in front of your eyes, you can see the other person.

If White knight moves, the roo k would check the Black king.

Discovered Attack A discovered attack is the same concept as a discovered check, except the attacked piece is not the king.

If White moves the knight, he would cr eate a discovered attack on the bishop, from the roo k on c1.

Double Check Double check occurs when a piece moves to put the king in check while uncovering a long-range piece behind it that also attacks the king. A double check forces a king move because both of the attacking pieces cannot be captured or blocked in only one move.

If White moved the knight in this position to either b4 or d4, the Black king would be in do uble check fro m both the knight and the ro ok.

Double Attack A double attack is the same concept as a double check, except that the attacked piece is not the king.

If White plays either Nb4 or Nd4, the Black pawn would be double attacked by both the knight and the roo k.

Queen pins and forks exemplar Task On the task page, “Queen pins and forks”, Black has a knight on e4 and a king on h7. Write an F on the squares where the White queen can fork the Black king and knight. Write a P on the squares where the White queen can pin the knight to the king. Explain your answer.

Context This task integrates the student’s knowledge of queen movements (diagonal, vertical, and horizontal), terminology, calculating ability, and mapping skills.

Task purpose This task demonstrates the student’s understanding of the queen’s powerful movements and how to attack two pieces at one time. The student calculates different possible outcomes and may express the solution by identifying points on the coordinate plane. The student extends patterns (horizontal, vertical, and diagonal) when finding all of the pinning and forking squares. This exemplar reinforces the power of the queen.

Student task The student will locate the Black pieces on the twodimensional coordinate plane and mark the squares where possible forks and pins from the enemy queen can occur.

Time required 10 minutes

Interdisciplinary links

Students will use written or oral presentation skills to explain their solution. Social studies and science are linked where calculating possible occurrences of an event (such as cause and effect) is studied.

Teaching tips Understanding what constitutes a pin and a fork and how the chess pieces move and attack are the chess skills required for this task. Forks and Pins are introduced in the Basic Tactics lesson and can be r einforced throughout the course, especially while the students ar e playing each other.

Concepts to be assessed and skills to be developed Mapping skills Creates Patterns Extends Patterns Pattern recognition Symmetry Problem-solving skills Reasoning and log ic Diagonals Communication Understanding of piece movements Use of coor dinate plane to describe locations Critical thinking

Suggested materials Give the students a copy of the task, “Queen pins and forks”.

Solution

Forks  - a White queen can fork the Black king and knight from f5, g6, h4, e7, h1, and b7. the Black knight to to the king fr om Pins - a White queen can pin the b1, c2, and d3.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand pins or forks and is unsure about how the pieces move. No logical log ical solution is g iven.

Apprentice Student identifies some of the possible forks and pins. The apprentice may include other squares that are not pins or forks.

Practitioner The practitioner understands the problem and correctly identifies identifies all the the for fo r ks and pins and draws them them on o n the the boar d.

Expert The student clearly understood the problem and arrived at the correct answer by identifying all the forks and pins on the diagrammed board and noticed the symmetry in the forks about the b1-h7 diagonal. The expert will also point out that the Black king could capture the queen, if she forked from g6. g6.

Queen pins pi ns and fork forkss Task Black has a knight on e4 and a king on h7. Write an F on the squares where a White queen can fork the Black king and knight. Write a P on the squares where the White queen can pin the the knight knig ht to to the king. Explain Explain your answer.

DRAWS LESSON 6

“Chess is a good way to learn, to keep your brain fit and the ego in check, a mental form of your local gymnasium.”

 Abelard (1079(10 79-1 1142), 14 2), dialectician,philosopher,theologian

A chess game that ends in a tie is called a draw. Similar to sporting events that may end in a tie with a final score of zero to zero, or one to one, there are several types of draws that can occur in chess. These different types of chess draws are: Insufficient mating mating material Stalemate Threefold Thr eefold repet r epetit ition ion 50-move draw Draw by agreement (the draw offer) Clock draws: Both Both flags ar e down Flag is down, but player with time remaining has insufficient mating material There is another type of draw, called insufficient losing chances, which occasionally occurs in chess tournaments. It is not necessary to introduce this type of draw in the beginner lesson plan, as it is unlikely to occur at this level and is too

complex for the novice player to understand. In a tournament, the player who wins the game gets one point and the losing player gets zero points. Both players receive half a point for a draw.

Insufficient mating material An insufficient mating material draw occurs when neither player has enough material remaining on the board to force checkmate. An endgame where only the kings are left on the board would be an example of a draw by insufficient mating material. King King + knight knig ht vs. king and king + bishop vs. king king are ar e also draws by insufficient mating material. The position below shows why a king and bishop are insufficient mating material. Let’s say that Black tried to get checkmated by moving his king into the corner. The White king in the position belo w is as close as he can get to to the Black king and he attacks both the g7 and h7 flight squares. The bishop attacks h8 and puts the Black king in check. Notice that White does not have enough material on the board to also attack the g8-square. Therefore, it is impossible for White to checkmate Black and the game is declared a draw by insufficient mating material.

Having only one pawn remaining on the board is not insufficient mating m aterial because the pawn pawn has the the poten po tential tial to promote to a queen. A queen is sufficient mating material (see Lesson Lesson 4). 4 ).

Stalemate By the rules of chess, the players must take turns moving. What if the player to move is not in check and has no legal moves available? This is called a stalemate and the game ends in a draw.

White is trying to win the above position. Pretend White’s last move was Rg7. Now it is Black’s turn. What can he do? All the possible king moves (…Kg8, …Kxg7, and …Kh7) are illegal because he can’t move into check. Since Black has no legal moves, the game is declared a draw by stalemate.

Now consider the same position, but Black now has a pawn on h4. Unfortunately for Black, he cannot claim a stalemate because he can move the pawn to h3.

Threefold repetition If the same identical position (for both the White and Black pieces) occurs three different times, the game is drawn by threefold repetition. The moves do not have to repeat consecutively, but usually they do. Three moves is an arbitrary number set as a limit so that the game doesn’t repeat and go on for ever. The most common type of threefold repetition is perpetual check. This occurs when one player, typically the one who is losing the game, finds a position where he can check the opposing king back and forth forever, with no way for the king to escape. Set up this position with White to move to dramatically make the point.

Black is way ahead in material and it looks like he is well on his way to winning the game. Note that all five Black pawns are one square from promoting to queens, with check! Some of the students will suggest that White should capture the free queen on b5, which would normally be a good move, except that White also needs a lot of free moves to capture Black’s extra material in order to even have a chance to win. But White can play 1.Qg6+. Black is then forced to play 1...Kh8 . White can continue  2.Qh6+ Kg8 3.Qg6+ (the second time in this position) 3…Kh8 4.Qh6+ Kg8, etc. This sequence of moves could happen forever, or perpetually. After the position repeats the third time, White can claim a draw by threefold repetition. When describing what is happening here, I tell the students to imagine that after every move, you take a photograph of the board. You then compare the photos. If three of the photos are identical with the same player to move, a threefold repetition draw can be claimed.

50-move draw If fifty moves take place (a complete move is when both

players have moved one time) where no pieces have been captured and no pawns have been moved, then the game is declared a draw. Fifty is an arbitrarily set number of moves put in place so that the game does not go on forever. The average length of a chess game between masters is about forty or fifty moves. The 50-move draw rarely occurs because the count to fifty moves usually starts after this point, late in the endgame. The 50-move draw would typically occur at the beginner level when the player with the advantage does not know how to checkmate the king. If a piece is captured or a pawn is moved, the fifty move count starts over again. A pawn move is progress toward promoting to a queen and a piece capture changes the position enough to justify starting the count over again.

Draw by agreement (the draw offer) Either player can offer a draw on any move. It is proper etiquette to offer a draw as the player makes his move (so as not to interrupt his opponent while he is thinking about his next move) and before starting his opponent’s clock. The draw offer stands for only one move. The opponent can accept the draw offer or decide to play on. If he chooses to continue the game, the draw offer is null and void. It is considered bad sportsmanship to continuously annoy your opponent by offering draws, which he keeps refusing to accept (usually because he is ahead and is trying to win). Some young children like to continuously offer draws. I tell the students that this is like asking their mom for a cookie over and over again (and she keeps saying no)…she gets annoyed…usually pretty quickly. I tell them that it is a better idea to wait a while and then say, “Mom, you look very pretty today. May I have a cookie?!”

Chess Clocks Introduce digital and analog clocks to the class if you have them. If you don’t have a chess clock, it is okay to skip this section. A chess clock is two separ ate clocks in one housing, with a button above of each clock. Only one clock runs at a time. When a player makes a move, he pushes the button above his side of the clock, which stops his clock and starts his opponent’s clock. It is proper etiquette to push the button with the same hand that you use to move the piece. Digital clocks are a newer technology and count down every second left in the game. Time runs out when the clock reads 0:00:00. Digital clocks have a time-delay feature that is useful in tournaments. Analog clocks have a flag that is raised by the big hand a few minutes before the top of the hour. The convention is to set the clock so that the end of the time control is at 6:00. [For a 30 minute game (G/30) set the clocks at 5:30 at the start of the game. For a 60 minute game (G/60), set the clocks at 5:00.] At exactly 6:00 the flag will fall and the player will run out of time. In a tournament, only one of the players involved in the game is allowed to call the flag. Even the tournament director cannot declare a win on time. The chess clock, of course, can be used to reinforce the time concepts that may be required teaching in the math curriculum. In chess tournaments, the players have a predetermined amount of time to make all of their moves in the game. For scholastic tournaments, the time control is normally a game in 30 minutes or a game in an hour. If a player runs out of time, his opponent can claim a win on time, provided he has sufficient mating material on the board. The players can use as much or as little time on each move as they would like, but don’t run out! It is best to pace your self. If a player moves too fast, chances are he will make an error. If he moves too slowly, the quality of the moves usually goes up, but he runs out of time and loses the game that way.

I use the analogy of taking a test in school. If the student spends all his time on the first problem, he may get it right, but will do poorly on the test because he didn’t answer the other questions. If he answers each question too quickly, the answers ar e usually wrong and incomplete. As a both a student and a chess player, the child must learn to f ind a balance.

Both flags are down If both flags are down, each player ran out of time. This is another type of draw, as long as one of the players notices that both flags have fallen. Usually this occurs when both players are short of time, and with their attention primarily focused on the boar d, they didn’t notice when the fir st flag fell.

Flag is down, but player has insufficient mating material If the player who claims a win on time has insufficient mating material, he can only claim a draw because a win is impossible on the board. All he needs is a pawn (the possibility to win) to claim a win on time because a pawn can promote to a queen, which is mating material.

Explain the types of draws exemplar Task Students are given a list of the different types of draws and will explain what each type of draw means. Have students explain how Black might be able to achieve each type of draw using the position on the “Explain the types of draws” task page. If White plays the best moves in the given position, which of the draw options does Black have a reasonable chance to achieve?

Context This task gives the student a chance to identify and explain the different types of draws in chess. Then the student must calculate and rationalize how the different types of draws may occur in a given problem and determine if the draw is a likely outcome, assuming the best play by both sides.

Task purpose The student demonstrates his knowledge of what a draw (tie) is in chess. The student theorizes about possible outcomes that could lead to the different types of draws and determines if there is a r easonable pro bability of that scenario o ccurring.

Student task The student will define how and why each of the types of draws works. Then the student will present a possible scenario, given a position with two kings, a White queen, and Black knight, for each type of draw as to how it might occur in the given position. Then the student will tell whether the scenario is probable, given that both players play the best

moves. This is a difficult task and requires some creative thought.

Time required 20 minutes, for the better players. Weaker player s may give up after defining the types of draws.

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This task links to subjects where critical and logical thinking, probabilities, creativity, and strategic problem-solving skills are required.

Teaching tips During the half-hour session when the kids are playing against each other, the teacher should take the opportunity to r einfor ce the different types of draws as they occur.

Concepts to be assessed and skills to be developed Consideration of many possible move co mbinations Reasoning and log ic Calculation Predicting possible future outcomes Probabilities of possible occurr ences Communication Definitions Identification Critical thinking Problem-solving skills

Suggested materials Give students a copy of the task page, “Explain the types of draws”. Students may also need a blank piece of paper for mor e writing space.

Solution Insufficient mating material --- Not enough material to checkmate the king, even if the other player tried to get checkmated and played all the wor st possible moves. If neither player has enough material to checkmate the king, the game is drawn by insufficient mating material.

Black can hope to fork the White queen and king, exchanging the knight for the queen or winning her for free. Either of these outcomes would leave White with insufficient mating material. The probability of this occurring is unlikely because White would have to make a terrible blunder to get forked.

Threefold repetition --- Identical position occurs on the board (for both White and Black pieces), with the same player to move, three different times. The moves do not have to, but

usually occur consecutively. Perpetual check is a common type of three-move repetition where one side forces the repetition with a series of checks.  A threefold repetition is also unlikely, as White would have no reason to repeat the same position three times.

Draw offer --- Player one makes his move and offers his opponent a draw. Player two accepts the draw o ffer. Black could offer a draw, but since he is way behind in material and has insufficient mating material and no chance to win, White would be foolish to accept the draw offer and should play on and try to win.

Stalemate --- The player to move has no legal moves with any of his pieces.  It is unlikely in this position that White would make a mistake and stalemate Black. Beginners have a much greater  probability of stalemating each other than masters.

50-move draw --- 50 moves occur (for each White and Black) without a pawn being pushed or piece being captured. Fifty is an arbitrary number set so that the game doesn’t go on for ever. A pawn moving for ward indicates pro gr ess toward promoting to a queen and a piece capture changes the position enough to justify starting the fifty-move count over again.  A 50-move draw would also be unlikely unless White couldn’t  figure out how to win the knight or if he does wins the knight, he doesn’t know how to checkmate with a king and queen vs. a king.

Therefore, after considering all of the types of draws, the probability of Black getting a draw is not good.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t remember what a draw is, let alone how to achieve a draw. No logical solution is given.

Apprentice Correctly identifies some of the draw types, but doesn’t know how to apply them to the given position.

Practitioner The practitioner correctly defines all the types of draws and comes up with feasible scenarios of how the different types of draws might occur.

Expert The expert correctly defines all the types of draws and comes up with specific and correct scenarios of how they might occur in the given position. This is a tough question and the expert who gets this one right is, in all likelihood, the best chess player in the class.

Explain the types of draws Task Define each of the types of draws. Suggest a scenario in which Black might be able to achieve each type of draw in the position below. If White plays the best moves, which of the draw options does Black have a reasonable chance to achieve?

Insufficient mating material Threefold repetition Draw offer Stalemate 50-move draw

FREE STUFF! LESSON 7

“The advantage is that mathematics is a field in which one's blunders tend to show very clearly and can be corrected or erased with a stroke of the pencil. It is a field which has often been compared with chess, but differs from the latter in that it  is only one's best moments that count and not one's worst. A single inattention may lose a chess game, whereas a single successful approach to a problem, among many which have been relegated to the wastebasket, will make a mathematician's reputation.”

 Norbert Wiener (1894 - 1964) Harvard & MIT mathematician, communication theor y

The biggest mistake made by young chess players is either hanging (leaving pieces vulnerable to capture or, in chess terms, en prise [French]) their own pieces or not realizing that their opponent has left his pieces hanging. When playing chess, most young players are off in their own world and don’t spend any time considering what their opponent is threatening. The Free Stuff! lesson is designed to point out to the students that not only from a chess perspective, but also from a real-life perspective, they must consider the actions of other people in the world around them. In chess, remember that your opponent’s pieces are just as important as your own. In life, of course, other people are just as important as you are.

The first part of this lesson is to show the students that “free stuff” relates to the situation on the boar d when a piece is attacked more times than it is defended. Counting the number of times a piece is attacked and defended is one of the most important concepts in chess. The most commo n for m of “free stuff” at the beginner level is a piece that is attacked once and undefended, making it vulnerable to capture. An analogy that the children will relate to, which will help them to not leave free stuff lying around on the chessboard, is looking both ways before crossing the street. In other words, look before you leap!

It is White to move in the above position. Notice that the Black pawn on d5 is attacked twice (the knight on c3 and the rook on d1). It is only defended once (the rook on d8). Because White has an extra attacker, he can safely capture the pawn with either the knight or the rook and win material. A good analogy is that of two-on-one drills that they may have practiced in soccer, hockey, or basketball. The two White pieces overpower the pawn.

Consider the same position, but remove Black’s bishop from h5 and place it on e6. Now Black has two defenders for the d5 pawn. White still has two attackers. White would now lose material if he tried to capture the pawn. 1.Nxd5 Rxd5 2.Rxd5 Bxd5 and White would lose a knight and a rook for a pawn and a rook (net loss of 2 pawns) or 1.Nxd5 Bxd5 where Black gains a knight for a pawn (also a gain of two pawns for Black) 2.Rxd5 Rxd5 where Black now wins a knight and rook for a bishop and pawn (a gain of 4 pawns). It is usually best to make a capture your least valuable piece first so that you have the most material remaining at the end of the capture sequence.

Now put the bishop back on h5 and place the Black queen on d7, instead of c7. Again the Black pawn is defended twice, this time by the queen on d7 and the rook on d8. Even though the pawn is only attacked twice, White can safely capture it with either the knight or the rook because Black would have to recapture with the queen first. The capturing sequence could go 1.Rxd5 Qxd5 2.Nxd5 Rxd5. Black does end up with the last piece standing on d5, but he gave up a queen and a pawn (10) for a knight and a ro ok (8).

For the second part of this lesson, start with the demo board set up with the pieces on their original squares and make up a game where there is lots of “free stuff”. The novice

chess teacher can easily make up a game with “free stuff” lying around. This lesson can take any direction that the students suggest…I try to make lots of bad moves that hang pieces and see if the students can find the “free stuff”. After each player moves, I will ask if there is any “free stuff”… sometimes there is and sometimes there isn’t. As the game progresses, make comments about the strengths and weaknesses of each move based on the previous lessons.

1.e4 b5? (the b5 pawn is hanging) 2.Bxb5 a6 3.Nf3? (the bishop is hanging)  3…axb5 4.d4 e6 5.Qe2 Ba6 (protecting the pawn) 6.h3 Nf6

7.Qxb5? (the queen is now hanging, White forgot that Black defended the pawn with 5…Ba6)  7…Bxb5 8.Bg5 Nxe4? (the pawn is hanging…but the knight is pinned to the queen… oops!) 9.Bxd8 Kxd8 (Point out the importance of recapturing a piece, in this case the bishop, so that at least Black gets something back for the queen. The real-life connection is getting change back after making a purchase at a store. Many children in this position will mourn the loss of their queen and then go on about their business, not realizing that they can recapture the bishop.) 10.Nc3 Ba6? (Black noticed that the bishop is under attack, but the knight is too! Better moves would be 10…Nxc3 o r 10…Bb4)  11.Nxe4 and so on.

Position after 11.Nxe4

Find the free stuff exemplar Task Students are given a copy of the task page, “Find the free stuff”. Tell them that it is White to move. Have students list all the possible capture moves where White will win “free stuff” and tell how many pawns (points) each move wins. Then ask them which move they think is the best move fo r White to play and to explain why.

Context This task integrates the student’s knowledge of piece movements and ability to see the whole board and calculate possible outcomes. The student will then select and explain the best move based on his analysis.

Task purpose The student must identify all of the different ways to win material by capturing unprotected pieces and then determine the best move and express the solution in algebraic chess notation. By looking for hanging pieces, a student’s chessplaying strength increases immensely because the student is aware of the entire chessboard and the many possibilities that exist.

Student task The student will write down, in algebraic chess notation (using a coordinate plane to describe location), all the moves for White in the given position that win material and tell what piece was captured and how many pawns (points) it is worth. The student will choose the best move and explain his reasoning.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. Situations and subjects where critical and logical thinking and strategic problem-solving are tested.

Teaching tips This topic is covered in Lesson 7, entitled, “Free Stuff!” During the half hour each session when the students are playing against each other, the teacher will have plenty of opportunities to reinforce the concept of “free stuff” by pointing out hanging pieces.

Concepts to be assessed and skills to be developed Problem-solving skills Consideration of many possible move co mbinations Reasoning and decision-making Number sense Communication Addition Subtraction Knowledge of chess piece movements Use of coor dinate plane to describe location Calculation Critical thinking Predicting possible future outcomes

Suggested materials

Give the students a copy of the task page, “Find the fr ee stuff”. Students may need a blank piece of paper to completely answer the question.

Solution

Moves that win material for White (single move captures, not taking recaptures into account):

axb7 Nxb5 cxb5 Nxc2 Rxb4 Rbxd1 Rexd1 Rxe3 fxe3 Qxe3 Bxf6 king) Nxf6+

wins a rook = 5 wins a pawn = 1 wins a pawn = 1 wins a queen = 9 wins a knight = 3 wins a bishop = 3 wins a bishop = 3 wins a pawn = 1 wins a pawn = 1 wins a pawn = 1 wins a knight = 3 (the g7 pawn is pinned to the wins a knight = 3 (the g7 pawn is pinned to the

king) Nxg7 Qxg7

wins a pawn = 1 wins a pawn = 1 and checkmates Black

Qxg7 the best move!! Note that Qxc7 does not win a free pawn, because the rook on b7 protects it.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t remember what the pieces are worth or how they move. No logical solution is given.

Apprentice Finds some of the “free stuff” and picks the move that may or may not win the most material.

Practitioner Finds all or most of the moves that win “free stuff.” May not recognize that Qxg7 is checkmate and pick Nxc2 as the best move because it captures Black’s queen.

Expert Completely solves the problem and correctly explains how much material is won by each move. Doesn’t include Qxc7 in the solution by recognizing that the Black rook could then recapture the queen. Correctly identifies Qxg7 as the best move because it is checkmate. The expert may even consider the recaptures possibilities.

Find the free stuff  Task It is White to move. List all the possible capture moves where White will win “free stuff” and tell how many pawns (points) each move wins. Which move do you think is the best move for White? Clearly explain your answer.

PAWN STRUCTURE LESSON 8

“Results show that just one year of chess tuition will improve a student's learning abilities, concentration, application, sense of logic, self-discipline, respect, behavior and the ability to take responsibility for his/her own actions.”

Garry Kasparov Wor ld Chess Champion

Pawn structure is a critical element in chess from a positional standpoint. Pawns can be strong or weak depending on their position in relationship to the other pawns on the board. Since pawns must capture an opposing piece to change files (which usually requires the opponent’s partial cooperation) and alter their structure, strong or weak pawns may last for the entire game. Pattern recognition is an important mathematical element in identifying pawn structure. Each player is trying to create a strong pawn structure for himself while trying to weaken his opponent’s structure. Pawns are stronger if they are side-by-side because they can protect each other. Weak pawns are typically lined up in front of one another on the same file, unable to provide protection. I use the analogy that it is good to have friends to protect you. In master-level chess, even a one-pawn advantage can be

the differ ence between winning and losing the game. Here ar e the differ ent types of pawns: passed pawns pro tected passed pawns isolated pawns isolated, passed pawns doubled iso lated pawns tripled iso lated pawns pawn chain base pawns backward pawns doubled pawns tripled pawns

Passed Pawns A passed pawn is a pawn that can move to the other side of the board and promote without an opponent’s pawn blocking it or guarding squares in its path. Passed pawns are strong pawns because one of the opponent’s pieces must guard against the pawn’s attempt to promote to a queen. Rather than allowing the pawn to promote, often the defending player must give up a piece, say a bishop or knight, for the passed pawn. The further up the board a passed pawn is, the more dangerous it becomes.

Protected Passed Pawns A protected passed pawn is a passed pawn that is protected by a friendly pawn. Protected passed pawns are the strongest pawns.

Isolated Pawns Isolated pawns are pawns that are all alone (and have no friends) with no other friendly pawns on adjacent files. Isolated pawns are especially weak pawns if they are o n a halfopen file where the opposing rooks can line up and attack them.

Isolated, Passed Pawns An isolated, passed pawn has the good attribute of being passed and the bad attribute of being isolated.

Doubled Isolated Pawns Doubled isolated pawns are two pawns lined up on the same file with no friendly pawn on an adjacent file to provide protection.

Tripled Isolated Pawns Tripled isolated pawns are three pawns lined up on the same file with no friendly pawn on an adjacent file to provide protection. The occurrence of tripled, isolated pawns is fairly rare.

Pawn Chain A pawn chain is a gr oup of pawns on adjacent files that protect each other.

Base Pawns A base pawn is the pawn that is at the base of a pawn chain and, therefore, has no pawn to protect it.

Backward Pawns A backward pawn is a base pawn on an opponent’s half-open file that is vulnerable to attack by rooks.

Doubled Pawns Doubled pawns are two pawns on the same file that have a pawn on an adjacent file that could provide protection. Doubled pawns are much stronger than doubled isolated pawns.

Tripled Pawns Tripled pawns are three pawns on the same file that have a pawn on an adjacent file that could protect them. Tripled pawns are fairly r are. If there were other pieces on the position below, they would have no bearing on how the pawns are defined.

The only protected passed pawn is on h6. The pawn on a3 is an isolated passed pawn. The a3, a6, and a7 pawns are tripled isolated pawns. The b3 and b4 pawns are doubled isolated pawns.

The g6 pawn is an isolated pawn. Black’s pawns on d7 and e6 form a pawn chain. White has a pawn chain on g3-f4-e5 and g3-f4-g5 -h6. The base pawns are on g3 and d7. Because the d7 pawn is on a half-open file for White, it is defined as a backward pawn. The pawns on g3 and g5 are doubled pawns  (not doubled isolated pawns because of the f4 or h6 pawn).

To put the pawn structure lesson to practical use, consider these two examples:

From a pawn structure perspective, what is White’s best move in this position? 1.Bxf6+ exchanging the bishop for the knight. Because Black does not want to end up behind a piece, he must recapture with 1…gxf6  Look at Black’s kingside pawns. The pawn on h7 is isolated and the pawns on f7 and f6 are doubled isolated pawns. In one move, White was able to wreck Black’s entire kingside pawn structure, making these pawns easier to capture later on in the game.

Consider a similar position (above) where White plays 1.Bxf6. Black needs to recapture the bishop with either 1…

exf6 or 1…gxf6. Which is better? In either case Black will have doubled f-pawns. 1…exf6 is the correct move because if Black plays 1…gxf6, the h2 pawn would become a passed pawn for White. With 1…exf6, the h2 pawn is not a passed pawn because Black’s g7 pawn can still prevent it from promoting. Always look for ways to weaken your opponent’s pawn structure and enhance your own. Of course, your opponent has the opposite strategy! Symmetrical pawn structures (where each player has pawns on the same files) in the endgame tend to be drawish because it may be difficult for either player to obtain an advantage by cr eating a passed pawn.

EN PASSANT (optional part of lesson)  En passant   is a tricky pawn move and if the class is struggling at all with the earlier lessons, it is best to wait a while before teaching en passant .  En passant   means “in passing” in French and is the third special chess move (the first two were promoting a pawn and castling). I saved en passant   for later in the course because it only occurs in one out of every 5-10 games and can be quite confusing to the beginning student.  En passant   only involves the pawns. Because a pawn can move one or two squares forward on its first move, an opposing pawn on an adjacent file that is on the fifth rank would not have the opportunity to capture it if it moved forward two squares.  En passant  is a type of pawn capture which only exists if a pawn is on the fifth rank and an opposing pawn on an adjacent file advances two squares forward from its original square. The pawn moving two squares forward can be captured by the pawn on the fifth rank as if it had moved only one square forward. This capture opportunity, however, only exists for one move, immediately after the opposing pawn advances two squares.

Assume it is White’s move. If he plays c4, Black can capture him en passant   by playing …dxc3. If White plays h4, Black can capture the h-pawn en passant   by responding … gxh3. Now let’s assume that it is Black’s move. If he plays …a5, White can play bxa6. If Black plays …c5, White can take en  passant   by bxc6. Remember, the en passant   capture opportunity is fairly rare, unlike this example with multiple en  passant   possibilities that I chose only to illustrate how this special move works.

Describe the pawns exemplar Task The student will use pawn adjectives to describe the types of pawns in the position on the task page, “Describe the pawns” and identify the strong and weak pawns.

Context This task tests the student’s understanding of pawn structure and promotes thinking about creating strong pawns for themselves and weak pawns for their opponent.

Task purpose This task gives the student the chance to identify strong and weak pawn structures and use the appropriate adjective to describe the individual pawns.

Student task The student will study the position on the “Describe the Pawns” task page and explain the good or bad characteristics of each pawn.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. The concept of adjectives used in the English language is stressed in this exemplar. Links are to any subject

where the student uses critical thinking to differ entiate between, and evaluate, the pros and cons of a situation.

Teaching tips After completing Lesson 8 on Pawn Structure, the teacher can make up their own examples of different pawn structures and ask the students to identify and classify them as strong or weak pawns. The teacher can also ask the students to identify strong and weak pawns in positions from their games against each other.

Concepts to be assessed and skills to be developed Definitions Identification Problem-solving processes Reasoning and decision-making Communication Use of adjectives Use of coor dinate plane to describe locations Pattern recognition Critical thinking

Suggested materials Give the students a copy of the task page, “Describe the pawns”.

Solution

The strongest pawn on the board is White’s pawn on g3, which is a protected passed pawn. White’s pawn on h2 is a base pawn (weak because, by definition, no o ther pawn can pro tect it). White’s pawns on e7 and e6 are doubled isolated pawns (weak attributes) and passed pawns (a strong attribute). In this example, the weak trait will be dominant because the Black king is blocking the pawns and will soon capture them. White’s c3 pawn is weak because it is an isolated pawn. Black’s a7 pawn is a passed pawn (strong) and an isolated pawn (weak). Black’s c4 pawn is neutral (it isn’t a passed pawn…because of the c3 pawn, but it also isn’t an isolated pawn…because the d5 pawn protects it). Black’s d5 is a base pawn on a half-open file, or a backward pawn (weak). It would be weaker if White had r oo ks that could attack it up the d-file.

Black’s h3 pawn is an isolated pawn (weak).

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand the concept of strong and weak pawns.

Apprentice Student identifies some of the pawns correctly. Apprentice fails to identify some of the pawns and misidentifies others.

Practitioner The practitioner understands the problem and correctly identifies most of the pawns. Practitioner may not realize that the d4 is backwards or that the pawns on e6 and e7 are not only doubled and isolated, but also passed.

Expert The student clearly understood the problem and identified all of the pawns correctly and clearly explained which of the pawns are strong and which ones are weak. The expert may also explain an appropriate course of action for each side.

Describe the pawns Task Using pawn adjectives, describe each of the pawns in the diagr am below and identify the strong and weak pawns.

SQUARE OF THE PAWN LESSON 9

…Chess is “a lot like football because you have to set up your offense and your defense, every once in a while you need to give up a piece of your team in order to make the big play. It’s a game of patience, and that pretty much defines how I run the ball. I’m patient, always looking for the opportunity and always trying to capitalize on the other person’s mistake.”

 Priest Holmes All-Pro NFL running back

The square of the pawn is a basic chess concept that applies to most chess endgames. The pawns become more valuable in the endgame since most of the opponent’s pieces that can block or capture the pawns on their way to their promotion square have been eliminated. The square of the pawn is an imaginary square that the opposing king must get into in order to win the foot race with a passed pawn that is trying to promote. This concept involves measuring distances, identifying shapes, and extending the pattern of a shrinking square in order to calculate the likely outcome of the game as the pawn and king race toward the promo tion square.

Consider this position. Black has insufficient mating material. White’s only chance to win is to pr omo te the b-pawn. His king is too far away to help out. The question is whether or not the pawn can advance to b8 before the Black king can catch it. Pawns and kings run the same speed, one square at a time. First, we define the square of the pawn. The four corners of the square of the pawn are the square the pawn is currently on, the promotion square, the square on the diagonal drawn to the eighth rank from pawn’s current position (which creates a right triangle), and then come back to the square on the board that picks up the fourth corner. The three corners (not including the square that pawn is currently on) are identified with stars below. If the Black king can get into the square, he can capture the pawn and draw the game.

If it is White’s move, he plays 1.b5, shrinking the square. The new corners of the square of the pawn are at b5, b8, e8, and e5. Black can play 1…Kf6, but he can’t make up any time while trying to get into the square. White will win the race, promote the pawn and checkmate with the king and queen. If it is Black to move, he plays 1…Kf6 (or 1…Kf5 or 1… Kf4) and he gets into the square of the pawn, runs down the pawn and captures it, and then claims a draw by insufficient mating material. Play out this race for the class to show how it works. Note that the square of the pawn is defined on the side of the pawn where the defending king is. Show the next position to the students with a Black pawn (which is moving down, not up like the White pawn) and ask them to identify the square and explain which side wins for both White and Black to move. Feel free to make up additional examples of your own to show the students.

White can draw if it is his move…the White king enters the square of the pawn by moving to the c-file. Black wins if it is his move. He advances his pawn to g4 and the White king cannot enter the square and catch up to it.

Consider this endgame po sition with Black to move.

The White king is solidly in the square of both Black’s pawns. The corners of the square of the White pawn are h5, h8, e8, and e5. Black must move his king to the e-file to get into the square of the White pawn with, say, 1…Ke7. Realizing that his h-pawn can’t outrun the Black king to h8, White responds 2.Ke4 . Notice that the White king cannot capture the threatened pawn on e5 because he would leave the square of the Black pawn on d4. Black can respond by playing 2…Kf7.

White is lost. The Black king can walk over and capture the White pawn and then come back toward the center of the boar d and help escort his two pawns up the board. The White king can only watch his pawn get captured, since he cannot leave the square of the d4 pawn (d4, d1, g1, g4). I often use a babysitter analogy here that the children will relate to. The White king must stay and baby sit for the Black pawns. Pretend the square of the pawn is the house. Ask the children what happens if the babysitter leaves the house…she gets in big trouble when mom and dad come home! Here is another example with Black to mo ve.

First let’s pick up the clues in the position. Black has isolated passed pawns on a6 and h6. White has two connected passed pawns on d4 and e4. Both kings ar e in the square of the other player’s pawns. Discuss and make the following moves while marking the corners of the square of the Black pawns by turning over captured demo board pieces and placing them in the appropriate squares of the demo board.

1…a5   The White king is still in the square of the a5 pawn. Note that there are several ways for Black to win this

position by advancing his pawns. Black could also play 1…h5.

2. e5

White pushes his passed pawn.

2…a4  Now the White king is out of the square of the apawn.

3.Kd2 Getting back into the square. 3…h5! The White king is about to have a big problem… he cannot stay in the square of both Black pawns and one of them will promote to a queen. The Black king will stop the White pawns, if they make a run fo r it.

Square of the pawn exemplar Task Students are given a copy of each of the task pages, “Square of the pawn,” and will identify the square of the pawn and explain why this is important to chess endgames. Who will win the game?

Context This task integrates the student’s ability to identify the square of the pawn and explain the likely outcome of the game based on calculating up to six moves ahead.

Task purpose This task gives the student the opportunity to extend the pattern of a shrinking square and calculate possible outcomes of the game based on the location of the defending king in relation to the square of the pawn.

Student task The student will identify the corners of the pawn’s square and may identify the edges of the square of the pawn by a solid line, shading the square, or listing the squares that are in the square. Then the student will explain that if the opposing king can get into the square, he can catch the pawn in a race before the pawn can promote to a queen. The student was purposely not given whose move it is and should consider the separate cases of White to mo ve and Black to move in the solution.

Time required 15 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This problem relates to the geometry of a square (all sides are the same length and at right angles to each other). Links are to the Measurement Standard of time and distance (social studies and science).

Teaching tips During the session when the students are playing against each other, the instructor may get some opportunities to reinforce the square of the pawn concept in endgame positions.

Concepts to be assessed and skills to be developed Extends patterns (shr inking square as the pawn advances) Pattern recognition Identify shapes – triangle and square (square and rectangle differences) Diagonals Estimating distances Problem-solving skills Consideration of many possible move co mbinations Reasoning and decision-making Communication Knowledge of chess piece movements Use of coor dinate plane to describe location Calculation Critical thinking Predicting possible future outcomes

Suggested materials Give the students a copy of each of the “Square o f the pawn” task pages.

Solution Square of t he White pawn

Since White always starts on the side of the board with 1 and 2, the pawn on b3 is racing toward its promotion square on b8. The Black king must try to run down the pawn. Note that the White king is too far away from the pawn to help out. The corners of the square of the pawn (marked by stars) are b3 (the square the pawn is on), b8 (the promotion square), g8 (drawn on the diagonal from b3 toward to the eighth rank), and g3 (the other corner that completes the square). Note that a critical piece of key information was not given the students… Is it White or Black to move? White wins if it is his move and it is a draw if it is Black to move. The student should identify that if it is White to move, the pawn moves to b4, shrinking the square’s corners to b4, b8, f8, and f4. The Black king can move to g4, but it is still outside the square. The pawn will continue forward on each move, and the Black king can never catch up to and get into the square of the pawn (which shrinks on each move) in order to catch him. White will safely promo te to a queen.

If it is Black to move, he can play either …Kg3 or …Kg4 and get into the square of the pawn. Black could then catch the pawn in time after 1…Kg4 2.b4 Kf5 3.b5 Ke6 4.b6 Kd7 5.b7 Kc7 6.b8=Q+ Kxb8.

Square of the Black pawn

In this problem the student should note that since Black starts on the side of the board with the 7 and 8, his pawn is moving downward and promotes on d1. In this case the corners of the square of the pawn are d4, d1, g1, and g4. The White king is already in the square of the pawn, so it doesn’t matter whose turn it is to move, the White king can catch the pawn. If it is Black’s move, the game continues, 1…d3 2.Kf2 (or 2.Kf3) d2 3.Ke2 d1=Q+ 4.Kxd1. If it is White’s move, he easily catches the pawn before it can pro mote.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t realize that the real question being asked is, “Can the king catch the pawn before it promo tes to a queen?” No logical solution is given.

Apprentice Student sort of understands that it is a race between the king and opposing pawn, but either doesn’t have the square drawn properly (may confuse square with rectangle), has the pawn moving the wrong direction (and hence the wrong square), or takes the wrong path with the king (the king doesn’t move directly towards the pawn in an attempt to capture it).

Practitioner Draws the square of the pawn correctly and reasons out the correct solution based on only one of the players to move. May not consider what might happen if it is the other player’s turn.

Expert Draws the square of the pawn correctly and calculates the correct solution based on the case of either player to move (which wasn’t identified in the task). Also writes down the correct path of the king and pawn to justify the answer. The expert may also mention that the king is too far away to be of any help to his pawn.

Square of the White pawn Task Identify the square of the pawn on the diagram below and explain why this concept is impor tant to chess endgames. Who will win the game?

Square of the Black pawn Task Identify the square of the pawn on the diagram below and explain why this concept is impor tant to chess endgames. Who will win the game?

CHECKMATE PATTERNS LESSON 10

“Chess teaches foresight, by having to plan ahead; vigilance, by having to keep watch over the whole chess board; caution, by having to restrain ourselves from making hasty moves; and finally, we learn from chess the greatest maxim in life - that  even when everything seems to be going badly for us we should not lose heart, but always hoping for a change for the better, steadfastly continue searching for the solutions to our  problems.”

Benjamin Franklin (1706-1790) statesman, philosopher, inventor, scientist, musician, economist

In this final lesson, we will delve deeper into checkmate patterns. This lesson is an extension of Lesson 4, Basic Checkmates.

Back Rank Mate Remember that ranks are rows, numbered by counting from your side of the board. Note that from Black’s perspective this numbering convention is opposite of that used for algebraic notation. Pawns start on the second rank and promote to queens on the eighth rank. The first rank (where your pieces start) is commonly called the back rank. A back rank checkmate occurs when the king is on the back rank, trapped in by his own pawns that prevent him fr om escaping to

the second rank in the event of a check. The opponent’s rook or queen then moves to the eighth rank, and puts the king in checkmate. In the following position, with White to move, he plays 1.Rd8 mate. Normally a back rank mate occurs when one of the players neglects to look at his oppo nent’s threats.

If it were Black to move, he could avoid mate by playing …Rc8 to protect the back rank or …Kf8 so that the king could escape via e7. It is a good idea to centralize the king in the endgame because the king is a powerful piece and most of the opposing pieces are traded off so that the probability of a checkmate in the middle of the board is slim. Black could also have played …f6, …g6, or …h6 to create a flight square for the king.

Smothered Mate Although the smothered mate does not occur as frequently as the back rank mate, it is a common-enough mating pattern to have its own name. Ask the students, whom do they think will win the position below? The students who pick up on the back rank mate concept will say Black, because he can play 1…Re1 mate. Excellent, but I didn’t say whose move it is! Let’s pretend it is White to move. Black is way ahead in

material (a seven-pawn advantage…two rooks for a knight). White looks to be in trouble, but notice that the White queen, knight, and Black king are all lined up on the same diagonal.

If the knight moves, there will be a discovered check from the White queen to the Black king (Lesson 5). Can you find a double check? 1.Nh6+ The White queen and the White knight both put the Black king in check. When a player is in double check, he must move his king because capturing either piece or blocking one of the checks doesn’t work because there are two attackers. Black is forced to play 1…Kh8  Now White sacrifices his queen by playing 2.Qg8+ A sacrifice is when you give up material voluntarily for some other, hopefully, greater advantage. In this case the queen is sacrificed for a forced checkmate. The Black king cannot capture the queen because the knight defends her. The only other choice for Black that gets him out of check is 2…Rxg8

Now White plays, 3.Nf7 mate. This is called a smothered mate because Black’s king is smothered in by his other pieces and cannot escape. For the rest of the lesson give the class these positions and ask them to find the mate in one move and explain why it is checkmate. Assume it is White to move in each of these examples. The cor rect answer is given below each diagram.

Rh1 mate

Qh8 mate

Qg7 mate

Qe5 mate

Ra7 mate

Bf6 mate

b6 mate

Nf6 mate

Find the checkmates exemplar Task Students are given both task sheets entitled, “Find the checkmates”. They are asked to find all the possible checkmate moves for White and explain why their answer is checkmate.

Context This task demonstrates the student’s ability to think one move ahead, find the checkmate, and be able to rationalize and clearly communicate the solution.

Task purpose The student demonstrates his understanding of a mating net by finding the checkmates in one move. The student will express the solution in chess notation (using a coordinate plane to describe location) and explain why the solution is correct by showing that there are no flight squares for the king.

Student task The student will demonstrate the concept of checkmate and forming a mating net around the king and explain why the solution is, in fact, a checkmate.

Time required 15 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain

their solution. Use of analytical thinking may be applied to any subject where a student is required to articulate a position and then prove his case. The student is intro duced to the concept of proofs, a skill required in geometry.

Teaching tips This topic is introduced in the Lesson 4, Basic Checkmates, and then taken a step fur ther in Lesson 10, Checkmate Patterns. During the playing session the teacher will have opportunities to reinforce the checkmate concept.

Concepts to be assessed and skills to be developed Pattern recognition Creates patterns (mating net concept) Use of coor dinate plane to describe location Problem-solving skills Consideration of many possible move co mbinations Reasoning and log ic Critical thinking Communication Knowledge of chess piece movements Calculation Predicting possible future outcomes

Suggested materials Give the students a copy of each of the “Find the checkmates” task pages.

Solution

White to move and mate in one

Rh8 mate --- The rook on h8 puts the Black king in check and takes away the king’s flight squares of h4 and h6. The queen covers h4, g4, g5, and g6. The king, like the queen, covers g5 and g6. Rh1 mate --- The rook on h1 puts the Black king in check and takes away the king’s flight squares of h4 and h6. The queen covers h4, g4, g5, and g6. The king, like the queen, covers g5 and g6. Qg5 mate --- The queen puts the Black king in check and takes away the king’s flight squares of h4, g4, g6, and h6. The White king also covers g6 and pro tects the queen on g5 . Qh3 mate --- The queen puts the Black king in check and takes away the king’s flight squares of h4, h6, and g4. The White king covers g5 and g6.

White to move and mate in one

Rb8 mate --- A back rank mate. The rook on b8 puts the king in check and takes away the king’s flight squares of f8 and h8. No Black piece can capture the rook or interpose to shield the check. Qd8 mate --- Also a back rank checkmate. The queen on d8 puts the king in check and takes away the king’s flight squares of f8 and h8. No Black piece can capture the queen or interpose to shield the check. Qxh7 mate --- The queen puts the king in check and attacks h8. The queen is protected by the bishop on c2 and cannot be captured by any Black piece. The other bishop on a3 attacks the f8 flight square.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand the checkmate concept.

Apprentice Student finds some of the checkmate moves and sugg ests other moves that are not checkmate.

Practitioner The practitioner finds most of the checkmates and identifies most of the reasons why each move is checkmate. He may add in a move that he thinks is checkmate, but isn’t. Overall, the student seems to understand the concept of checkmate.

Expert The expert finds all of the checkmates and gives the logic to back up each solution by identifying the mating net correctly. No incorrect checkmates are presented.

Find the checkmates Task In position below, find all the possible checkmate moves for White and explain why each move you chose is checkmate.

Find the checkmates Task In position below, find all the possible checkmate moves for White and explain why each move you chose is checkmate.

Teacher Tips for Chess Play Time The optimal time for a chess class is one hour. The lesson should take place in the first half-hour of the class. Set up the classroom so that there are not chessboards within reach of any of the students. You want their full attention on the lesson. Also, fo r non-experienced teachers, if yo u have sofas in your classroom, do not allow the children to sit on them during the lesson. They will naturally end up sitting o n each other and not paying attention. Have the students separated, in separate chairs, if possible. Approximately thirty dollars will be needed to invest in a hanging wall demonstration board that can be purchased thro ugh the United States Chess Federation or some other online chess site. After the lesson, pair up the children with similar abilities and let them play against each other. If there are an odd number of children in the class, the teacher may play against one of the students while helping the others with their games. The teacher can also pair up two of the students as partners on one board as long the children understand that they must take turns; they don’t get two moves for every one move by their opponent! As they play, you may want to let some of the experienced older children help out the younger ones. For beginner classes, there will be questions about how the pieces move while the children are playing, such as, “Which way does the knight move again?” or “How much is a rook worth?” In the beginning, some of the children will be a little confused, but don’t worry, after a couple lessons most will catch on. As you watch the games and answer questions, correct any errors in piece movements that you see. Ask them from time to time, how many points they captured to reinforce piece values and addition. Occasionally there will be tears when one of the children loses. This is a natural part of growing up. Try to console them and tell them that by losing they can learn from their

mistakes about how to play better next time. Chess masters lose thousands of games in order to achieve the master title. Watching the children play is a good time to reinforce lessons you have already taught. Have the students count material, identify strong and weak pawns, point out pins and forks, identify free stuff, etc. Here are some common challenges that occur during chess play time and the proper way to handle the situation.

Touch move Always have the children play with the “touch move” rule in effect. It is good chess form, and the rule is strictly enforced in tournaments. One of the children will undoubtedly touch a piece, and then change his mind. The other child says, “Touch move.” The first child will respond, “You didn’t call it.” If you always enforce the “touch move” rule, and teach it well, the frequency of this dispute will decr ease.

Disputes over the position Here is where your diplomacy skills will be tested! Let both children tell their side of the story. Don’t allow them to move the pieces as each pr esents their case. Have them call o ut the pieces and squares. If you allow them to touch the pieces, you will be amazed how fast the board can get messed up and the actual position will be difficult to recreate. If it is unclear who telling the truth, I will often give the benefit of the doubt to the child who is behind. If you don’t want to take sides, mo st children accept a coin flip as fair way to settle the dispute.

Talking during the game Chess is a quiet game and children are not allowed to talk during chess tournaments. There is a natural tendency for the children to chatter as they are playing for fun. I let them talk, as long as it doesn’t get too loud. However, don’t let the children help out their friends on the board next to them, since this isn’t fair to other players.

Moving t oo quickly The majority of the children will tend to move too quickly. Remind the students that chess is a slow game. Recall the story of the Tortoise and the Hare…the slower hare wins. Children tend to be rewarded in school for quick answers. Good chess play requires deeper thinking. Some children will be impatient because their opponent doesn’t move fast enough for their liking. They will move their piece, and immediately say, “Move.” Point out that their opponent has every right to take time to think, and is actually playing smart, because chess is a slow game that requir es deep thought. You can also mention to the class that chess masters sometimes take over an hour to make just one move! Some of the younger children who move too fast may not even let go of the piece they moved, in anticipation of making their next move. Tell the students that their hands must be pulled back so that their opponent can see the whole board and not feel rushed to make their next move. Most children tend to spend more time on each move when they reach fourth or fifth grade. At this age, they tend to be more patient and realize that there are lots of ideas to consider when selecting the best move. The children who play in tournaments also tend to slow down at this age, as they have enough maturity and experience to draw the conclusion that moving slowly equates to winning more trophies! Teaching the students to take the time to be a good detective and pick up the clues in the position before jumping into analysis will slow some of them down. You can ask them about the strategy they use to put a picture puzzle together. The smart plan is to first sort out the border pieces and separate the pieces by color. By using this approach, the puzzle goes together quicker than a pure trial-and-error solution of grabbing pieces and randomly trying to make them fit. Randomly grabbing chess pieces and moving them quickly does not work well either.

Capturing kings Announcing check is not required. Most children will say check because they like the sound of it and it is a good excuse to talk! Children who are learning chess for the first time will equate winning the game to capturing the opposing king, not checkmating checkmating the the king. king . The concept of checkmate checkmate can take time for some o f the children children to understand. understand. A player has made an illegal move if his king is in check (under attack) after the completion of his move. When a child captures a king, remind him that kings cannot be captured, and ask what was the last move (the illegal move) played and then back up the game and have the student who made the illegal move choose a different move that is legal and doesn’t leave his king in check. Have the children raise their hand when they think they have checkmated the king so that you can verify that it is indeed checkmate. Otherwise, some of the children will capture the king while you are at a different board, proclaim victory, and mess up or reset the board…wiping out the evidence of the illegal king capture. In about 95% of these cases, the student captured the king and didn’t put his opponent in checkmate. Children in scholastic chess tournaments are also required to raise their hands at the end of a game so that a tournamen our namentt director director can verify the corr ect result. result.

End of t he playi playing ng session Most children will be in the middle of their first or second game when time runs out o ut in the the hour session. sessio n. When you announce that time is up, there will be moaning and requests to play a few more moves! Most of the time, one of the students will proclaim victory as soon as he realizes that he has more material than his opponent. A diplomatic way to handle the situation is to say that one player has an advantage, but didn’t win because we ran out of time (mor e moans!).

Sportsmanship Sportsmanship Spor tsmanship is big part of o f chess etiquette. etiquette. After After winning the game, a student may loudly proclaim victory to everyone within within earsho t. Of course, co urse, the child who loses may feel badly. A good way to deal with victory celebrations is to point out that if the result were reversed, the student probably wouldn’t appreciate it if his opponent celebrated. Most children childr en get the point. Benjamin Franklin offered wise words on this subject: “You must not, when you have gained a victory, use any triumphing or insulting expressions, nor show too much of the pleasure you feel; but endeavour to console your adversary, and make him less dissatisfied with himself by every kind and civil expression that may be used with truth; such as, you understand the game better than I, but you are a little inattentive, or, you play too fast; or, you had the best of the the game, g ame, but something happened to to divert your yo ur thoug thoughts, hts, and and that turned it in my favour.”

Only Only pawns can prom pro mot e Younger children tend to forget that only pawns can promote to a queen. Some children will ask if they can get their their queen back if they they get a knight or other piece to the other side of the board.

Forfeit vs. Resign For some reason, 99% of the children do not know the definition of the word forfeit. Forfeiting in sports means losing because because a player o r team did not show up for the the game. Resigning means giving up and acknowledging that your opponent won the chess game. I encourage the children to never resign because as long they are still playing, there is a chance that their opponent will make a mistake and lose the game or stalemate the king, a common occurrence at this level. Since there there seems s eems to be a stro ng tendency to to r esign, esig n, I tell them that they must show me a valid driver’s license in order for me to allow them to resign. This works well as by the time they are sixteen they will hopefully have a good feel for when a game is hopelessly lost and then be able to discern when resigning is appropriate. Captured Captured (or (o r grounded), g rounded), not “kill “killed” ed” Most children will say, or think, that they “killed” a piece when they capture it. For obvious reasons, change their vocabulary to “captured” (or “grounded” if you are talking in the context of opening presents story in Lesson 2). Threefold repetition The child who is behind in material may move a piece back and forth three times and declare the game a draw by threefold repetition. In order to claim a threefold repetition, the positioning of ALL the chess pieces on the board must r epeat thr three ee times, not just one of o f the player’s player ’s pieces. Counting material material off the t he board I strongly recommended that the intermediate and advanced chess player count the material that is still on the board, not off it. By counting material taken off the board, errors can occur by failing to notice a piece hidden from view, counting captured pieces from the game next to you, or counting counting er ro r s caused by promo ted ted pieces. pieces.

At this beginner level, however, it is more important that the younger students concentrate their attention on learning what the pieces are worth and practicing addition. Children like to touch their opponent’s captured pieces as they count them and keep them on their side of the table like little prisoners. If they start taking pieces off the board to count them, it is pretty much guaranteed that the pieces won’t end up on the proper squares when the game resumes. Most children are quite protective of captured pieces. I once had a kindergarten girl promote her first pawn ever. I was so happy for her that I told her she could have her queen back and placed her captured queen on the promotion square. She asked if instead of putting it back on the board, could she take her captured queen away from her opponent and keep it on her side of the boar boar d so that she she could hold ho ld it. Who was I to to say no?!

Quick piece captures Children have a tendency to capture a piece as so on as they see that a capture is possible. Quick captures without much thought are quite common, pr obably because the student gets a prisoner to play with. Also, recapturing with a pawn instead of a piece is quite common. Usually this doubles pawns and messes up the pawn structure (see Lesson 8). Teaching patience is especially impor tant when there are several ways to recapture a piece. Scholar’s Mate (or the four-move checkmate) Don’t teach this, it is bad chess! Children exhibit strong affinity for immediate gratification. If one of the children learned Scholar’s Mate at home, then teach the class how to defend against it. If a child persists on bringing out his queen early, I tell them that I will help their opponent defend against it.

REPRODUCIBLES

APPENDIX A

CHESS AND MATHEMATICAL STANDARDS

CHESS RUBRIC  NOVICE

Understanding There is no solution, or the solution has no r elationship to the task. Inappropriate concepts are applied and/or procedures are used. The solution addresses none of the chess components presented in the task.

Strategies, Reasoning, Procedures No evidence of a strategy or procedure, or uses a strategy that does not help solve the problem. No evidence of using any kind of chess reasoning. There were so many errors in the chess procedure/reasoning that the problem could not be resolved.

Communication There is no explanation of the solution or the explanation could not be understood or it is unrelated to the problem. There is no use or inappropriate use of chess representations There is no use or mostly inappropriate use of chess notation and terminology.

 APPRENTICE

Understanding The solution is incomplete, indicating that parts of the problem are not understood. The solution addresses some, but not all, of the chess components pr esented in the task.

Strategies, Reasoning, Procedures Uses a strategy that is partially correct and leads in some way toward a solution, but not the complete solution. Some evidence of chess reasoning. Some parts of the solution are correct, but the correct answer was not achieved.

Communication There is an incomplete explanation and it may not be clearly presented. There is some use of cor rect chess reasoning. There is so me use of chess terminology and notation.

PRACTITIONER

Understanding The solution shows a broad understanding of the problem and the major concepts necessary for its solution. The solution addresses all of the components presented in the task.

Strategies, Reasoning, Procedures Uses a strategy that leads to a solution o f the problem. Uses effective chess reasoning. All parts are cor rect and a correct answer is achieved.

Communication There is clear explanation. There is appro priate use of chess reasoning. There is effective use of chess terminology and notation.

 EXPERT 

Understanding The solution shows a deep understanding of the problem, including the ability to identify the appropriate chess concepts necessary fo r its solution. The solution completely addresses all of the chess components pr esented in the task. The solution puts to use the underlying chess concepts upon which the task is desig ned.

Strategies, Reasoning, Procedures Uses a very efficient and sophisticated strategy leading directly to the solution. Employs r efined and complex reasoning. Applies procedures accurately to correctly solve the problem and verify the results. Verifies solution and/or evaluates the reasonableness of the solution. Makes relevant chess observations and/or connections.

Communication There is clear, effective, concise explanation that details how the problem is solved. All the steps are included so that there is no need to infer how and why decisions were made. Chess representation is actively used as a means of communicating ideas that relate to the solution of the problem. There is precise and appropriate use of chess terminology and notation.

National Council of Teachers of Mathematics Standards Content Standards – explicitly describe the content  that students should learn Number and Operations Standard Students learn to understand numbers, ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and how they relate to one another; compute fluently and make reaso nable estimates.

Algebra Standard Students learn to understand patterns, relations, and functions; represent and analyze mathematical situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; analyze change in various contexts.

Geometry Standard Students learn to analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; specify locations and describe spatial relationships using coordinate geometry and other representational systems; apply transformations and use symmetry to analyze mathematical situations; use visualization, spatial reasoning, and geometric modeling to solve problems.

Measurement Standard Students learn to understand measurable attributes of objects and the units, systems, and processes of measurement; apply appropriate techniques, tools, and formulas to determine measurements.

Data Analysis and Probability Standard Students learn to for mulate questions that can be addressed with data and collect, organize, and display relevant data to answer them; select and use appropriate statistical methods to analyze data;

develop and evaluate inferences and predictions that are based on data; understand and apply basic concepts of pr obability.

Process Standards – highlight ways of acquiring and  using content knowledge

Problem Solving Standard Students learn to build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving.

Reasoning and Proof Standard Students learn to recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures; develop and evaluate mathematical arguments and proofs; select and use various types of reasoning and methods of proof.

Communication Standard Students learn to organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teacher, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas pr ecisely.

Connections Standard Students learn to recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics.

Representation Standard Students learn to create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical

representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena.

Chess Correlated to the National Council of Teachers of  Mathematics Standards Although math concepts can be introduced through chess, especially when taught to the younger students, chess should be mainly used to reinforce mathematical concepts. The chess course should be taught in a fairly condensed fashion so the students don’t have time to forget what they have already learned. Some extension activity ideas ar e presented below. Here is a sample alignment of a second-grade math curriculum to chess as it relates to each mathematical standard recommended by the NCTM.

Content Standards – explicitly describe the content that students should learn Number and Operations Standard The concept of material in chess relates to the values of the individual pieces (pawn =1, knight=3, bishop=3, rook=5, and queen=9). Normally the player who is ahead in material is willing to trade pieces because this simplifies the position on the board and magnifies his advantage. Although other factors also play a major role in positional analysis (such as space, piece placement, king safety, pawn structure), most children at the beginner level will consider a material advantage to be the most impor tant type of advantage. The difference in material between what both players have remaining on the board is what is important, not the total sum

of the material r emaining for each player. For younger children (K-3 rd grade), chess can be used to reinforce the concepts of addition and subtraction by counting material. Teachers can easily make up their own extension activities, once they understand the basic chess principles. Older children (4 th-8 th  grade) should have no problem determining who is ahead in material and by how much. Here are some examples of where counting material can be used as a Number Sense.

Uses ordinal numbers (1st – 8 th grade) Rows in chess are referred to as ranks. Ranks are counted from each individual players perspective with the 1 st  rank being closest to their side of the board and the 8 th  rank the furthest away. In other words, the pawns start on the 2 nd rank and promote on the 8 th r ank.

Compares two sets of objects and represents them with a number sentence & Recalls addition and subtraction facts through 18

Both of these concepts are demonstrated in chess by calculating which side is ahead in material (1 = value of a pawn). For example, trading a bishop and a knight for a rook and two pawns would be a good trade because 3 + 3 < 5 + 1 + 1 or 6 < 7. Using subtraction to calculate which side is ahead: 7 (pawns acquired) – 6 (pawns given up) = 1 (pawn advantage).

Place value: models an regrouping

understanding

of

the

concept

of 

Regrouping can also be used to determine a material advantage. I like to regr oup the pieces that the students capture in their games into groups of ten because tens are easy to add. Examples of groups of ten may be a queen and a pawn; two rooks; a rook, a knight and two pawns; or a knight, two bishops and a pawn.

Uses addition/subt raction terminology minus, …)

(sum, difference,

Addition/subtraction terminology can be used in material calculations. For example, the sum  of a rook and a bishop is eight pawns. You can also add up the values of all of the captured White and Black pieces and then calculate the difference between them to determine who is ahead in material and by how many pawns. For example, a rook minus a knight is two pawns.

Practices computation subtraction problems:

skills

to

solve

addition

and

Piece values and material calculations can be used to practice each of these computational skills.

identifies missing number ( _ + 8 = 17, 12 - _ = 5)

( __ + Rook + Pawn = Queen) or ( __ + 5 + 1 = 9)

(Queen – Bishop – ___ = Pawn) or (9 - 3 - __ = 1)

develops commutative property ( 5 + 4 = 4 + 5) (Rook + Knight = Knight + Rook) or (5 + 3 = 3 + 5)

explores associative property Queen + ( Rook + Knight ) = ( Queen + Rook ) + Knight or 9 + (5 + 3) = (9 + 5) + 3

adds three-one digit numbers (column addition) Bishop Rook + Queen

3 or

5 +9

17

adds/subtracts regrouping

17

two-digit

numbers

with

one

Bishop + Pawn + Rook + Queen – Rook – Knight – Rook = ? or Bishop + Rook + (Pawn + Queen) – (Rook + Rook) –  Knight = 3 + 5 + 10 – 10 – 3 = 5 or 18 – 13 = 5

explores multiplication as repeated addition using manipulatives 3 Queens = 9 + 9 + 9 = 3 x 9 = 27

Selects appropriate operation in problem-solving situations Relates to piece values and figuring out whether White or Black is ahead. Students will r ecognize that pieces of the same color are added to determine each player’s total. In chess, we are interested in who is ahead and by how much (a concept children much younger than second grade can easily grasp). Students will realize that subtraction is necessary to calculate the difference of each player’s totals to determine who is ahead in material.

Uses estimating skills to determine if an answer is reasonable When calculating different chess variations, the player must count what the differ ence in the material is and then look at the position and judge if the pros of the variation outweigh

the cons. For example, a player may think to himself, “I can win a pawn if I do this, but I delay developing my pieces. Is this wor thwhile?” The student may also estimate that giving up two rooks for a queen is close to an even trade. Evaluating different chess positions in order to determine the best move is estimating in an advanced form. Another important estimating concept in chess is r elated to the chess clock and estimating time. A chess player is r equired to make a specified number of moves in a certain amount of time, or lose the game. The student must estimate how much time is needed to win the game and at what critical points spending extra time is required. This is analogous to the student taking a test in schoo l where he has a specified amo unt of time to answer a given number of questions. Estimating time remaining also ties into  Reads and writes time to the hour, half hour, and quarter hour using digital and face clocks in the Measurement Standard.

Understands fractions as equal parts of a whole (1/2, 1/3, 1/4, 2/3, 3 /4,...) Explores fractions as equal parts of a set Reads, writes, and uses word names (one-half = 1/2) Explores t erminology (fraction, whole number, numerator, denominator) Fractions not only can be examined in terms of material value (for example, a bishop is worth 3/9 of a queen, or 1/3), but also below under Explores the concept of area by covering a surface with colored tiles using the chessboard as the surface to be covered (for example, “What fraction of the board is cover ed by the White pieces at the start of the game?” Answer: 16/64, or 1/4.) Fractions involving time remaining in the game using the

chess clock can also also be incorpor incorpo r ated ated here.

A lgebra Standard Standard Chess has a strong correlation to the Algebra Standard. To play chess well, you must become proficient in predicting the results of each move. Creating Creating and Extending Extending patt erns taught during the chess course include piece movements, fighting for the center in the opening, checkmate patterns, tactics patterns, the threefold repetition draw (a repeating move order), pawn structure patterns, and the pattern created by the square of the pawn shrinking as the pawn moves forward. These patterns occur in every chess game, from the simple patterns presented here for the beginner, to complex patterns that must be recognized and evaluated by the chess master.

Geometry Standard Chess is a great vehicle for learning two-dimensional geometry (of course, three-dimensional geometry doesn’t apply to the game). Geometry concepts occur all over the 8x8 or 64-square chessboard. Algebraic chess notation is the concept of using ordered pairs to describe location on a coordinate plane. The concept of the x,y coordinate plane, which is normally taught in school around third grade, can be understood understood by studen students ts in kinderg kindergarten arten or first gr ade. Here Here are some math-chess math-chess cor relations: circle, Identifies, draws, and describes geometric shapes: circle, triangle, square, rectangle Using the 8x8 square chessboard, the teacher can be quite creative presenting different square and rectangular shapes. Triangles (especially right triangles) are also abundant on the chessboar chessboard d by dr dr awing awing a line fro m the the corner cor ner of o f one square to another.

Lesson 9 (Square of the Pawn) introduces the common endgame concept of a race between a pawn and the defending king to the pawn’s pawn’s promotio pro motion n square. squar e. In In this lesson, the student student is asked to define the corners of the square of the pawn. Identifying the corner of the pawn’s square that is on the eighth rank, but not the promotion square, involves drawing a diagonal line from the square the pawn sits on, to the eighth rank, forming a right triangle. The student then picks up the last cor ner, to complete com plete the the square of the pawn. pawn.

Explores concepts of parallel, perpendicular, horizontal, vertical, and diagonal The rook moves horizontally and vertically. Horizontal and vertical movements are perpendicular to each other. Bishops move diagonally. The queen is a combination of the rook and bishop and, therefore, moves horizontally, vertically, and diagonally. The concept of parallel is introduced in the Basic Checkmates lesson in the form of the queen and rook roller where the queen and rook use parallel powers to force the enemy king against the edge of the board and into checkmate. The teacher can give one student a White king, queen, and rook, and the other student a Black king and have them practice queen and rook rollers in class. The 64 squares of a chessboard offer plenty of creative possibilities for the teacher to create other exercises to explore these concepts.

Follows directions when given positional words

The chessboard is a wonderful surface on which to give the students directions to follow with positional words. See Ant and the Aardvark Exemplars in Appendix C for exemplars.

Develops the concept of symmetry in simple (2-D) shapes

Symmetr Symmetr y frequent fr equently ly occurs o ccurs on the 2-D chessboar d. At the the start of the game, the boar d is set up symmetr symmetr ically. In the opening, many students will stumble onto the symmetry concept by accident. The player with the Black pieces often copies the moves made by the White player (who moves first), making the position symmetrical. Usually, it is best to refrain from copying too many moves. Normally the student playing White discovers the symmetry (and more often than not, becomes annoyed by it!) as he notices that Black is copying his moves. After noting White’s annoyance, the the student student playing Black usually continues to to co py for a while longer! Symmetry is introduced in the lesson on pawn structure. Symmetrical pawn structures tend to lead to more drawish endgames because of the lower probability (ties into Data Analysis and Probability Standard) of either side creating a passed pawn. Asymmetrical pawn structures lead to greater winning and losing chances for both White and Black because passed pawns are easier to create. The teacher can also create specific positions to develop the the concept co ncept of symmetr y.

Explores the concept of area by covering a surface with colored t iles iles The 64-square chessboar chessboar d is a gr eat surface to explore the concept of area by covering parts of it with colored tiles or even chess pieces. Fractions can also easily be explored by blocking out areas o n the the chessboar chessboar d.

Explores coordinate plane (+,+) to describe location (ordered pairs) Chess scorekeeping in algebraic notation is the language of chess reading and writing. Each move is recorded by describing which piece moves and the square it moves to. The location of each square is described in a coordinate plane by using an ordered pair. In algebraic notation, the x- coordinate is a letter (a-h), and the y- coordinate is a number (1-8). Even though the coordinate plane is typically introduced in third grade, the majority of second graders will have no problem grasping the concept earlier. In fact, the majority of first graders and many children in kindergarten understand this concept when it is taught in the chess context. Children who have played the game Battleship, Battleship, have already been introduced to the (x,y) coor coo r dinate dinate plane system. Because the coordinate plane isn’t usually introduced into the math curriculum until third grade, this concept is usually introduced to the students through chess, not reinforced. Because the teacher will have the students call out the squares where they want the pieces move to during the class, most of the the students students will quickly pick up the the coor co or dinate plane concept.

Measurement Standard Relative distances are explored in Lesson 9 through the chess concept of the Square of the Pawn. Time and distance are important concepts in chess. Measuring and estimating time is also important in chess tournament games involving a clock.

Reads and writes time to the hour, half hour, and quarter hour using digital and face clocks

Chess clocks come with either digital or analog face clocks. The clock is set differently for various time controls. The chess convention is for the first time control to end at 6:00. If the time control is G/30, meaning game in 30 minutes, both clocks should be set at 5:30. The chess clock, which is actually two different clocks located side by side, is a handy device to teach students how to learn to tell and measure time. The student can also write down the time taken by each player on each move by reading the time on the clock.

Data Analysis and Probability Standard Deep analysis and calculation enters chess at the higher levels beyond the scope o f this class. When teaching teaching chess as a game and not making an effort to incorporate the math concepts directly, graphing normally does not enter into the course. However, from a math perspective, there are many ways to incorporate graphing and probability and statistics into the chess class as an extension activity. Here are some examples:

Uses objects, o bjects, pictures, pict ures, and symbols symbols t o make simple simple graphs Adding up piece values in different combinations can be used to make simple graphs. Graphing different combinations with colored squares, or maybe coins placed on a chessboard is another another idea for gr aphing aphing exercises.

Develops mat mathem hemat atical ical thinking thinking using graphs g raphs Answers questions by comparing information on a graph Creates graphs or diagrams to display and compare data After graphing different combinations of piece values, the

student can compare the lengths of a bar graph to get an idea of by how much White or Black is ahead in material.

Develops terminology (key, legend, tally, row, column, data) Chess has its own terminology for rows and columns. Rows are called ranks (with the 1 st rank closest to you and 8 th rank furthest away) and columns are called files (lettered a, b, c, d, e, f, g, h from White’s left to right). The concept of ranks and files is used in chess scorekeeping as algebraic notation and describes a location in a coordinate plane.

Uses Venn Diagrams to display and co mpare data Chess is not usually taught with Venn Diagrams. The teacher can, however, create many of their own Extension exercises with Venn Diagrams, showing commonalities of different piece movements, common squares attacked by different pieces, or comparing stalemate and checkmate with king and queen vs. king endings.

Explores combination problems (numbers of combinations using 2 shirts and 3 ties) “Combinations,” in chess language, are tactics that may involve many pins and/or forks (or other elementary tactics presented in Lesson 5) and are a sequence of moves involving multiple threats. The building blocks of chess combinations are introduced in Lesson 5, Basic Tactics. The transposition of different move orders that arrive at the same final position is another example of exploring the concept of co mbinations in a chess context. From an advanced perspective, the game of chess is actually an exercise in continuous calculation of different variations and combinations of move orders and possible positions. Chess combination problems can be broken down

into simple lessons for young students that are just learning to play.

Develops an understanding of situations where probability of outcome is zero or one The probability of a queen moving on the first move is zero (all the other pieces are blocking her). This idea can be duplicated with specific positions using any of the chess pieces. The “touch move rule” (if you touch a piece you have to move it) can also be demonstrated here. Say you touch your king and there is a legal move with the king, the probability of moving the king is one. If there are no legal moves available for the king, the probability of the king mo ving is zero . Another example, from Lesson 6 on Draws, is the probability of winning a game in which only the kings remain on the board is zero because neither side can even put the other in check, let alone checkmate (insufficient mating material draw).

Explores likely or unlikely outcomes based on data collected from a number of trials (coin toss, card flip, dice, and spinners) In the second half of each session when the students are playing against each other, often both players want to be White because White has the advantage of the first move. Instead of tossing a coin, the chess convention is to hide a White and a Black pawn in each hand behind your back. Have one of the students pick a hand to determine his color. The odds of picking the hand with the White pawn is the same as correctly calling a coin toss (both 50%).

Process Standards  – highlight ways of  acquiring and using content knowledge It is important to note that ALL of the Process Standards are deeply embedded in the Content Standards.

Problem-Solving Standard In a societal sense, chess is frequently referenced as the ultimate test of a person’s ability to calculate and analyze data to solve a mental problem. In professional sports, for example, we hear over and over again how the coaches are involved in a chess g ame, trying to o ut-calculate each other. The game of chess involves solving problems and successfully determining favorable outcomes from a myriad of possible combinations.

Reasoning and Proof Standard Mastering critical thought processes in chess play epitomizes critical thinking, calculation, and reasoning. Pattern recognition, understanding, and predicting the likely results of actions link heavily to the Algebra Standard and the Data Analysis and Probability Standard. The concept of checkmate links clusters of reasoning to achieve a type of proof that there is no escape for the king.

Communication Standard Organizing and thinking through chess analysis is an important part of the game. Writing, reading, and speaking in chess language (algebraic notation) are skills that help the student think and expr ess his mathematical thoughts and ideas. See Exemplars at the end of each teaching lesson and in Appendix C.

Connections Standard Chess ideas, many of which are mathematical in nature, connect and sum up the patterns and concepts that are presented at the basic level in this work. Scholastically, chess not only has connections to math, but also to language arts, social studies, and science. The logical thought processes learned and applied thro ugh chess relate strongly to spor ts and any endeavor in the field of business that the student may pursue later in life.

Representation Standard Students can identify with ideas and thought processes that are represented in different forms through chess. Real-life representations and analogies can be powerful teaching tools.

Representing and communicating chess ideas may be approached in many different ways. For example, the movement of the pieces, as described in algebraic notation, is a representation of chess moves, concepts, and the execution of planning and strategy.

A PP PPENDIX ENDIX B

FUN CHESS GAMES FOR FOR THE TH E CLASS

Line Chess “Line Chess” is a fun game that gives the the students students pr actical experience with the chess clock. The chess teacher should have a chess clock available to demonstrate how the clock is used in tournament play (see Lesson 6 – Draws). Break the class into two teams. Balance out the teams so that the better players are evenly split up. The students will be standing in a straight line, hence the name, “Line Chess,” on their respective side of the board. Set the clocks at 5 minutes each. The player at the front of the line makes his move and pushes the button on his clock with the same hand he moved the piece with. He then walks to the back of the line. You will have to remind some of the children to push the button on the clock. Don’t let the next player in line push it; i t; it should be the player who just made the move. The teacher should sit at the table where he can see the clock and be ready to quickly undo any illegal moves. The teacher may need to keep the children focused on staying in their line. Line chess is best for classes of ten students or less so that there isn’t too much down time before each student takes his next turn. If there are too many students on each team, they they will tend tend to to dr ift out of line and g et out of cont co ntrr ol. Give time updates for the first few minutes so that the students get a sense of timing and a feel for the clock. As the five-minute limit approaches for one of the teams, the teacher should stay quiet about time remaining on the clock. Any student can call flag or time on the other team if they see that their opponent’s flag has fallen. There will be a natural tendency for the stronger players to help out the weaker ones on the team. I usually allow the students to help their teammates a little bit, but if it gets out of hand, you may want to have everyone keep quiet. Whether or not I enforce a no helping policy is determined by the personalities pers onalities o f the students students and the the class dynamics.

Most of the students will move too quickly because their focus tends to be on the clock and not the board. Try to slow these students down a little. You may also have to speed up a few of the students who are taking too much time. Line Chess is a fun way for the student to develop a feel for the concept of time and learn how to properly use the chess clock.

Postal Chess “Postal Chess” is a fun game that gives the students a chance to to talk through thro ugh chess ideas and wor k as a team. Explain to the students that in real life, postal chess is a game where two players, who may never meet each other, can play chess chess from fr om different parts parts of the the world wor ld thro thro ugh the mail. Each player is allowed to take about three days to decide on a move before mailing it to his opponent. Postal chess games can take several years to complete. Both players are allowed to move the pieces on their board and consult chess books, but neither player is allowed to ask a friend for help or plug the position into a computer. Break the class into two equal groups of roughly equal ability. Teams with five or more players can be a little counter-productive as some of the students may not contribute and start goofing off. The stronger players in the class can challenge each o ther ther with with possible variations vari ations while the the weaker players on the team learn from the ideas of their stronger peers. Locate the groups on opposite sides of the room and allow allo w each to to have a chessboar d. The students students are ar e permitt per mitted ed to move the pieces on their board. The teacher is the mailman. Once the team decides on their move, they write down on a piece of paper and hand it to the mailman who delivers the move to the other team and then makes the move on the demo board. The teacher should write down the moves of the game so he can go over the game with the students later and make suggestions for improvemen impro vementts. It may take several lessons to complete the postal game and then analyze it with the class.

Simon Sim on Says Chess “Simon Says Chess” is a game developed by Anthea Carson and myself that reinforces piece movements, algebraic notation, chess terminology, and tests the student’s ability to follow directions. The teacher may choose to incorporate Simon Says Chess to reinforce previous lessons. Simon Says Chess Chess is especially especially fun for childr childr en third third grade g rade or o r younger. Have each student set up a chessboard at the starting position. The teacher should have all the children play White (or Black) and have the boards face the same direction, so their moves are easier to check. The teacher will then call out moves for the children to make on their board. The teacher can walk around the room and make sure that everyone has made the the proper pro per mo ve before g oing on to the next next move. Here is a sample game (not all the moves are good moves):  Move White’ Whit e’ss e-pawn forward as far as it i t can go. (1.e4) go. (1.e4)  Move Black’s Black’s f-pawn to a square where it can be captured. captured. (1…f5)  Put the Black king ki ng in check the t he only way you can. (2.Qh5+) can.  (2.Qh5+)  Make the only onl y legal move for Black. (2…g6) Black.  (2…g6)  Move one of White’ Whi te’ss bishops to t o attack a Black Blac k knight. (3 knight.  (3..Bc4)  Have Black capture c apture the most valuable valuabl e White Whi te piece pi ece that t hat he can. (3…gxh5)  Have White put the t he Black king in i n check. (4.Bf7+) check.  (4.Bf7+)  Make Black’s Black’s only legal move that captures “free stuff”. stuf f”. (4… (4 … Kxf7)  Have White capture capt ure the “free stuff”. (5.exf5) stuff”.  (5.exf5)  Attack White’ Whi te’ss f-pawn with a knight. kni ght. (5…Nh6)

 Develop White’s b1 knight to its best square. (6.Nc3)  Have Black capture the “free stuff”. (6…Nxf5)  Move White’s d-pawn to a square where it can be captured. (7.d4)  Attack White’s pawn on d4 with a bishop. (7…Bg7)  Defend White’s attacked pawn with a bishop. (8.Be3) Capture White’s least value piece available with your knight. (8…Nxd4)  Move White’s undeveloped knight to e2. (9.Nge2)  Have Black fork White’s king and rook. (9…Nxc2+)  Move White’s king to a square on the kingside half of the board. (10.Kf1)  Have Black capture the “free stuff”. (10…Nxa1)

The teacher can follow this example or make or make up their own Simon Says example game.

Who Wants To Be A Chess Millionaire? “Who Wants To Be A Chess Millionaire?” is a game intended for classes where the students are typically third grade or older. The hit television game show “Who Wants To Be A Millionaire?” is the model for the game. Most children at this age level have seen the television show and have a feel for the game. The teacher creates a chess position on the demonstration board and the students take turns being the contestant. Give the class four multiple-choice answers (a, b, c, and d). The class will study the position. When all the students have individually decided what they think the correct answer is, the contestant can use his life lines. First the contestant polls the audience. You may need to have the other students shut their eyes when they vote so that they don’t look around the room and vote with the majority. Then the contestant can phone a fr iend. The contestant may ask one of the other students why he chose his answer. You may need to keep the rest of the audience quite as some of the other students will want to give their ideas as well. Finally, give the contestant a 50-50. This usually isn’t much help since I eliminate two of the incorrect answers that provide the least amount of help. Some of the more clever students may want to do the 50-50 life line first. Have them save the 50-50 life line for last because it is mor e challenging for the audience if they have to choose between four answers instead of two. After the 50-50, it is time for the contestant to give his answer. You may wish to reward correct answers with a piece of candy or some other prize. Adjust the level of difficulty of the questions to match the abilities of the students in the class. The teacher can make up their own questions to fit the lessons that are the presented in this boo k.

Sample Question for a younger class Which is the best move for White in this position?

a) b) c) d)

3.d3 3.Bc4 3.Ng5 3.Na3

The correct answer is b) 3.Bc4 because it develops a minor piece and prepares for castling on the kingside. a) 3.d3 is a bad move because it blocks the diagonal of the bishop on f1. c) 3.Ng5 is a bad move because White is moving this knight twice before developing the other pieces and the knight is “free stuff” if Black correctly responds 3…Qxg5 . d) 3.Na3 is a bad move because “a knight on the rim is dim.”

Sample Question incorporating chess history and geography The famous world championship match in 1972 between Bobby Fischer and Boris Spassky took place in the capital city of Iceland. What is name o f the capital of Iceland? a) b) c) d)

Oslo London Reykjavik Warsaw

The cor rect answer is c) Reykjavik

APPENDIX C

ADDITIONAL EXEMPLARS

Ant on a knight exemplar Task Give the student the task page, “Ant on a knight”. Assume that an ant is riding on a knight (the way the ant will move) that starts on d3. Aardvarks are on b2, b3, b4, b5, b6, c1, c2, c3, c5, c6, d1, d2, d4, d5, d6, d7, e2, e5, e6, f4, f5, f6, g1, g2, g3, g4, g5, h4, and h6. The ant cannot land on any aardvarks (or he will be eaten). The ant wants to arrive at the picnic on g8 and have a good meal. What is the minimum number of moves that it will take the ant to get to the picnic? Map out the ant’s path.

Context This task integrates the student’s knowledge of knight movements, calculating ability, cr eativity, and mapping skills.

Task purpose This task tests the student’s understanding of knight movements. Mapping skills, following directions using a coordinate plane, critical-thinking skills, and calculating abilities will be demonstrated.

Student task The student will calculate and map out the correct path in order to reach a predetermined destination on a blank chessboard. The first step is to mark the aardvarks on the chessboard. In this task, the astute student will realize that he can start at d3 or work backwards from the picnic at g8.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This is an exercise that relates to any subject where the student is required to calculate a direction and map out a solution. Subject can be linked to social studies and science (predator/pr ey). There is also a link to art for younger students who may wish to dr aw the ant, aardvark, and picnic.

Teaching tips The only chess knowledge required to solve this problem is an understanding of how a knight moves (horizontal and vertical movement). The rest of the task requires calculating possible paths and mapping out the solution. There are many easy variations of this problem that the novice chess-playing teacher can create that are similar to this ant and the aardvark exemplar.

Concepts to be assessed and skills to be developed Mapping skills Problem-solving skills Critical thinking Calculation Reasoning and log ic Communication Understanding of knight movements (horizontal and vertical) Use of coor dinate plane to describe location Art (for younger students…drawing ant, aardvark, and picnic)

Suggested materials Give the students a copy of the task page, “Ant on a knight,” that includes a blank chessboard for them to draw the solution on.

Solution

First mark the aardvarks (black disks), the ant’s starting location (White knight), and the picnic (black star) on the map (chessboard). Then, wor k either forwards o r backwards to g et the only solution. Correct path to picnic: N-e1-f3-h2-f1-e3-c4-a5-b7-d8-f7-h8-g6-e7-g8 Minimum number of moves…14

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand how the knight moves. The path(s) chosen seem random. No logical solution is given. The ant doesn’t find the picnic and starves or lands on (and gets eaten by) an aardvark along the way.

Apprentice The ant makes it part of the way, but never ar rives at the picnic on g8 .

Practitioner The practitioner finds the correct path to arrive at the picnic. The path taken is log ically explained.

Expert The expert finds the correct path explains his methodology in a clear, concise, and correct manner. The expert may work the problem forward and backward, and explains his choices clearly along the way.

Ant on a knight Task Assume that an ant is riding on a knight (the way the ant will move) that starts on d3. Aardvarks are on b2, b3, b4, b5, b6, c1, c2, c3, c5, c6, d1, d2, d4, d5, d6, d7, e2, e5, e6, f4, f5, f6, g1, g2, g3, g4, g5, h4, and h6. The ant cannot land on any aardvarks (or he will be eaten). The ant wants to arrive at the picnic on g8 and have a good meal. What is the minimum number of moves that it will take the ant to get to the picnic? Map out the ant’s path.

Ant on a bishop exemplar Task Give the student the task page, “Ant on a bishop”. Assume that an ant is riding on a bishop (the way the ant will move) that starts on a1. Aardvarks are on c3 & e5. The ant cannot land on, move through, or jump over the aardvarks (or he will be eaten). The ant is hungry and wants to arrive at the picnic on h8 as soo n as possible. Map out the shortest paths to the picnic. What is the minimum number of moves that it takes to get to the picnic?

Context This task integrates the student’s knowledge of diagonals (bishop movement), calculating ability, creativity, and mapping skills.

Task purpose This task tests the student’s understanding of diagonals with bishop movements. Mapping skills, directions on a coordinate plane, following directions, critical thinking skills, and calculating abilities will be tested. Recognizing patterns and the concept of symmetry are both important in arriving at the correct solution.

Student task The student will calculate and map out several paths in order to reach a predetermined destination on a blank chessboard.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This exercise relates to any subject where the student is required to calculate a direction and map out a solution. A link to social studies, science (predator/prey), and geography in relation to mapping longitude and latitude are explored. There is also a link to art for younger students who may wish to draw the ant, aardvark, and picnic.

Teaching tips The only chess knowledge required to solve this problem is an understanding of the diagonal movement of a bishop. The rest of the task requires calculating possible paths and mapping out the solutions. There are many variations of this problem that the teacher can easily create that are similar to this Ant and the Aardvark example.

Concepts to be assessed and skills to be developed Mapping skills Symmetry Problem-solving skills Reasoning and log ic Communication Understanding of diagonal movements (bishop) Use of coor dinate plane to describe location Art (for younger students…drawing ant, aardvark, and picnic) Calculation Critical thinking

Suggested materials Give the students a copy of the task page, “Ant on a bishop” that includes a blank chessboard for them to draw the solution on.

Solution

Aardvarks are the black disks; the picnic is the black star.

There ar e four possible solutions (each taking five moves): Solution Solution Solution Solution

1: 2: 3: 4:

a1-b2-a3-e7-f6-h8 a1-b2-a3-f8-g7-h8 a1-b2-c1-g5-f6-h8 a1-b2-c1-h6-g7-h8

Note that the 1 st  and 3 rd, and the 2 nd  and 4 th  solutions are symmetrical about the a1-h8 diagonal.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand the bishop’s diagonal movement. The path(s) chosen seem random. No logical solution is given. The ant doesn’t find the picnic and starves or gets eaten along the way.

Apprentice Some of the diagonal paths are logical. The ant may jump over an aardvark or arrive at the picnic in more or less than five moves.

Practitioner The practitioner finds at least three ways to ar rive at the picnic in five moves. The paths taken are logically explained.

Expert The expert finds all four paths and explains them in a clear, concise, and correct manner. The expert makes the observation that the solution is symmetrical about the a1-h8 diagonal.

Ant on a bishop Task Assume that an ant is riding on a bishop (the way the ant will move) that starts on a1. Aardvarks are on c3 & e5. The ant cannot land on, move through, or jump over the aardvarks (or he will be eaten). The ant is hungry and wants to arrive at the picnic on h8 as soon as possible. Map out the shortest paths to the picnic. What is the minimum number of moves that it takes to get to the picnic?

Save the queen exemplar Task By not following good chess habits, White touches his queen too quickly before thinking out his plan and has to move her because of the “touch move” rule. Given the position on the task page, "Save the queen", what fraction of possible queen moves puts her on a safe square where she can’t be captured the next move?

Context This task integrates the student’s knowledge of chess piece movements and calculating ability and translates the problem into a mathematical form. The student then integrates probabilities and fractions to form a solution.

Task purpose This task demonstrates the student’s understanding of how the chess pieces move coupled with calculating different possible outcomes and expressing the solution by identifying points on the coordinate plane. It then requires students to express their findings in terms of a fraction.

Student task The student will calculate the squares where the

queen can move to safely and not be captured.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. Any subject, such as science, where calculating possible results of an event and expressing the solution in terms o f a fraction is required.

Teaching tips Knowing how the queen legally moves is the only chess requirement needed to solve this problem. The solution is then a calculation using addition and then converting the answer into a fr action.

Concepts to be assessed and skills to be developed Knowledge of chess piece movements Concept of “What is a legal move?” Reasoning and log ic Calculation Addition Predicting possible future outcomes and move combinations Number sense Fractions Probability Use of coor dinate plane to describe location Communication Critical thinking

Suggested materials Give the student a copy of the task page, “Save the queen”.

Solution

Possible queen moves (16): Qa6 Qe6 Qb5 Qe5 Qc4 Qe4 Qd3 Qe3 Qd2 Qe1 Qd1 Qf3 Qxe8 Qg4 Qe7 Qh5 Of these choices, Qc4, Qd2, and Qd1 are the only safe squares where the queen won’t be captured by a Black piece.

Correct answer: 3/16

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand or remember how the queen moves. No logical solution is given.

Apprentice Finds some, but not all, of the possible queen moves. May not understand why c4, d2, and d1 are her only safe squares.

Practitioner The practitioner understands the problem and explains clearly how he arrived at the correct answer by either listing the possible queen moves or marking them on the chessboard.

Expert The expert understands the problem and explains clearly how he arrived at the correct answer by both listing the possible queen moves and marking them on the chessboard. The expert will specifically note the reasons for each of the unsafe move s.

Save the queen Task By not following good chess habits, White touches his queen too quickly before thinking out his plan and has to move her because of the “touch move” rule. Given the position below, what fraction of possible queen moves puts her on a safe square where she can’t be captured the next move?

Start of game probabilities exemplar Task How many possible different legal moves can White make with his fir st move in the game? (See the diagr am on the "Start of the game pro babilities" task page.) At the start of the game, White randomly touches a piece (which is capable of a legal move) and has to move it because of the "touch move" rule. What is the probability that it is a knight move? The answer is given in the form of a fraction.

Context This task integrates the student’s knowledge of chess piece movements and calculating ability and translates the problem into mathematical form. The student then integrates probabilities and fractions to for m a solution.

Task purpose This task demonstrates the student’s understanding of how the chess pieces move, coupled with calculating different possible outcomes. It then requires students to express their findings in terms of fractions and pro babilities.

Student task The students will use a diagram of a chessboard for the task entitled, “Start of game probabilities,” with the pieces on their starting squares to calculate possible answers to the stated question.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. Subjects like science, where calculating possible occurrences of an event is required, link to this exemplar. Critical-thinking skills are used to calculate probabilities and fractions.

Teaching tips Knowing how the pieces legally move is the only chess requirement needed to solve this task. The solution is then arrived at by calculation using addition (also multiplication… if the student knows how), fractions, and probabilities. This exemplar is only for the older children. Younger children who don’t know fractions and probabilities won’t understand the task.

Concepts to be assessed and skills to be developed Knowledge of chess piece movements Concept of “What is a legal move?” Reasoning and log ic Calculation Addition Multiplication Predicting possible future outcomes and move combinations Number sense Fractions Probability Communication Critical thinking

Suggested materials Give students a copy of the task page, “Start of game probabilities”.

Solution

On White’s fir st move he can only leg ally move the pawns and knights (all the other pieces are trapped in by pawns). There are eight pawns, each with two possible moves, (2+2+2+2+2+2+2+2 or 8 x 2) and two knights, each with two possible moves, (2+2). Therefore, 16 + 4 = 20 is the total possible number of legal moves that White can make on his first move. Probability that a knight must move given a piece was touched: Two knights can move and eight pawns can move. Therefore, the probability of a knight move is 2/(2+8) = 2/10 or 1/5 or 20 %.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t understand or remember how the pieces move. No logical solution is given.

Apprentice Student correctly reasons that only the pawns and knights can move on the first move of the game. Student misses that each pawn has a choice of one move forward or two moves forward OR that each knight has two possible moves. The solution and explanation are incomplete. The apprentice may understand the chess part of this task, but does not have a firm grasp of fractions or probabilities.

Practitioner The practitioner understands the problem and explains correctly how he arrived at the correct answers by either drawing on the board or putting the problem into a mathematical equation.

Expert The student clearly understands the problem, draws the answer on the diagrammed board, and explains the correct mathematical equation. Reduces the 2/10 to 1/5 fraction and converts answer to 20%.

Start of game probabilities Task How many possible different legal moves can White make with his fir st move? At the start of the game, White randomly touches a piece (which is capable of a legal move) and has to move it because of the “touch move” rule. What is the probability that it is a knight move? Give your answer in the form of a fraction.

New threats exemplar Task In the position on the “New threats” task page, Black’s previous move was pushing his pawn from d7 to d5. List all of the moves that Black can make on his next move that he couldn’t do before moving his pawn to d5. What are all the new threats that he created by moving to d5 that can win material on the next move? Which move wins the most material?

Context This task integrates student’s knowledge of chess piece movements, visualization skills, and calculating ability. Many young chess players are not aware of what their opponent is threatening and only focus on their own plan. The student typically sees one threat and doesn’t look for any additional threats. This task encourages the students to co nsider that their opponent’s moves and threats are equally important as their own.

Task purpose This task tests the student’s understanding of piece movements, piece captures, knowledge of piece values, and calculating ability. The student will express the solution in algebraic chess notation (using a coordinate plane to describe location). The student will use addition and subtraction by counting material to determine the best move.

Student task

Student will write down all the new possible legal moves in the position after Black plays …d5. The student will then evaluate which threats win material and then pick the threat that wins the most material.

Time required 10 minutes

Interdisciplinary links Students will use written- or oral-presentation skills to explain their solution. This task can be related to any subject that shows the student that the world is a big place and does not revolve around them by reinforcing the concept that they must consider the actions of others. There is a strong link to the business world, where a professional must look at deals or sales from a client’s or competitor’s perspective. Links also apply to social studies (geography using the coordinate plane) and science (critical-thinking skills).

Teaching tips Identifying threats is intertwined into several of the chess lessons, mainly piece movements, tactics, and free stuff. During the half-hour when the students are playing against each other, the teacher will have many opportunities to reinfor ce the concepts of piece captures and new threats.

Concepts to be assessed and skills to be developed Problem-solving skills Consideration of many possible move co mbinations Reasoning and decision making Number sense

Calculation Critical thinking Communication Knowledge of chess piece movements Use of coor dinate plane to describe location

Suggested materials Give the students a copy of the “New threats” task page.

Solution

The star is on the square (d7) that the d5 pawn moved from. The mathematical concept of sets and subsets are present in the solution. The new possible moves that Black can play after …d5 (which he couldn’t play befor e) are: …d4 …dxc4 …dxe4

…Nd7 …Bxh3 …Bg4

…Qxa4 …Qb5 …Qc6 …Qd7

…Bf5 …Be6 …Bd7

The new possible mo ves that win material are: …d4  (forking the bishop and knight) …dxc4 (This is a tough idea to see. This move captures the pawn, but White can recapture with Nxc4. Only the Expert may realize that if this recapture with the knight occurs, Black could then play …b5, forking the two knights with the b-pawn and winning material as a result of the fork, thereby making Nxc4 a mistake) …dxe4 (wins a pawn, because the pawn is also attacked by the knight on f6 and is defended only once by the White pawn on f3) …Qxa4  (which wins the knight = 3) …Bxh3   (which wins the queen (9) for a bishop (3)..… a net gain of 6).

Of course, …Bxh3 winning the queen for a bishop nets the most material for Black. Black could then win additional material following this up by playing one of the other moves given above.

Rubrics and Benchmarks

Novice Student is confused by the question and doesn’t remember exactly how each piece moves and captures and what the pieces are worth. No logical solution is given.

Apprentice The apprentice will see some of the new threats and may notice that capturing the queen is the best move. Not identifying all of the threats, however, leads to an incomplete solution.

Practitioner The practitioner correctly lists all of the new possible moves for Black and correctly identifies that …Bxh3 is the move that nets out the most material. He may get so excited when he sees that the White queen can be taken that he doesn’t fully explain the results of the other possible moves.

Expert The expert correctly identifies all of the new possible moves for Black and all of the moves that threaten to win material. Each move is carefully examined, including the d4 move that forks the bishop and knight and maybe the pawn fork resulting after 1… dxc4 2.Nxc4 b5. In the end, of course, he selects … Bxh3 as the threat that wins the most material.

New threats Task In the position below, Black’s last mo ve was pushing his pawn from d7 to d5 . List all of the moves that Black can make on his next move that he couldn’t do before moving his pawn to d5. What are all the new threats that he created by moving to d5 that can win material on the next move? Which move wins the most material?

GLOSSARY absolute pin when a piece is pinned to the king and cannot move because the king would be placed in check algebraic notation a chess language that designates the moving piece and the square it moves to as a location in a two-dimensional coordinate plane analog clock a chess clock with a traditional clock face and a flag which falls at the top of the hour to signify that a player has run out of time attacker a piece that attacks an o pposing piece back rank another name for the first rank, the rank closest to the player back rank mate a checkmate that occurs when the king is attacked on the back rank by a queen or rook and is blocked by his own pawns that prevent him from escaping via the second rank backward pawn a typically weak base pawn on a half-open file that may be vulnerable to attack by opposing rooks base pawn the pawn in the pawn chain that is closest to the player bishop (symbol – B) a piece worth three pawns that moves diagonally in any direction until it runs into another piece or the edge of the board Black player with the dark-colored pieces who moves second in the game Black move designated in algebr aic notation by a move number and three do ts preceding the move like, 1…Nf6 capture when a piece moves to a square where an opposing piece is resting and removes that piece from the board castling a special move involving the king and a rook that gets the king out of the center and develops the rook that usually occurs in the opening and is the only time a player can move two pieces in one turn center the middle of the board that includes the squares e4,

e5, d4, and d5 check when the king is placed under attack checkmate the object of the game which occur s when the king is put in check and there is no way to escape combination a series of forced moves used to improve the position using tactical building blocks (like pins and forks) defender a piece that defends one o f its own pieces a larg e, twodemo board (or demonstration board) dimensional chess board that hangs on the wall so that the entire class can easily see a chess position developing a piece  (also called development) when a piece (knight, bishop, rook, or queen) moves off its starting square to a better square, incr easing its potential digital clock a type of chess clock with a digital face (showing numbers only, no clock hands) moving a piece and attacking an discovered attack opponent’s piece with a bishop, rook, or queen that is hiding behind the piece that moved moving a piece and checking the discovered check opponent’s king with a bishop, rook, or queen that is hiding behind the piece that moved double attack a discovered attack where the moving piece also attacks the opponent’s piece double check a discovered check where the moving piece also attacks the king doubled isolated pawns two pawns lined up vertically on the same file with no friendly pawn on an adjacent file to provide protection doubled pawns two pawns lined up vertically on the same file that have a friendly pawn on an adjacent file that can provide protection draw chess terminolo gy for a game ending in a tie draw offer the event that occurs when one of the players makes his move and verbally offers a draw to his opponent endgame the phase of the game when only a few pieces are remaining on the board en passant (meaning “in passing” in French) a special pawn

capture that exists for only one move and occurs when a pawn on the fifth rank captures an opposing pawn on an adjacent file that advanced two squares forward, as if it only moved one square forward en prise (meaning “in take” in French) referring to piece that is vulnerable to capture exemplar  an example problem to test the student’s understanding of a particular subject matter extension activity educational term relating to an exercise or example that a teacher can use to reinforce a concept previously taught 50-move draw a rare type of draw where 50 moves haven take place with no pieces being captured and no pawns moved files columns on the chessboard designated by a letter from a to h flag the device that falls at the top of the hour on an analog clock that signifies that a player has run out of time flight square (or escape square) a square that a king can move to in order to escape checkmate forcing move a move, like a check, that for ces the opponent’s immediate response fork a common type of tactic that occurs when a piece attacks two or mor e pieces at once free stuff (chess slang) another way to say hanging pieces half-open file a file where one player has a pawn and the other player doesn’t have a pawn hanging when a piece or pawn is left unguarded and exposed to capture (en prise is the proper chess term)

“I adjust” what is said when a player wishes to center a piece on the square it occupies and not be forced to move it because of the “touch move” rule illegal move  moving a piece in a way contrary to the piece’s correct movement or leaving the king in check after making a move insufficient mating material when a player does not have enough material left on the board to force checkmate introduce the educational term for the first time a concept is introduced to the class isolated passed pawn a pawn that has the bad attribute of being isolated and the good attribute of being passed isolated pawn a weak pawn that cannot be protected by another pawn because there are no friendly pawns on an adjacent file king (symbol – K) the most valuable piece on the boar d that moves horizontally, vertically, or diagonally, only one square at a time kingside the half of the board where the kings begin the game on (the e-, f-, g-, and h-files) knight (symbol – N) worth three pawns and the only piece that can jump over other pieces, moving in a capital “L” shape “knight on the rim is dim” a chess rhyme describing that a knight is poorly placed on the edge of the board due to its limited short-range capabilities major pieces ro oks and queens mate a commonly used term that means the same as checkmate material sum of the values of the pieces mating material having enough material to force checkmate mating net chess term for when the king’s flight squares are eliminated, making checkmate possible middlegame the middle part of the game typically beginning around move ten, after the pieces have been developed, and lasting until only a few pieces remain on the board minor pieces knights and bishops open file a file not blocked by any pawns

opening the first ten or so moves of the game when most of the pieces ar e developed and the kings have castled passed pawn a pawn that can move to the other side of the board and promote without an opponent’s pawn blocking its path or on an adjacent file with the potential to capture it pawn  (symbol – left blank) the least valuable piece on the board that can only move in a forward direction and can promote to another piece, usually the queen, when it reaches the other side of the board pawn chain pawns on adjacent files connected on a diagonal line, so that they protect each other the most common type of threefold perpetual check repetition, when the player who is typically losing the game forces a position where he can check the other king back and forth forever piece chess terminology for knights, bishops, rooks, or queens (pawns are referred to as pawns and kings as kings) pin a common type of tactic where a long-range piece (queen, rook, or bishop) attacks an opponent’s piece, which is shielding another one of the opponent’s pieces of equal or gr eater value promotion o r promoting a pawn the event that occurs when a pawn gets across the board to the eighth rank and usually becomes a queen protected when a piece is defended by a friendly piece, usually making it unwise for the opponent to capture it protected passed pawn a passed pawn that is protected by a friendly pawn queen (symbol – Q) the most powerful piece on the boar d worth nine pawns that moves horizontally, vertically, or diagonally until it runs into another piece or the edge of the board queenside the half of the board where the queens begin the game o n (the a-, b-, c-, and d-files) ranks the chess name for rows that run horizontally across the board reinforce the educational term for reinforcing a topic that has

already been introduced to the class resigning when a player concedes the game roller a type of checkmate maneuver where a rook and queen (or two rooks or two queens) take turns moving past each other in order to shrink the box around the opposing king, eventually leading to checkmate rook (symbol – R) the piece worth five pawns that moves horizontally and vertically until it runs into another piece or the edge of the board rubric  a measurement tool used to assess the student’s understanding of a problem or exemplar sacrifice voluntarily giving up material in or der to gain some other type of advantage or a checkmate Scholar’s Mate (also known to children as the four-move checkmate) a quick, easily avoided checkmate, where one player wins by bringing his queen out early score sheet a chess game recording sheet with spaces for 60 moves for each player to r ecord the game on skewer a type of tactic analogous to a pin, where the more valuable piece is in fr ont of the less valuable piece smothered mate when the king is checkmated by a knight and is surrounded by his own pieces (rook and two pawns) that prevent escape square of the pawn an imaginary square the defending king must get into in or der to win the foot race with the pawn to the promotion square stalemate a type of draw where the player to move has no legal moves starting position the beginning of the game with White to move tactics the short-term, immediate threats and attacks that make up individual battles between pieces threefold repetition a type of draw that occurs when the same identical position occurs three different times tempo a single move, relating to time threat an aggressive move that attacks an opposing piece “touch move” rule when a player is forced to move a piece

he touches, provided it is a legal move “touch take” rule when a player touches an opponent’s piece and must capture it, if he can legally tripled isolated pawns a fairly rare event where three pawns are lined up vertically on the same file with no friendly pawn on an adjacent file to provide possible protection tripled pawns a fairly rare event where three pawns are lined up vertically on the same file with a friendly pawn on an adjacent file that can pro vide pro tection Venn diagram a visual aid used to display and compare data showing the intersection of two or more data sets White player with the light-colored pieces who moves fir st in the game White move designated in algebr aic notation by the move number followed by a period, like 15.Nf3

ABOUT THE AUTHOR  At age six, Todd Bardwick learned how to play chess from his father, Alan, an expert strength tournament player. Alan utilized many of the chess teaching ideas presented in this book. Back in the early 1970’s when few children played in r ated tournaments, Todd consistently improved his game and was nationally ranked most of his youth for his age gr oup. After leading his high school chess team to several state titles, Todd went to college and graduated first in his class from the University of Colorado at Boulder in 1985 with a B.S. in Civil Engineering. After college, he moved to San Diego for five years where he worked as a rocket scientist (structural analyst). Moving back to Denver in late 1989, Todd worked as an entrepreneur and continued his chess-playing career. In 1993, Todd achieved the National Master title awarded by the United States Chess Federation (USCF). Of Todd’s numerous tournament achievements, most notable is winning the Denver Open Championship five consecutive years (1992-1996) against strong competition, where his perfor mance rating was over 240 0. In the early 1990’s, Todd discovered his passion for teaching chess to adults and children. From 1993 until the paper’s closing in 2009, he wrote a popular monthly chess column for the Rocky Mountain News, one of the nation’s largest newspapers. In 1995, Todd founded the annual Rocky Mountain Chess camp that has grown to become one of the largest chess camps in the United States. Students come from across the nation to participate in the camp. In 2002, The Chess Detective ®  column was born in School Mates, the national children’s chess magazine published by the United States Chess Federation. School Mates

later became Chess Life for Kids magazine. Visit www.ColoradoMasterChess.com to see additional columns that Todd has written for the Colorado Chess Informant. Having taught over 10,000 chess classes, Todd has been one of the country’s leading full-time chess-teaching masters for many years. His logical and fun approach to the game and reputation as an excellent teacher has inspired Todd to form the Chess Academy of Denver where he teaches well over 750 students per year through private lessons, school classes, chess camps, and year-round camp workshops for adults and children. Todd also regularly trains elementary school teachers who want to learn how to incorporate chess and its educational benefits into their classrooms. Educationally, Todd runs school district chess programs, teaches in Gifted and Talented programs, and trains parents and teachers on a weekly basis on how to effectively teach chess to children in their school enrichment programs. Todd accepted the invitation to speak at the 2002 National Gifted and Talented conference for teachers and parents about the benefits of chess and how to improve a child’s math skills using chess as a vehicle. In 2006, Todd published his second book, Chess Workbook for Children – The Chess Detective’s Introduction to the Royal Game, a companion student workbook to Teaching Chess in the 21st  Century. Todd published his third book, Chess Strategy Workbook , in 2010. This is an intermediate level chess book for students who have mastered the concepts taught here in Chess Workbook for Children. Todd’s students have achieved accolades in life and chess. Successes include gaining early admission to top universities, like Stanford and Yale, becoming Presidential Scholars, being ranked number one in chess in the United States for their age gr oup and winning state and national chess titles. Todd is available for speaking engagements, chess teacher training, chess lessons, chess classes, and simultaneous chess exhibitions. Todd can be reached through his website at