Chess Mathema*cs Exercises CHAMPS Mul*plier EventLondon, December 8th 2018

John Foley

Erasmus+ CHAMPS Project Co-Ordinator: Slovak Chess FederationProject Partners: Chess in Schools and Communities, UK

Ludus, PortugalUniversity of Girona, SpainSkalica Primary School, SlovakiaVeľká Ida School, Slovakia

Erasmus+ Project Manager Štefan Marsina

Intellectual Outputs John FoleyRita AtkinsJorge Nuno SilvaStanislav StrýčkoJosep Serra

School Experience Viera HaraštováVladimir StrýčkoStanislav VlčekMark Szavin

Context

CHESSA traditional gamePlayed for 1,500 yearsA classical gameAn abstract strategy gamePlayed across the worldSimple board and piecesMentally challengingEducational benefits

MATHEMATICSFundamental to everything we doEvolving since ancient timesBasis of scienceNumeracy, Arithmetic & MathematicsKey skill for citizensRegarded as difficultDifferent pathways to accessing mathsGames based learning

Connections between chess and mathematics

problem solving concentration requiredplanning aheadlogical analysisfind the best answerpattern recognitionco-ordinate system in geometry/geography

mental arithmeticthe queening squarecounting movescounting attackers v defenderspiece exchangesome kids are good at both chess and maths

Why use Chess & Mathematics?

Many math problems can be presented on the chessboard

Children feel comfortable working with chess themes

Game based learning: mathematical games are fun

For teachers, very little chess knowledge is required

Instructive, classic, fun problems that children enjoy

Problem Solving

Official national curriculum: maths is about “problem solving”

Teachers pressured to get pupils to pass exams using standard techniques

Singapore, the leading maths country in the world, adopted the problem solving approach

For every problem, reflect on the solution method

Chess & Mathematics in PracticeMathematics enrichment Add variety to your chess lessons with

some mathematics

What is Chess-Maths?

Collection of mathematical problems and games that use the chessboard and/or the chess pieces as its medium

Essential Chess knowledge• The chessboard: files and ranks

• Naming the squares

• How pieces move and capture

• Concept of ‘controlling a square’

• Concept of ‘attacking a piece’

• Value of the pieces

• Piece colour is often irrelevant

• White goes up the board in diagrams

Final DraftNovember 2018

50 Chess and Mathematics Exercises

for Schools

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1 Each square has a name2 Identify the Square Colour3 Chess Arithmetic4 Piece Categorisation5 Four rooks puzzle6 Counters on a Line [11]7 Counters on a Line [16]8 Avoid Three in a Line9 Nim10 Nim flipped11 Golden Coin Game12 Northcott’s Game13 Sliding Rooks Game14 Wythoff’s Game [Q]15 Wythoff’s Game [QQ]16 Cross the Line Game17 The Opposition Game18 Rook Corner Puzzle19 Shortest Rook Tour20 Race to the corner [rook]21 Rook Tour on a Mutilated Chessboard22 Chomp23 Minimum distance maps24 How Many Routes? [pawn]25 How Many Routes? [rook]

26 Bishop Zigzag Puzzle27 The Invention of Chess28 The Fallen Pieces29 The Light Pawn30 Army Power Puzzle31 Maximum number of knights32 Twelve knights problem33 The domino tiling puzzle34 The tromino tiling puzzle35 Dividing the board36 Tiling the board37 Two queens puzzle38 Five queens puzzle39 Eight queens puzzle40 How many Squares on a Chessboard?41 How many rectangles on a chessboard?42 Pythagorean Checkmate43 Corner attack puzzle44 Piece power contours45 Mystery combination piece46 Fairy piece contours47 Positional logic [1]47 Positional logic [2]48 Tournament Scoring Puzzle49 King’s random walk50 Kings random jump

Index

15 Wythoff’s Game [QQ]

SET UPPlace queens on h5 and g8.

MOVESThe queen can only move West, South West orSouth.

METHOD OF PLAYEach turn, the player may move either of theQueens.

WINNING CONDITIONThe first player to move a queen to a1 is the winner.

18 Rook Corner Puzzle

MOVESThe rook is not allowed to visit the same square twice.

OBJECTIVECan the rook cover all the squares on the board and finish onh8?

44 Piece power contours [e]

QUESTIONWhich piece is depicted by this power contour?

49 King’s random walk

9

9 9

9

13

13 13

13

DEFINITIONA random move is made by chance. Each move is equallyprobable.

TASKStarting at a8, a king makes two random moves. What is theprobability that the king returns to a8?

From Questions to Answers

NEXT STAGE IN THE PROJECT

Feedback from

v Teachers

v Children

How to present exercises

ClassificaEon of exercises

Problem solving methods

Novembro 2018

50 Exercícios de Matemática e Xadrez

para as Escolas

IO1

Versión preliminarNoviembre 2018

50 Ejercicios de Ajedrezy Matemáticas para las

Escuelas

IO1

Chess Mathema*cs Exercises CHAMPS Mul*plier EventLondon, December 8th 2018

John Foley