Chess and Mathematics

First Rank is a fortnightly term-time newsletter for everyone interested in chess for education. In this issue, we present an early view of the recently concluded Erasmus+ CHAMPS which developed an innovative approach to teaching mathematics through the medium of chess.  The material will form the basis for an ECU Chess and Maths course for primary teachers and chess instructors.

See previous editions of our newsletter

The purpose of the CHAMPS project

The purpose of the CHAMPS (Chess and Mathematics in Primary School) project is to develop a new category of ‘chess-maths’ exercises in which mathematical games and puzzles are represented in a chess format. The objective is to highlight some mathematical ideas which can be communicated via the chessboard and pieces. As far as the children are concerned, they enjoy playing chess so being given some chess-like problems seems natural. It does not feel like a maths lesson. Conversely, some maths lessons may be enriched by such exercises without the need to be a chess player.

Basic ideas of the CHAMPS project

  • The mathematics exercises are presented in chess format
  • There are 50 exercises suitable from age 6 to 11+
  • Mathematical content appropriate for the target age is identified in each exercise
  • Solution methods use a structured approach familiar to maths teachers
  • The emphasis is on problem-solving
  • Methodology derived from George Pólya as used by Singapore schools
  • Accessible to teachers who do not play chess

The Singapore Method

A teaching method in the national mathematics curriculum from kindergarten until 6th Grade (age 11/12) in Singapore which has come top in the OECD Pisa international rankings

  • Method is based on three steps: Concrete, Pictorial, and Abstract
  • Step-by-step approach improves children’s problem-solving skills
  • The method focuses on fewer areas than most national curricula but goes deeper
  • Read more …

George Pólya

  • Hungarian/American mathematician (1887 – 1985)
  • His most famous book “How to Solve It” (1945) sold over 1 million copies.
  • His greatest contribution was to categorise methods (“heuristics”) for problem-solving 
  • These heuristics can be used to solve mathematical and non-mathematical problems
  • Some advice: “If you can’t solve a problem, then there is an easier problem you can solve: find it.”
  • Read more …

The Method of Simplification

You usually need to simplify the task.  Here are two examples:

Q1a: Can you place 12 knights on the board so they cover all squares?
This is a rather tricky question that is difficult for children to solve. Simplify the question by presenting a part-solution:

Q1b: Which knight should be placed on a new square so every square is covered?

A. Nf7 – g6
B. Nf2 –  f4
C. Nd3 – b3
D. Nc6 – a6

Q2a: Place eight queens on the chessboard so no queen is attacking another queen
This is a classic problem that is not easy to solve for young children. You can simplify it like this:

Q2b: Five queens are placed on the chessboard. Add three more so that no queen can attack any other.

A. b3, f8 & h4
B. b8, f4 & h3
C. b8, f4 & h1
D. b3, f4 & h8

It’s time for a new level of teaching

Since chess was introduced to schools in Europe, we have been fighting to be regarded as a proper educational tool. To be able to achieve credibility, we need to demonstrate teaching methods for cognitive and social development, not to develop chess skills.​

The CHAMPS project is exactly what I think we should be looking for. Chess gives the framework which encourages children to learn.  Within the 64 squares of the chessboard and with the help of the 32 pieces the possibilities are almost unlimited for what and how we teach. The unique thing with the CHAMPS project is that everything is taken to a new level. Modern didactic ideas are used, and every exercise has got a clear purpose and is tested in practice. We must adopt this approach in all areas where we use chess as an educational tool.

Jesper Hall,
Chair ECU Education

The ECU Chess and Maths course

The ECU has developed a one-day Chess and Maths training course for primary school teachers.  This is in addition to the ECU School Chess Teacher Certificate. We are planning to offer the new course around Europe from June 2019. If you or your organisation/federation is interested in hosting a course please contact:

The Anecdote of the Week
The Chess and Rice Story

Chess and Grains of Rice
A classic chess and maths problem arises from the invention of the game. It involves a lot of rice. There are many versions, but the most common one is this:

The Emperor of India in the 6th century was so pleased with one of his advisors who had invented the game of chess that he offered him a reward of his own choosing.  He said to the wise man:

Name your reward!”

The wise man responded:

O, Emperor, my wishes are simple. I only wish for thisGive me one grain of rice for the first square of the chessboard, two grains for the next square, four for the next, eight for the next and so on for all 64 squares, with each square having double the number of grains as the square before.“

The Emperor agreed, amazed that the man had asked for such a small reward – or so he thought.

What do you think, was it a small reward that the wise man asked for? And can you calculate how many grains of rice if only half the board is filled?

ECU Education Calendar 2019
ECU School Chess Teacher Training Courses 

Gran Canaria  29-30 MarchPep Suarez 
Murcia, Spain 3-4 May Pep Suarez 
Albacete, Spain 25-25 MayPep Suarez 
London, England 1-2 JuneJohn Foley

ECU Chess and Mathematics Teacher Training Course

London, England 31 May John Foley

The Chess and Rice Story

Half the board would contain 4,294,967,295 grains of rice.  If one grain of rice weighs 25 mg, the total weight is over 107 tonnes which is equivalent to the weight of a blue whale! A mathematical solution is here.

Twelve Knights Problem Answer 1a = B
Five Queens Problem Answer 2a = A