Algebraic Notation — Knight’s Tour and Other Applications

Algebraic Notation is a method for recording coordinates in 2 or 3 dimensions. We started our exploration of this fascinating topic by looking at games like chess, checkers, bingo, battleship and many others. In chess, when a Knight moves it is notated by Nf3 if it were to move to the f column and the third row. Why N? Because the King uses K. Bingo uses moves like B11. Battleship sinks ships by using B3. 

We then looked at a map of Wellesley with the surrounding towns of Natick, Weston, Needham, Newton, and Dover. Each square area on a map uses algebraic notation although paper maps are somewhat outdated given GPS and smart phones. So then we explored what global positioning system uses to locate a point on the planet by looking at latitude and longitude. On my smart phone, we used the compass application to find our location like 42 degrees, 14’55” N, 71 degrees 19’38” W. We looked at a map of the world where they could see that we are 42 degrees north of the equator and 71 degrees west of the Prime Meridian. We discussed the meaning of minutes and seconds to represent 60 increments of distance between degrees and minutes, respectively. This would take a whole other lesson so we just touched on this. Every time we use GPS, our device is talking to at least three satellites that locate our coordinates using algebraic notation of latitude and longitude.

In order to build mastery of this important concept, I had them trace a Knight’s Tour using algebraic notation. Then they were asked to use 64 moves in algebraic notation to a knight’s tour using numbers or geometric representation. The most difficult challenge for the 3-6th graders was to follow a geometric knight’s tour and record the algebraic notation.

For those students who have never done knight’s tours, a knight is placed on any square ("cell") on a rectangular grid and is moved until all cells are covered; a knight cannot visit the same square twice. On an 8x8 board, number each move from 1-64. You can start from any one of the 64 squares on the chess board. You do not need to know how to play chess; you just need to know how a knight moves. The knight moves in an "L" pattern; two squares horizontally or vertically; then one square to the right or left; knights may jump over other moves.

During the week, students should attempt to translate as many knight’s tours using algebraic notation as possible and continue to find their own knight’s tours. The most ambitious students will find their own knight’s tours and then plot them using algebraic notation.

I am preparing them for algebra using the Cartesian coordinate system which specifies points on a plane by a pair of numerical coordinates. This is how all computer graphics are computed; many of our students love to play video games; why not teach them to create their own games?