4.2. April 18, 2002: Chess

"A mathematician is a machine for turning coffee into theorems."--Paul Erdös

Caveat Lector: This is a web-friendly version of the activity sheet CHESS. You can also download the file (RTF) for your own use. (RTF is Rich Text Format, which can be opened in Microsoft Word, AppleWorks, ClarisWorks, Okito Composer, TextEdit, Mariner Write, and likely other word processors of varying vintages on varying platforms.)

COORDINATE SYSTEMS: CHESS

Here are the group roles. We will use the die that Ms. Lee has handed out to our group to decide who gets which role.

Remember, no islands!

highest number
question person/reporter
authorized to ask Ms. Lee or Mrs. Sooy the group's questions

next highest
reader
reads directions and makes sure everyone understands them

3rd highest
materials person
organizes necessary materials and makes sure everyone has something to work on

lowest number
scribe (monitor)
writes notes (keeps everyone on-task)

Today, we will learn about a coordinate system that shows up outside math classrooms: chess.

NOTE: If someone doesn't know how to play chess, don't worry. Everything the group needs to know is in the Chess Box. (It won't make everyone a chess grandmaster--the rules can get complicated--but we're doing math, not tournament chess.) If someone in the group knows how the pieces move, even better.

If anyone does want to play some chess, stay in at lunch and ask to borrow the Chess Box. That's what it's for.

MATERIALS: Before we start, we'll need the Chess Box ("Learn Chess Fast Gift Set"), paper, and pens or pencils.

Take a few moments to see what's in the box. Don't break anything and don't lose anything. It's not fair to the people who'll use this box afterward.

The box does say "for ages 8 and up," but so does Monopoly. We all know how old we are.

1. Go ahead now and read pp. 13-25 as a group before reading the SITUATION and SOLUTION below. When we're done, everyone should know which piece is which, how they move, and how they capture other pieces.

THE SITUATION

You're playing chess at a friend's house and you're in the middle of a game when you realize it's time to go home.

Normally you'd leave the chessboard and come back to it tomorrow. The problem is, Zap the Martian is visiting your friend, and Zap is clumsy. You just know Zap will knock everything over before you can come back, but you and your friend want to be able to finish the game.

A SOLUTION

Chess players usually don't have clumsy visiting Martians to deal with. However, sometimes they want to record their moves so they can go back and study a game, and it's easier to have a method for writing it down without having to draw the board each time. This method is called algebraic notation.

(You could videotape everything, but can you imagine sitting through a 3-hour video of a chess game? Not everyone is that hardcore.)

2. Now that we know how the pieces move, we need a coordinate system for the chessboard. Just as we can use Cartesian (x, y) coordinates to describe functions, we can use algebraic notation to describe chess.

(It's called "algebraic"--al-jeh-bray-ick--because it uses letters and numbers, like we do in algebra.)

3. Read pp. 26-29 as a group and see if you can make sense of this new coordinate system.

4. Write the group's answers to:

• the questions at the bottom of p.28
  
• Quiz No. 2 on p.29 (no fair looking at the answers until everyone's tried it!)
  

5. The group's final goal is to create a series of posters that show how all the chess pieces move (don't worry about capturing). Each person should contribute to at least one poster.

In addition to the pieces we've met already, we will include the Wizard (see 7) and a piece that we will invent (see 8).

6. For each piece you should draw the entire chessboard with only that piece. Each piece should start at a specific square:

• King (K): a4
  
• Queen (Q): f6
  
• Knight (N): e3
  
• Rook (R): b7
  
• Bishop (B): d5
  
• Pawn: g2
  

The letters in parentheses are used to represent the pieces when they're being moved. Notice that "N" stands for Knights since "K" is already taken for Kings.

Why is there no letter for pawns? The reason is that there are more pawns than any other kind of piece, so any time you refer to a pawn you don't need a letter.

Each poster should say, in algebraic notation, what squares each piece can move onto.

7. In Omega chess, there's a piece called the Wizard (W). Suppose the Wizard is at e4. Here are the squares that the Wizard can move to from e4:

d5, f5, d3, f3, d1, f1, h3, h5, b3, b5, d7, f7

Draw the Wizard's moves on a chessboard grid.

8. Invent a new chess piece. It cannot move like any other chess piece that we've seen (this includes the Wizard). Describe its moves using algebraic notation and no diagram. Include this piece on one of the poster.

9. The group should turn in:

• group discussion notes
  
• posters and records
  
• individual reports
  

Each individual report should say:

• how I contributed to the group, with 2 specific examples, such as "I explained why I thought the bishop couldn't move to h7 from f4" or "I drew the poster with the Bishop and the Rook and checked my diagrams with the group to move sure I got them right."
  
• a scenario where I might use a coordinate system to describe a game, which can't be the same as the SITUATION in this handout
  
• comments from two group members on your contributions
  

Remember:

• 1. Be polite.
  
• 2. Be constructive.
  

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 18 May 2002