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Activity: Shape Exchange Game

DRAFT!!!

RATIONALE
I got a game similar to this from a magazine when I was young (probably Ranger Rick's Nature Magazine or Highlights for Children). Much later, when I learned algebra, I found that some of the concepts were familiar and comfortable. Who knows? ...maybe it'll work for others. If not, it's at least a pleasant solitaire game.

MATERIALS

• One copy of the basic shapes , optionally the expansion set . (Alternatively, black and white versions of the basic shapes and expansion set.)
• Stiff backing and adhesive (or print onto heavy paper).
• Scissors or paper cutter.

PREPARATION

1. Print the basic shapes onto heavy paper (or print and mount onto backing). If desired, also print the expansion set. I strongly suggest making these somewhat different, such as mounting onto a different color or marking the backs.
2. Cut out the pieces.
3. Separate the single shapes from the equation (=) cards.

PROCEDURE

1. Shuffle the shape cards and deal out a string of them, face up. Start with perhaps 8, but 15 makes a good number once you've learned the game.
2. Shuffle the basic set's equation cards. For an easy game, deal out 6, face up. For more of a challenge, try using just 5. (A game with five cards is not always winnable, but it's also useful to learn what equations form a potentially winnable combination.) Arrange the equation cards so that the single shape is on the right-hand side.
3. Use the equations to exchange shape cards. Try to eliminate cards. Count it a "win" if you get down to one card.

EXAMPLE

(This uses T for triangle, S for square, and C for circle):

Equations:

1. S C = S
2. C S = C
3. T T = T
4. T C = C
5. C C = C

Cards:

S C T T C S S

Steps:

• use equation 3 to replace T T with a single T : S C T T C S S becomes S C T C S S
• use equation 1: S C T C S S becomes S T C S S
• use equation 4: S T C S S becomes S C S S
• use equation 2: S C S S becomes S C S
• use equation 2: S C S becomes S C
• use equation 1: S C becomes S

You can also use the equations backwards. Say you've reduced the above sequence to S S:

• use equation 1 to expand the first S into S C : S S becomes S C S
• use equation 2: S C S becomes S C
• use equation 1: S C becomes S

ALTERNATIVES AND OTHER DETAILS:

The shapes need to be in the same order as in the equations. For example, equation 1 (above) can only be used to reduce S C; it can't be used on C S.

The orientation of the triangle doesn't matter - point up, down, or sideways.

Slide the cards together as you reduce the number, to make it easier to see the patterns.

Variations (not thoroughly tested!):

• Use the equations upside-down if that's how you deal them.
• Add equations from the expansion set.
• Vary the number of equations you use. Perhaps draw equations just until you think you have enough, then play. Try to use just a few equations to win.
• Add your own equations.
• Use the black & white set and color it. Make different colors of each shape, and then add color equations that are separate from the shape equations. (I'll eventually do this and put it online.)
• Deal out the cards in a rectangle instead of a line, and slide the cards always to the bottom and right. Use the equations vertically by rotating them a quarter-turn clockwise.
• To get really complicated, add another shape. Note, however, that this will require quite a few more equations in order to be winnable!

Copyright © 1998, Elizabeth E. Roettger. Permission to reproduce the instructions is granted only when full copies, including this paragraph, are reproduced and distributed.

Last updated: 09 Nov 1998. URL: http://www.nthelp.com/eer/HOAshape.html