Who, What, When, Where, Why?
Algebra 1 Students
After learning about operations with monomials
Anywhere you want
Because you want your students to practice operations with monomials.
Be the first player to move all of your pawns to the opposite side of the board.
- 70 Expression cards. I wrote the following expressions on index cards that were cut in half. You may find it useful to write the expression twice so that it can be read from opposite directions.
The 70 expressions:
0, 1, 2, 1/2, 3, 1/3, 3/2, 2/3
x, 2x, 3x, 4x, 5x, 6x, x^2, 2x^2, 3x^2, 4x^2, 6x^2, 9x^2
y, 2y, 3y, 4y, 5y, 6y, y^2, 2y^2, 3y^2, 4y^2, 6y^2, 9y^2
x+y, x+2y, x+3y, 2x+y, 2x+2y, 2x+3y, 3x+y, 3x+2y, 3x+3y
x-y, y-x, x-2y, 2y-x, x-3y, 3y-x, 2x-y, y-2x, 2x-2y, 2y-2x, 3y-2x, 3x-y, 2y-3x, 3x-3y
xy, 2xy, 3xy, 4xy, 6xy, 9xy
x/y, y/x, 2y/x, x/3y, y/2x, 3y/2x, 2x/3y, y/3x, 3x/2y
- 6 blank dice or 6 dice with stickers. Write the monomials x, 2x, 3x, y, 2y, and 3y on the six sides.
- 16 pawns in four different colors. I used water bottle caps with color paper glued on and arrows drawn. I believe the arrows are necessary to keep track of which pawns are moving in which direction.
Shuffle the expression cards and place them in a 6x6 array with the four corners missing. Along each side place four pawns. See image below:
Place the pawns so that each arrow is pointing toward the nearest card. That is the direction the pawns need to move to get to the opposite side of the board.
Player 1 rolls all six dice. He is trying to use two dice at a time to create the expression in the direction of the arrow. A player may add, subtract, multiply, or divide to create the expressions. Players may make up to two moves per turn, either one move with two pawns or two moves with one pawn.
From the image below, you can see that the yellow player has the following expressions he can move to; x/3y, y-2x, 3xy, and x-y.
He rolls the following monomials:
Using 3y * x, he gets 3xy and can move his pawn ahead one space. And with 2x-2x, he gets 0 and can move that same pawn ahead one space.
After rolling the 6 dice, a player may keep any dice that he likes and re-roll the rest. A player can only re-roll once per turn.
Play moves to the next player.
Take a look at the green pawn that is still off the board. pawns may 'jump' over other pawns that are in their way.
The green player rolls the follow monomials:
Using 2y*y he gets 2y^2 and moves his pawn.
Then using x*2x he gets 2x^2 and 'jumps' over the yellow pawn to the next space.
As the game continues, the middle of the board will get congested and pawns may 'jump' over multiple pawns on their turn. This is a good strategy to get to the opposite side faster.
The yellow player was the winner this round . he was able to get all 4 pawns to the opposite side of the board before the rest of the players.
Hints, Tips, and Suggestions:
Make sure the arrows are pointing in the correct direction at all times.
There will be times when players will only be able to move once on their turn or in some cases not at all. In the image above, the red player was moving left and was unable to move because the green pawn was in the way.
Writing the expression twice on each card is recommended so that it's easier for all players to read them.
Since you are creating 70 cards but only need 32, you could have two simultaneous games running with one deck.
Players may move their pawns in any direction as long as they only move to adjacent spaces.
To create a longer version of the game, start with a 7x7 array of expression cards with the corners missing and 20 pawns, 5 of each color.