Home | Algebra | Graphing | Additional Investigations | Mining through Coordinates

 Mining Through Coordinates Grab a partner. Together, on a grid of a coordinate plane, plot 10 "mines," each one just large enough to cover three lattice points (the intersections of the grid lines). Pick a starting point somewhere in the 3rd quadrant and a finishing point somewhere in the 1st quadrant. The goal will be to cross the mine field without hitting any of the mines. To play, go to the agreed starting location in the third quadrant. With the mines already placed on the paper, one player should state aloud a desired coordinate (as close as possible to the finishing location) that he or she thinks can be reached by a straight path, while also trying to avoid crossing any of the mines. The opponent places an x on the stated coordinate on the field and draws a line segment (best done with a ruler!) between the starting position and the x. If the line segment crosses any mine in the field, then the player who chose the coordinate loses. If the line segment does not cross any mines, then, from this new position, the same player picks another coordinate to strive for, repeating the process until he or she can reach the finishing location in the 1st quadrant (or until a mine is hit). Then the next player tries different paths with the same goal in mind. The player who can complete the mine field in the least amount of turns (line segments drawn) is the winner. An online version of this game can be found at the Shodor Foundation. Submit your idea for an investigation to InterMath.