Coordinate System Board Game

An interactive, competitive classroom math game designed by Sahra Industrial Design, uniting 2D Cartesian mapping, 20-sided dice mechanics, and Pythagorean distance calculation on a dynamic 4-quadrant plane[cite: 5].

Apparatus & Layout

The Game Board

4-Quadrant Playing Surface

A 20 × 20 grid centered at the origin (0,0) spanning -10 to +10 along both X and Y axes, complete with geometric curves (Circle, Parabola, Ellipse, Hyperbola, and Sloped Lines)[cite: 5].

Coordinate System Board Game with 20-face dice and geometric curves

Polyhedral Coordinate Generation

Includes two 20-face polyhedral dice (color-coded for X and Y components) to roll random integer coordinates spanning positive and negative quadrants[cite: 5].

Rules & Mechanics

Game Mechanics

1. Rolling the Axes

Roll both 20-sided dice simultaneously: one die dictates horizontal X coordinate displacement, while the other sets vertical Y coordinate displacement[cite: 5].

2. Cartesian Navigation

Move left/right along columns for ±X and up/down along rows for ±Y relative to the central (0,0) origin[cite: 5].

3. Geometric Curve Encounters

Plotting locations challenges players to identify whether their coordinates fall within embedded loci: Circle, Ellipse, Parabola, or Hyperbola zones[cite: 5].

Multi-Player Flexibility

Accommodates individual practice or multi-player competitive rounds with no limit on participant numbers[cite: 5].

Math & Benchmarks

Vector Magnitude

Coordinate Quadrant Reference

Quadrant X Axis Y Axis
Quadrant I Positive (+1 to +10) Positive (+1 to +10)
Quadrant II Negative (-1 to -10) Positive (+1 to +10)
Quadrant III Negative (-1 to -10) Negative (-1 to -10)
Quadrant IV Positive (+1 to +10) Negative (-1 to -10)
Pythagorean Distance Computation

Calculate the true vector displacement (distance) from origin (0,0) to plotted coordinate (X, Y)[cite: 5]:

Vector Magnitude = √(X² + Y²)

Reinforces Euclidean metric calculation, powers, roots, and sign cancellations on negative integers[cite: 5].