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Math OER
Sonar and Spies Playground

We don't all have to take the same coordinates to get to the same destination.

- Janelle Monae

This playground is about Sonar and Spies, our extra fun version of the game Battleship for two or more players who have pencil and paper.

Preface

Our game is not about doing math. But the rules use math jargon to be clear and brief. If you need to, review the following terminology:

• angles that are acute, right, or obtuse: they are smaller, equal, or bigger than the corner of a square
• lines that are parallel or perpendicular: never cross like railroad tracks, or cross like a plus sign
• the four basic polygons: rectangle, triangle, parallelogram, and trapezoid
• axis: a horizontal or vertical number line, these cross with a common zero
• quadrants: the four regions northeast, northwest, southwest, and southeast
• coordinate points: the point written (2, 3) tells us to go right 2 on the horizontal axis, then up 3
• integers: the positive and negative counting numbers (no fractions or decimals allowed!)

When using coordinate points remember that we are not Superman. To get to the top of a skyscraper, we must go horizontally first along the street and then up to the top of the skyscraper. We are not Superman, who could go up first and then sideways.

Game Rules

Setup

1. Your game board is made with a horizontal axis and a vertical axis labeled −9 to 9.

2. Your fleet of ships is represented by the four basic polygons. You have one of each.

3. All polygons must have their corners on coordinate points with integer coordinates.

4. All polygons must have at least two sides that are horizontal or vertical.

5. All polygons must have an area of at least 6 square units.

6. On your gameboard leave a quadrant empty, put two ships in another quadrant, and the other two quadrants have one ship each.

Here is an example setup:

Goal

The game ends when a player identifies which of another player's polygons are in which quadrants.

Optionally, play more than one game and have the winner score as many points as the total area of his or her own fleet. This makes using larger shapes worthwhile. The first player to 80 points wins!

Your Turn

On your turn do one of three things that ask a question to one other player:

You may do a sonar sweep. Pick a point on either axis. The other player tells you (yes or no) if any of his or her shapes have corners with that coordinate. (If you pick a point on the horizontal axis, your sweep goes up and down. If you pick a point on the vertical axis, your sweep goes left and right. Notice that our sonar is flawed and goes right through the middle of shapes! It only detects corners.)

You may try to contact a spy. Pick a coordinate point. The other player tells you which polygon, if any, contains that point.

You may receive a spy's report. Ask the other player a yes-or-no question of the format

Blank Gameboard

Here is a blank gameboard if printing it would be helpful.

It is a bit awkward, but you can also play using a website geoboard.