Welcome welcome page Zoom Room Zoom logo ToDoodles Jamboard logo Calculator scientific calculator on Desmos       valid HTML 4.01
Skill Topics
Shapeshifting Topic Mad  Science Topic Justice Topic Typicality Study Skills
Application Topics
Playgrounds Health Decisions Topic Personal Finance Decisions Topic Business Decisions Topic
Being a Mather Class Library LCC Resources Achievements

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.


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:

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


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:

example setup


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

Which quadrant has/lacks a right/acute/obtuse angle or perpendicular/parallel lines?

Blank Gameboard

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

blank game board

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