# Math Project

```Thanks to Milton Bradley, Battleship is one of the most widely known games all
over the world. There are many different versions of Battleship from pencil and paper to
electronic to Star Wars Battleship, and Mathematical Battleship.
The game Battleship was developed in the 1930’s as a commercial game, and was
a pencil and paper game. The game of Battleship had many different names when it first
came out. Some of them being: Broadcast-The Game of Naval Strategy, Combat- The
Battleship Game, and Salvo which soldiers came up with just after World War One.
Since the game was originally a pencil and paper game, if people in the 1970’s
did not want to draw out a grid they were able to buy grid paper with land and sea already
labelled on it. The yellow area on the paper represented land and the blue represented the
water. An example of the paper is shown below:
Milton Bradley in 1967 produced their first version of Battleship. The game was no
longer pencil and paper, but included two trays (one for each player) and plastic pegs to
put into the slots located on the grid of the tray.
In 1983 Battleship was updated by Milton Bradley International to a electronic game that
required 4 AA batteries.
During 1991 a computerized version of Battleship was designed and we know it to be
Minesweeper.
Rene Descartes was a French Mathematician who lived from 1596 to 1650. Descartes
developed the coordinate grid system we use today. To honour his invention the
coordinate grid system is called the Cartesian plane.
A Cartesian coordinate system, also known as rectangular coordinate system, can be used
to plot points and graph lines.
The following is an example of rectangular coordinate system
A Cartesian coordinate system is basically, a set of two number lines. The horizontal line
is called x-axis and the vertical line is called y-axis.
Notice that it has 4 quadrants:
- In quadrant I, x and y are positive
- In quadrant II, x is negative, but y is positive
- In quadrant III, x and y are negative
- In quadrant IV, x is positive, but y is negative
- The center, or intersection of the two axis is equal to (0,0)
Example:
Line
In math, a line is always straight. Lines go on forever in both directions.
Here is a picture of a line. A real line is only one-dimensional, but the picture is bigger,
so you can see it more easily.
Negative
A negative number is a number less than 0. We use this symbol for negative numbers: &quot;&quot;. For example, -10 means negative ten. You can imagine this as a temperature ten
degrees below zero.
Ordered Pair
An ordered pair is a list of two numbers, where the order of the numbers is important.
The first number tells the horizontal distance from the origin. A positive number indicates
distance to the right. A negative number indicates distance to the left. The second number
tells the vertical distance from the origin. A positive number indicated distance up. A
negative number indicates distance down. We write the coordinates of a point as an
ordered pair, inside parentheses. Some examples of ordered pairs are (1, 2) and (6, 77).
Origin
The origin is the point where all of the axes cross/intersect. In the plane, the origin has
coordinates (0, 0). In this picture of a plane, the origin has been marked with a red dot:
Plane
A plane is two-dimensional. It seems flat, like a thin piece of paper. However, unlike
pieces of paper, planes have no edges. A bug could crawl along a plane forever without
falling off.
Here is a picture of part of a plane. It has been colored green to make it easier to see.
Point
A point is one place in space. A point is represented by a pair of numbers (x, y). x stands
for any value on the x-axis and y stands for any value on the y-axis.
The two axes divide the plane into four quarters. These quarters are called quadrants.
They are numbered from one to four, starting in the upper right-hand corner and moving
counter clockwise.
Scale
The distance between marked points on a graph or number line is called its scale. These
two number lines use different scales:
A chameleon's skin is covered with flat, hard objects. These are also called scales. The
word scale has several other meanings. How many can you find?
Axis
An axis is a line that we use to find or draw points and shapes. If we want to talk about
more than one axis, we say &quot;axes.&quot; When y = 0, your point is always located on the xaxis. When x = 0, your point is always located on the y-axis.
Here is a picture of two axes in a plane:
Battleship Math Game Instructions
-
Each team will hide their four battleships.
The ships can only go vertically or horizontally, they are not allowed to go
diagonally, and they cannot overlap.
-
Teams will then take turns being the Attackers and Defenders.
The Attackers will give an ordered pair of numbers to the Defenders. Ex. (2,1).
The Attackers will then write the numbers down so they do not call them again.
If the Attackers hit a Battleship then the Defenders will mark it with an X. The
Attackers will fill in their circle whether it was hit or miss.
Then it is the defenders turn.
You must say when a Battleship has been sunk, otherwise you lose a turn.
The first group to sink all of the other teams Battleships WINS!
Aircraft carrier -- 5 points long
Battleship -- 4 points long
Submarine -- 3 points long
Destroyer -- 3 points long
PT-Boat -- 2 points long
References:
Basic Mathermatics.com (2008). “Cartesian Coordinate System.” Retrieved on October
15, 2011 from Basic-mathematics.com Web Site: http://www.basicmathematics.com/cartesian-coordinate-system.html
Drexel University (1994-2011). “Math Forum at Drexel: Coordinate.” Retrieved on
October 15, 2011 from Drexel University Web Site:
http://mathforum.org/cgraph/cplane/glossary.html#coordinate
Elliott Avedon (2010). “Battleship Games.” Retrieved on October 15, 2011 from the
University of Waterloo from Elliott Avedon Virtual Museum of Games,
Battleship Games Web Site:
http://gamesmuseum.uwaterloo.ca/VirtualExhibits/Whitehill/Battleship/index.htm
Google Images (2011). “Cartesian Coordinate System.” Retrieved on October 15, 201