Coordinates and Game Design

Students are asked to come up with a way of identifying location on a grid, which provides the justification for coordinates.

image{images/1dPosition.png}

Computers use numbers to represent a character’s position onscreen, using number lines as rulers to measure the distance from the bottom-left corner of the screen.

If we placed the image of a dog on a screen and drew a number line running from 0 (on the left) to 1000 (on the right), it would look like this.

We could then measure the distance back to the left-hand edge. If we shared that number with anyone else who knows about our number line, they would be able to duplicate the exact position of the Dog.

Select a volunteer to leave the room for a moment. Place the printed Dog image somewhere on the number line you’ve drawn on the board, and have the class quietly choose the number that represents the Dog’s location. Remove the Dog and invite the student back into the room. Can they position the Dog at the right place, based on the number chosen by the class?

This number line lets us communicate the position of the Dog using a single number! Unfortunately, it only represents the distance from the left-hand edge of the screen. That means the dog could be at any height in the center of the screen, and it would always have the same number to represent its position.

By adding a second number line, we can locate a character anywhere on the screen in either direction.

A 2-dimensional coordinate consists of both the x- and y-locations on the axes.

Suppose we wanted to locate NinjaCat’s position on the screen. We can find the x-coordinate by dropping a line down from NinjaCat and read the position on the number line, then find the y-coordinate by running a line to the y-axis.

A coordinate pair is always written in the form of (x, y) with the x before the y (just like in the alphabet!).

The coordinate pair (200, 50), for example, indicates that the x-coordinate is 200 and the y-coordinate is 50.

Math-phobic students often fail to realize that common sense and intuition can be helpful in exercises where the answer is a number! The first two prompts in the "Synthesize" section directly get at this misconception, but you may want to pay special attention to those students while they are working.

Students explore a coordinate activity in which a Cartesian point is used to compute the position of a character in a game. From there, they brainstorm a game of their own.