Students review the importance and need for coordinates in the context of a video game and brainstorm a game of their own.
Lesson Goals 
Students will be able to:

StudentFacing Lesson Goals 

Materials 

Preparation 

Key Points for the Facilitator 

Click here to see the prior unitbased version.
 coordinate

a number or set of numbers describing an object’s location
 horizontal axis

axis on a coordinate plane that runs from left to right
 vertical axis

number line on a coordinate plane that runs from bottom to top, indicating values in that direction
🔗Navigating a Grid 20 minutes
Overview
Students are asked to come up with a way of identifying location on a grid, which provides the justification for coordinates.
Launch
Placing a Character on a number line 🖼Show image Computers use numbers to represent a character’s position onscreen, using number lines as rulers to measure the distance from the bottomleft corner of the screen. For our videogame, we will draw the number line so that the screen runs from 0 (on the left) to 1000 (on the right).
We can take the image of the Dog, stick it anywhere on the line, and measure the distance back to the lefthand edge. Anyone else who knows about our number line will be able to duplicate the exact position of the Dog, as long as they know the number.

What is the coordinate of the Dog, if it’s on the lefthand edge of the screen?

What is the coordinate of the Dog, if it’s on the righthand edge of the screen?

What is the coordinate of the Dog, if it’s in the center of the screen?

What coordinate would place the Dog beyond the lefthand edge of the screen?

What coordinate would place the Dog beyond the righthand edge of the screen?
OPTIONAL: Draw a number line on the board, and select a volunteer to leave the room for a moment. Place the printed Dog image somewhere on that line, 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 lefthand 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.
Investigate
By adding a second number line, we can locate a character anywhere on the screen in either direction. The first line we drews is called the xaxis, which runs from left to right. The second line, which runs up and down, is called the yaxis. A 2dimensional coordinate consists of both the x and ylocations on the axes.
Placing a Character in two dimensions 🖼Show image Suppose we wanted to locate NinjaCat’s position on the screen. We can find the xcoordinate by dropping a line down from NinjaCat and read the position on the number line. The ycoordinate is found by running a line to the yaxis.
A coordinate pair is always written in the form of (x, y). When we write down these coordinates, we always put the x before the y (just like in the alphabet!). Most of the time, you’ll see coordinates written like this: (200, 50) meaning that the xcoordinate is 200 and the ycoordinate is 50.
To develop an intuition for coordinates, have students complete Estimating Coordinates (Page 4).
Common Misconceptions
Mathphobic 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 on this workbook page.
Synthesize

Should any of the characters have xcoordinates that are very similar? How come?

Should any of the characters have ycoordinates that are very similar? How come?

How do you think this concept relates to a video game? Answers vary: we need to know where characters are on the screen, we need a way for players to interact with certain parts of the screen, etc
🔗Bridging to video games 30 minutes
Overview
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.
Launch
In pairs, have students explore the Ninja Cat Desmos graph (Desmos).
Investigate

Students complete the Brainstorm Your Own Game (Page 5) worksheet and decide on a Player, Target, Danger, and Background for their game.

Students will use a Google Draw template (click "Make a copy" when prompted) to create a sample "screenshot" of their game by inserting images via Google Search.
Screenshot should include:

Labeled estimates of coordinates for each character.

2 characters that have the same xcoordinate.

2 different characters that have the same ycoordinate.
Synthesize

When the "Game Over" screen is supposed to be off screen, what coordinates might hide it?

What would be the coordinate of the dog before it gets onscreen?

Why do we estimate? Practice number sense, get better at working with numbers

What constitutes a good estimate?

How can we improve our estimation skills? Practice, get more comfortable with numbers and more comfortable with making guesses
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). Bootstrap:Algebra by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.