Cartesian Coordinates

What is the Cartesian Coordinate System?

The Cartesian coordinate system is a way to locate a point in space by assigning coordinates at 90 degrees to each other.

The Fundamental Skills:

The fundamental skills involved include:

• Understanding how to find a point given its coordinates
• Understanding how to assign coordinates to a point
• Understanding how to know which coordinate goes with which axis

Words to Use:

• Axis
• Coordinate
• Origin

Prerequisite Skills:

• Counting
• Alphabet

Ways to Practice:

There are multiple ways that these skills can be introduced to a child, long before the Cartesian coordinate system is introduced in school.

• Using a ruler to measure an object
• Playing Battleship
• Describing chess moves
• Finding cities on a map
• Using longitude and latitude
• 3D printing
• Street addresses
• Spreadsheets
• Computer screens

Advanced Skills:

More advanced skills include:

• Understanding negative coordinates
• Calculating distances
• Plotting in 3 dimensions
• Considering 4 or more dimensions

Non-transferable Skills:

The following skills are leaves and should not be focused on:

• Quadrants
  • Memorizing the 4 quadrants may be required when studying trigonometry but is generally not a skill that is useful for understanding other concepts. A related, but more fundamental skill is understanding that angles are drawn starting at the x-axis and rotate in a counterclockwise direction.
• Plotting functions
  • Calculating (x,y) pairs for functions and plotting these points in order to understand the shapes of functions is tedious and unnecessary. Computers do a fine job of this. Drawing axes and plotting points is fundamental to truly gaining an understanding of how to use a coordinate system. But once this is understood well, further practice with manually plotting points is not helpful.

Related Concepts:

• Orthogonality
• Number Line
• Infinity
• Graphing
• Independent and Dependent Variables

Resources:

• Desmos – graphing calculator