The Cartesian Coordinate System Can Be Fun!

Teaching the Cartesian coordinate system can be fun when placed in the context of students. The xy coordinate system offers many opportunities for creativity and fun in the classroom.

Establish context.

Most students are interested to find out that the Cartesian coordinate system was developed by the mathematician Descartes during an illness. As he lay in bed, he noticed a fly buzzing around on the tiled ceiling. He realized it would be possible to identify its unique position at any given time and created the system when he recovered as a way to do that.

Students identify with this story, and you might even want to give them an opportunity to tell a partner about a time when they themselves were ill and confined to bed. You might even take a few minutes to discuss the kinds of activities they do when they are sick.This is a wonderful way to establish learning context.

Incorporate dance.

Instruction begins with the number line and the awareness that positive means “to the right” and that negative means “to the left.” Substituting the following words during the Cupid Shuffle is a fun way to reinforce this concept and to integrate dance into the classroom:

“To the right, to the right – that’s positive, positive,

Left, to the left – that’s negative, negative,

Kick, now kick (resume lyrics)”

This activity gets the heart pumping which results in more blood flow to the brain, and it releases all kinds of helpful brain chemicals, too. In addition to these benefits, you will notice after a while that kids are humming it to themselves as they work.

Make connections.

Introduce the Cartesian coordinate system simply as two number lines. Since they already have knowledge of the number line, this means their brains will be able to connect this new learning to something they already know.

It makes sense that “down” would be negative and “up” would be positive, and this is a good time to help students make connections to science. Illustrate the concept with a thermometer and temperatures above and below zero, and discuss also above and below sea level.

The more connections you can help students make, the more authentic is the learning. And the more they are going to remember!

Build Vocabulary.

The two number lines of the Cartesian coordinate system divide the plane into four quadrants – quad meaning 4. You may remind students that quadrilaterals have four sides, and many of them will recognize the prefix from ATV vehicles or four-wheelers which are frequently referred to as “quads.”

The coordinate system has its own vocabulary, and introducing the terms at this point is a good idea. Word walls are the most efficient way to build vocabulary so coordinate system words should be added as you explain that each location or “point” has its own unique name called an “ordered pair,” and so on.

Games and activities with words on the word wall are invaluable to learning any new vocabulary!

Use It or Lose It!

Sometimes it is hard to find time to provide opportunities for students to actually USE what they have learned. We all feel the time crunch which propels us on to the next topic!

Here are suggestions for finding time for coordinate system practice and repetition.

Brain Breaks

One way to find time for practice and repetition is to create the Cartesian coordinate plane on the floor of your classroom. Masking tape works really well on carpet since the vacuum will pass right across it. It will work for bare floors, also, but you will want to speak with your custodian first and ask if they would be willing to work around it for a couple of weeks.

There are a variety of ways to work with the floor coordinate system. I sometimes give out ordered pairs at the door and students go stand in that position at the beginning of class. At the end of learning cycles, I may ask students to get up and stand in a particular quadrant according to the letters which begin their first/last names. (“If your last name begins with ____, go to Quadrant II.” ) I might also classify them by homeroom, but in any case this gives them a “brain break” and gives them practice navigating the Cartesian plane.


After Test Activities

Time after tests is "found time" and can be an important part of classroom time management, helping you find time for students to use the skills they have learned about the Cartesian coordinate system.

Facebook Activity

This activity is my new favorite and gives students an opportunity to use their knowledge of the Cartesian coordinate system in a creative way that is right in the middle of their context.

Students must create a profile for a point in either Quadrant I or III with the profile picture being its graph. The idea here is that ordered pairs in Quadrant I are both positive while both numbers are negative in Quadrant III. Basically, then, everything in the third quadrant is negative while everything in the first is "happy, happy, happy!"

The "Family" list should include points in the same quadrant, and the "Friends" list includes points in any other quadrant except the opposite one.

Favorite songs and TV shows for Quadrant I points should be happy and upbeat while those for points in Quadrant III should be serious and sad.

In the About Me section, expect Quadrant I points to be happy and positive, spending most of their time in activities such as playing, dancing, and singing. Expect Quadrant III points to be sad and unhappy, spending most of their time crying, pouting, or whining.

One of my favorite parts of this assignment is a friend request they receive from a point in the opposite quadrant. They must send an email to the point explaining why they cannot be friend (too different, etc.)

As an art opportunity, students must then draw pictures of their "home quadrant." Quadrant I will typically be bright and colorful, and those of Quadrant III will be gray, dark, and dreary.

Clicking on the picture of the assignment below will open the project for printing.


Coordinate system practice with Facebook.

Art Projects

Pictures on the Cartesian coordinate system created from a list of ordered pairs is a fun activity. I require that all points be labeled properly with correctly written ordered pairs and that points be connected accurately with a ruler.

Then I ask them to create their own picture, providing a list of points which may be given to another student to plot.

Go to Teaching Math with Art from Cartesian Coordinate System

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