Flip open your textbook to the chapter that introduces the coordinate plane. I’ll wager $5 that the first coordinate plane students see includes a grid. Here’s the top Google result for “coordinate plane explanation” for example.

A gridded plane is the formal sibling of the gridless plane. The gridded plane allows for more power and precision, but a student’s earliest experience plotting two dimensions simultaneously shouldn’t involve precision or even numerical measurement. That can come later. Students should first ask themselves what it means when a point moves up, down, left, right, and, especially, diagonally.

The two url links above will take you to a web-based exploration designed by the good people at Desmos. The first url link will take you to Dan Meyer’s blog post explaining the rationale behind the activity (The text above is taken from his blog post). The second url link is the actual activity.

I am including a pdf of the following image for use in a classroom without technology.

What do you notice? What do you wonder?

• What is this person’s favorite fruit on this graph?
• Which fruit does this person find hard to eat, but worth the effort?
• What is this person’s least favorite fruit on this graph?
• What are three things you can say about this person’s feelings about green and red apples?
• What are three things you can say about this person’s feelings about seedless and seeded grapes?

Even if you do not have access to computers in your classroom, you might still check out the url links to see how the activity goes. One of the fun things that students do is construct their own coordinate-plane-gridless fruit graph, which is something that can definitely still do with paper and colored pencils.

If you use this with your students, leave a comment below to let us know how you use it and how it goes.