In this activity, students extend the vertical and horizontal axes to create the 4 regions, called quadrants of the coordinate plane. The coordinate plane is a system that can be used to communicate the locations of points. Students plot points and identify in which quadrant they are located.

The key idea for students to understand is that the coordinate plane is formed by two axes, which are vertical and horizontal number lines. Just as number lines were extended to include negative numbers, these axes have been extended to create the 4 quadrants. Points in these quadrants can be described by using negative and positive numbers as the - and -coordinates. Invite students to share their reasoning about how to identify the quadrants for the points , , and . As time allows, consider asking the following questions:

• “If a point has a negative -coordinate, what quadrants could it be in?” (Quadrants II and III)
• “If a point has a negative -coordinate, what quadrants could it be in?” (Quadrants III and IV)
• “If a point has a positive -coordinate, what quadrants could it be in?” (Quadrants I and IV)

To involve more students in the conversation, consider asking:

• “Do you agree or disagree? Why?”
• “Who can restate ___’s reasoning in a different way?”
• “Does anyone want to add on to _____’s reasoning?”

In this activity, students select points in different regions of the coordinate plane and use ordered pairs to describe them. Students must name specific coordinates in order to hit different parts of an archery target embedded in a coordinate plane. All points within the archery target contain negative coordinates.

The purpose of this discussion is to allow students to describe points in the plane that involve negative coordinates. Display the archery target from the Task Statement for all to see. Ask students to share their responses for coordinates in the various regions of the target and record them for all to see. Record the points exactly as students describe them, and encourage students to be precise. If not mentioned by students, ask whether it’s possible to use coordinates to describe the exact center of the target. If necessary, suggest using decimals or fractions as coordinates.