Getting Started 
Misconception/Error The student does not indicate an understanding of how points in the coordinate plane are graphed and described by coordinates. 
Examples of Student Work at this Level The student:
 Does not identify the location of any of the points correctly.
 Focuses on just one coordinate when determining the location of the point.
 Graphs coordinates separately as two points.

Questions Eliciting Thinking Can you give an example of a point that is of the form (x, y)? Can you show me how to graph this point?
What are the coordinates of this point (graph a point for the student that is in the first quadrant)?
How are coordinates related to the locations of the point they describe?
Which axis is the xaxis, and which is the yaxis? 
Instructional Implications Review graphing points in the first quadrant (5.G.1) and then, provide explicit instruction on graphing points with integer coordinates in the coordinate plane. Relate the x and yaxes to basic number lines and explain the conventions for graphing [e.g., the xaxis is usually horizontal and the yaxis is vertical, in which case ordered pairs are given in the form (x, y)]. Be sure the student understands basic terminology related to graphing in the coordinate plane: xaxis, yaxis, coordinates, ordered pair, points, origin, and quadrants. Discuss the signs of the coordinates of points in each quadrant and the form of the coordinates of points on axes. Provide extensive experience with both graphing points given their coordinates and describing the coordinates of graphed points.
When the student is proficient graphing points given their coordinates and describing the coordinates of graphed points, review how the quadrants are numbered. Then provide problems in which the student is asked to give examples of points (by giving their coordinates) in each quadrant and on each axis. Likewise, give the student coordinates of points and ask the student to state the quadrant in (or axis on) which the point is located. Encourage the student to be precise in describing the locations of points on axes by identifying the axis and stating whether the point is on the positive or negative portion of it. Guide the student to develop general descriptions of the coordinates of points in each quadrant and on each axis. 
Moving Forward 
Misconception/Error The student does not recognize points with a coordinate of zero as located on an axis. 
Examples of Student Work at this Level The student identifies all points correctly with the exception of points on the xaxis. The student says the point given by (x, 0) is in quadrant II.
The student may also label a quadrant incorrectly but correctly identify it as the location of a point. The student says the point given by (x, 0) is in quadrant II and (x, y) is in quadrant “C.”

Questions Eliciting Thinking What if a point is on the xaxis? Is it also in a quadrant?
When a point is on the xaxis, what is its ycoordinate?
When a point is on the yaxis, what is its xcoordinate? 
Instructional Implications Make explicit the difference between being located in a quadrant and located on an axis. Then, provide problems in which the student is asked to give examples of points (by giving their coordinates) in each quadrant and on each axis. Likewise, give the student coordinates of points and ask the student to state the quadrant in or axis on which the point is located. Encourage the student to be precise in describing the locations of points on axes by identifying the axis and stating whether the point is on the positive or negative portion of it. Guide the student to develop general descriptions of the coordinates of points in each quadrant and on each axis.
Address any misconceptions about how the quadrants are conventionally identified. 
Almost There 
Misconception/Error The student has difficulty precisely describing the locations of points on axes. 
Examples of Student Work at this Level The student correctly shows the location of (x, 0) but describes its location:
 As between two quadrants rather than on an axis. The student may also label a quadrant incorrectly but correctly identify it as the location of a point.
 Generically as “on a line.”

Questions Eliciting Thinking I see you graphed (x, 0) correctly. Can you tell me on which axis you graphed it?
Is there a more precise way to describe its location? 
Instructional Implications Encourage the student to be precise in describing the locations of points on axes by identifying the axis and stating whether the point is on the positive or negative portion of it. Model this precision by saying the point is located “on the negative portion of the xaxis.”
Address any misconceptions about how the quadrants are conventionally identified. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student says that:
 (x, y) is located in quadrant II since its xcoordinate is negative and its ycoordinate is positive.
 (x, 0) is located on the negative portion of the xaxis since its xcoordinate is negative and its ycoordinate is zero.
 (x, y) is located in quadrant IV since its xcoordinate is positive and its ycoordinate is negative.

Questions Eliciting Thinking What do the signs of the coordinates tell you about the direction to go from the origin when graphing?
Can you be more precise in describing the part of the xaxis where (x, 0) is located?
What if x represented a negative number? What kind of number would –x be? 
Instructional Implications Revise the worksheet for this task to include the following: (x, y), (0, y) and (0, y). Ask the student to describe the locations of these points again assuming that x > 0 and y > 0.
Ask the student to describe, in general terms, the coordinates of points in each quadrant and on each axis by saying something like, “Points in the first quadrant are of the form (x, y) where both x and y are positive.” 