Getting Started 
Misconception/Error The student is unable to correctly graph points in the coordinate plane. 
Examples of Student Work at this Level The student reverses the x and yaxis, reverses x and ycoordinates, or interchanges the positive and negative portions of the axes.

Questions Eliciting Thinking How do you know where to plot the point? What does the ordered pair (x, y) mean?
On a coordinate plane, which is the x and which is the yaxis? In an ordered pair, which is the x and which is the ycoordinate?
Where did you start counting from? Which direction did you move to plot the xvalue and which direction did you move to plot the yvalue? 
Instructional Implications Provide instruction on graphing points in the coordinate plane. Be sure to include points in all four quadrants and on both axes. Ask the student to both graph points given their coordinates and to give the coordinates of graphed points.
Provide the student with additional opportunities to graph figures in the coordinate plane given the coordinates of their vertices. Include coordinates that are positive, negative, and zero. 
Moving Forward 
Misconception/Error The student is unable to correctly identify the coordinates of graphed points. 
Examples of Student Work at this Level The student locates two points on the graph that will serve as the other vertices of a square. However, the student is unable to correctly identify their coordinates. For example, the student:
 Reverses the order of the coordinates writing the ycoordinate first.
 Writes all coordinates as positive numbers.
 Errs in counting the number of units between vertices and provides incorrect coordinates.

Questions Eliciting Thinking How did you determine the coordinates of the points you graphed?
Can you show me how you would graph the coordinates you wrote? 
Instructional Implications Review how to identify the coordinates of graphed points. Be sure the student understands conventions with regard to graphing and describing coordinates (e.g., the horizontal axis is the xaxis and the xcoordinate is listed first). Have the student describe in general the sign of the coordinates in each quadrant (e.g., for all points in the second quadrant, the xcoordinate is negative while the ycoordinate is positive). Provide additional opportunities to identify the coordinates of graphed points in all four quadrants and on both axes. 
Almost There 
Misconception/Error The student locates the vertices of a figure other than a square. 
Examples of Student Work at this Level The student graphs the first two coordinates correctly but then graphs additional points that serve as the vertices of a figure other than a square such as a rectangle. The student, however, correctly identifies the coordinates of the additional points.

Questions Eliciting Thinking What qualities does a square have? Does your shape match those qualities? How can you determine if the lengths of the sides of your figure are equal?
How did you decide to put the new corners at (3, 1) and (3, 5)? What shape did you make?
What is the relationship between squares and rectangles? Are they the same? 
Instructional Implications Be sure the student understands how to count units between vertices to determine the lengths of sides. Then review the definitions of square (a polygon with four congruent sides and four congruent angles), rectangle (a polygon with four right angles), or any other relevant polygon. Emphasize the relationship between squares and rectangles (all squares are rectangles but only some rectangles are squares). Then ask the student to draw a figure that is a rectangle but not a square and a figure that is both a rectangle and a square.
Provide the student with additional opportunities to graph specified figures and describe the coordinates of their vertices. 
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 graphs the two given points correctly and finds the coordinates of two additional vertices, at either (1, 1) and (1, 5) or at (7, 1) and (7, 5), to form a square. The student then finds the coordinates of a second pair of vertices to form a square.

Questions Eliciting Thinking Do squares always have to be oriented with their sides vertical and horizontal?
Suppose the two given vertices were opposite each other. Could you find another pair of opposite vertices to form a square? 
Instructional Implications Give the student the coordinates of one vertex and ask the student to find the coordinates of all possible sets of vertices that will make a given figure such as a 3 x 5 rectangle. 