Getting Started 
Misconception/Error The student makes significant errors when graphing points in the coordinate plane. 
Examples of Student Work at this Level The student:
 Reverses the x and yaxes, reverses x and ycoordinates, or interchanges the positive and negative portions of the axes.
 Graphs some or all of the vertices incorrectly.

Questions Eliciting Thinking 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? Which direction did you move to graph the xvalue and which direction did you move to graph the yvalue?
Can you show me how you graphed the vertices?
What type of figure did you graph? Does it look like a polygon? 
Instructional Implications Review 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. Consider implementing the CPALMS Lesson Plan Chameleon Graphing (ID 5728). Provide the student with additional opportunities to graph specified figures given the coordinates of their vertices.
Define a polygon as a closed figure with three or more sides. Show the student examples and nonexamples of polygons. Provide the student with additional opportunities to graph polygons in all four quadrants with integer and rational number coordinates. Clarify for the student the correct way to name points, line segments, and polygons. Remind the student that the order the points are listed indicates the order of the vertices in the polygon. 
Moving Forward 
Misconception/Error The student is unable to determine the perimeter of the polygon. 
Examples of Student Work at this Level The student correctly graphs the polygon but:
 Is unable to correctly determine the lengths of the sides.
 Decomposes the polygon and finds the perimeter of each rectangle.
 Does not attempt to find the perimeter or does not show enough work to determine a strategy.
 Calculates the area (correctly or incorrectly) instead of the perimeter.

Questions Eliciting Thinking What is the length of each side of the polygon? Can you show me how you counted? Did you count the grid lines or the unit lengths?
Why did you skip the unit lengths at each axis? Is that length still a full unit, even if the grid line does not connect?
Can you explain to me how you used integer operations to calculate each length? Is there a way you can check your answers to see if they make sense? Is it possible to have a negative side length?
How can you determine the dimensions of the graphed figure? How do you find the perimeter of a polygon? How is that different from finding the perimeter of each decomposed section of the polygon?
What is the difference between the perimeter and area of a figure? 
Instructional Implications Review the concept of length and give the student opportunities to find lengths on a number line by counting unit lengths. Relate finding length on a number line to using a ruler. Explain how vertical and horizontal lengths are measured in the coordinate plane. Directly address the misconception that length is calculated by counting notches or grid lines or that length can be negative. Emphasize the meaning of the unit length by providing a unit of measure such as centimeters. Eventually transition the student to calculating distances (rather than counting unit lengths) between points with the same first coordinate or the same second coordinate on a coordinate plane. Guide the student to use absolute value symbols to represent lengths [e.g., represent the distance from A(6, 3) to B(6, 4) as AB = 3 – (4) = 7 or as AB = 4 – 3 = 7].
If needed, review the difference between the area and perimeter of a figure. Offer the student additional opportunities to calculate both area and perimeter of figures graphed on the coordinate plane. At this point, consecutive vertices should have the same xcoordinates or the same ycoordinates.
Model showing work in an appropriate written form. Guide the student to find and label each length and to clearly show how the perimeter is calculated by writing an equation such as P = 7 + 16 + 11 + 5 + 4 + 11. Encourage the student to complete all computational work on the side, so it is not the focal point of the written communication of the method of solution. 
Almost There 
Misconception/Error The student makes minor errors when calculating a length or the perimeter. 
Examples of Student Work at this Level The student:
 Makes a minor counting error when finding the length of one side. All other work is correct.
 Makes a minor calculation error when finding the perimeter.
 Does not show work to support answer or shows work haphazardly.

Questions Eliciting Thinking Can you verify your calculations?
How did you determine each of your length calculations? Is there a way you can determine which one is correct? 
Instructional Implications Provide feedback to the student concerning any errors made. Allow the student to revise his or her work.
If needed, model showing work in an appropriate written form. Guide the student to find and label each length and to clearly show how the perimeter is calculated by writing an equation such as P = 7 + 16 + 11 + 5 + 4 + 11 = 54 units. Encourage the student to complete all computational work on the side, so it is not the focal point of the written communication of the method of solution. 
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 polygon correctly, determines the length of each side, and uses the lengths to determine the perimeter of the polygon as 54 units.

Questions Eliciting Thinking How could you determine the area of the figure? Would you have to decompose it into smaller shapes? Do you have to decompose the figure to determine perimeter?
How would you determine the perimeter of a rectangle using only the coordinates (and not the graph)? 
Instructional Implications Challenge the student to determine the perimeter (or area) of a polygon without graphing the coordinates when given the vertices with the same first coordinate or the same second coordinate. Guide the student to use the corresponding coordinates from adjacent vertices to calculate lengths. Guide the student to use absolute value symbols to represent lengths [e.g., represent the distance from A(6, 3) to B(6, 4) as AB = 3 – (4) or as AB = 4 – 3].
Consider implementing the MFAS task Patio Area (6.G.1.3) which involves determining the area of a rectangle graphed on the coordinate plane. 