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:
 Graphs some or all of the vertices incorrectly.
 Reverses the x and yaxes, reverses x and ycoordinates, or interchanges the positive and negative portions of the axes.
 Is unable to graph rational number coordinates.

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?
Where would you locate 5.5 on the xaxis? Is it between negative four and negative five or between negative five and negative six?
What type of figure did you graph? Does it look like a polygon?
What is a diagonal? Can you show me which lengths you are asked to find? 
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 being sure to include both positive and negative rational number coordinates.
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 lengths of the diagonals. 
Examples of Student Work at this Level The student correctly graphs the polygon but is unable to correctly determine the lengths of the diagonals. The student may attempt to calculate the lengths but does so incorrectly.

Questions Eliciting Thinking How did you determine the length of each diagonal? Did you use counting?
How could you use the coordinates of the vertices to find the lengths of the diagonals? 
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. Caution the student to include the fractional portions of the length. 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 F (2, 8.25) to H (2, 7.75) as FH = 8.25 – (7.75) = 16 or as FH = 7.75 – 8.25 = 16]. 
Almost There 
Misconception/Error The student does not use a correct unit when describing lengths. 
Examples of Student Work at this Level The student correctly graphs the polygon and finds the numerical value of each length (i.e., EG = 8 and FH = 16). However, the student provides no unit of measure or uses an incorrect unit. For example the student:
 Describes a length as 8 spaces, 8 squares, or 8 cubes.
 Writes lengths as if they are coordinates of points.

Questions Eliciting Thinking You said that EG = 8 but did not provide a unit of measure. How can you describe the unit of measure?
How is length measured? What are some units of measure for length? 
Instructional Implications Review the nature of length and units typically used to measure length. Explain that if no unit of measure is given, length can be described generically using the term unit. Allow the student to revise his or her work. 
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 and determines the length of each diagonal as EG = 8 units and FH = 16 units.

Questions Eliciting Thinking Did you use counting or subtraction to find the lengths?
Can you represent the lengths using coordinates of the vertices and absolute value symbols?
Could you find the area of polygon EFGH? What strategy would you use? 
Instructional Implications Correct any notation errors the student might have made (e.g., writing = 8 units). Explain the difference between (notation that names a segment) and EG (notation that represents the length of a segment). Allow the student to revise any notation errors made.
Challenge the student to determine the area of polygon EFGH by composing it into rectangles or decomposing it into triangles and to represent the area using an appropriate unit of measure.
Challenge the student to determine the perimeter (or area) of a polygon when given vertices with the same first coordinate or the same second coordinate, without graphing the coordinates. 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 other MFAS tasks for standard 6.G.1.3 for additional practice calculating lengths on the coordinate plane. 