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 ycoordinates or interchanges the positive and negative portions of the axes, and is unable to locate the fourth vertex of the rectangle.
 Reverses the x and ycoordinates for two of the points.
 Does not know how to graph an ordered pair.

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?
From what point did you start counting? In which direction did you move to plot the xvalue and then 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 graph points given their coordinates and to give coordinates of graphed points. Consider implementing CPALMS Lesson Plan Chameleon Graphing (ID 5728).
Provide the student with additional opportunities to graph specified figures given the coordinates of their vertices. Teach associated vocabulary, as needed (e.g., vertex, vertices, sides, and angles). 
Moving Forward 
Misconception/Error The student is unable to correctly find lengths of horizontal and/or vertical segments in the coordinate plane. 
Examples of Student Work at this Level The student correctly graphs the three given vertices and identifies the coordinates of the fourth vertex of the rectangle, but:
 Counts the number of unit squares that surround the rectangle and includes additional squares at the vertices.
 Counts the number of unit squares in the interior of the rectangle that border the sides.

Questions Eliciting Thinking How did you determine the lengths of the sides of the rectangle? What is the unit of measure for length?
Did you count the grid lines, squares, or the lengths between the lines? 
Instructional Implications Review the concept of length and how it is measured. Directly address the misconception that length is calculated by counting grid lines or squares and give the student additional opportunities to find lengths by counting unit lengths on number lines. Guide the student to extend this approach to calculating horizontal and vertical lengths in the coordinate plane.
Review how rulers are used to measure lengths. Equate a unit of measure such as an inch to the spaces between notches on a number line. 
Almost There 
Misconception/Error The student makes an error in calculating a length or the area. 
Examples of Student Work at this Level The student correctly graphs the three given vertices and identifies the coordinates of the fourth vertex of the rectangle but:
 Counts unit lengths to find the length of the sides of the rectangle and is off by one.
 Finds the perimeter of the rectangle rather than its area.
 Uses the wrong unit of measure, writing the area as 42 or 42 units rather than 42 square units.

Questions Eliciting Thinking How did you determine the area of the rectangle?
What is the difference between the perimeter of a rectangle and the area of a rectangle?
What is the difference between 42 and 42 square units? 
Instructional Implications If needed, review the difference between the concepts of area and perimeter. Be sure the student understands the difference between linear units and units of area. Offer the student additional opportunities to calculate both area and perimeter of figures graphed on the coordinate plane. Have the student work with a partner to compare answers and reconcile any differences. 
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 correctly graphs the three given vertices, identifies the coordinates of the fourth vertex, finds the length and width of the rectangle, and calculates an area of 42 square units. 
Questions Eliciting Thinking Is it necessary to find the fourth vertex of the rectangle in order to determine the area? Why or why not?
Is it necessary to find the fourth vertex of the rectangle in order to determine the perimeter? Why or why not?
What is the difference between 42 units and 42 square units? 
Instructional Implications Challenge the student to relocate only two vertices to transform a given rectangle into a square. Have the student calculate the area and perimeter of the newly formed square.
Challenge the student to identify the coordinates of the vertices of at least two different rectangles having an area of 20 square units.
If the student is not doing so already, encourage the student to interpret expressions of the form a â€“ b as meaning the distance between two points whose coordinates are a and b or the distance from a to b on the number line. Provide the student with additional opportunities to represent distances between points with the same x or ycoordinates using absolute value symbols and to to determine the distance between them by counting. 