Getting Started 
Misconception/Error The student does not have an effective strategy for further classifying the quadrilateral. 
Examples of Student Work at this Level The student graphs the given vertices and classifies the quadrilateral based only on its appearance.

Questions Eliciting Thinking What is a parallelogram (or rhombus, rectangle, or trapezoid)? What must be true of a quadrilateral in order for it to be a parallelogram?
How could you determine if the opposite sides of the quadrilateral are parallel? What formula would you use?
How could you determine if the lengths of the sides of the quadrilateral are equal? 
Instructional Implications If necessary, review the slope, distance, and midpoint formulas. Provide additional opportunities for the student to use the formulas and provide feedback.
Be sure the student understands the slope criteria for parallel and perpendicular lines. Review the conditions that are necessary and sufficient for a quadrilateral to be each of the following: parallelogram, rhombus, rectangle, square, and trapezoid. Then guide the student to develop an overall strategy for solving the problem presented in this task, i.e., (1) graph the vertices to determine a general idea of the shape, (2) calculate the slopes of the sides to determine if the figure is a parallelogram or rectangle, (3) and, if the figure is a parallelogram, determine the lengths of the sides in order to classify it further.
Provide additional opportunities to use the slope, distance, and midpoint formulas to determine properties of geometric figures in the coordinate plane. For example, ask the student to conclude what is true as a consequence of:
 Two segments having the same slope.
 Two segments having slopes that are opposite and reciprocal.
 The three sides of a triangle having the same length.
 Consecutive sides of a quadrilateral being perpendicular.
 The diagonals of a quadrilateral having the same midpoint.
If needed, provide feedback on the appropriate use of notation.
Consider implementing MFAS task Type of Triangle (GGPE.2.4). 
Moving Forward 
Misconception/Error The student’s work shows some evidence of an effective strategy for further classifying the quadrilateral, but the implementation is incomplete and/or contains significant errors. 
Examples of Student Work at this Level The student correctly calculates the slopes of the sides of the quadrilateral and concludes that the quadrilateral is a parallelogram. No additional work is done to determine if the quadrilateral is also a rhombus, rectangle, or square. Whether or not the quadrilateral could be a trapezoid is not addressed.
The student correctly calculates the lengths of the sides of the quadrilateral and concludes that the quadrilateral is a parallelogram and rhombus. No additional work is done to determine if the quadrilateral is also a rectangle or square. Whether or not the quadrilateral could be a trapezoid is not addressed.
The student makes a consistent error in using the slope, distance, or midpoint formula. For example, in using the midpoint formula, the student subtracts the coordinates rather than adding them. 
Questions Eliciting Thinking Can a quadrilateral be both a parallelogram and a rectangle? Both a square and a rectangle? Both a rhombus and a square?
What else can you do to determine if the parallelogram (or rhombus) is also a rectangle, square, or trapezoid?
Can a parallelogram also be a trapezoid? 
Instructional Implications If necessary, review the slope, distance, and midpoint formulas. Provide additional opportunities for the student to use the formulas and provide feedback.
Review the definitions of the special quadrilaterals. Encourage the student to make a flow chart or a Venn diagram that shows the relationships among them. Ask the student to produce examples, if possible, of quadrilaterals that are of two specified types, e.g., a quadrilateral that is parallelogram and a rectangle, a square and a rectangle, a rhombus and a square, a rhombus and a rectangle, or a trapezoid and a rectangle.
Review the conditions that are necessary and sufficient for a quadrilateral to be each of the following: parallelogram, rhombus, rectangle, square, and trapezoid. Ask the student to consider the most efficient approaches to determining whether a quadrilateral is of a special type. For example, ask the student to identify the various conditions under which a quadrilateral is a parallelogram and to decide which might be easiest to demonstrate.
If needed, provide feedback on the appropriate use of notation.
Consider implementing MFAS task Type of Triangle (GGPE.2.4). 
Almost There 
Misconception/Error The student does not provide a complete explanation or justification. 
Examples of Student Work at this Level The student determines the quadrilateral is both a parallelogram and a rhombus but does not justify why the figure is not a rectangle, square, or trapezoid.

Questions Eliciting Thinking Is the quadrilateral also a rectangle? Square? Trapezoid? How do you know? 
Instructional Implications Remind the student that a complete explanation also includes a justification for determining that the quadrilateral is not a rectangle, square, and trapezoid. Ask the student to show why the quadrilateral is not any of these figures. Provide additional opportunities to both prove and disprove simple geometric statements about figures in the coordinate plane.
If needed, provide feedback on the appropriate use of notation.
Consider implementing MFAS tasks Diagonals of a Rectangle (GGPE.2.4) and Midpoints of Sides of a Quadrilateral (GGPE.2.4). 
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 calculates the slopes and lengths of the sides (or the midpoints of the diagonals) and determines the quadrilateral is both a parallelogram and a rhombus. The student explains that the quadrilateral is neither a square nor a rectangle since the figure contains no right angles as evidenced by the slopes of consecutive sides. The student further explains that the figure cannot be a trapezoid since both pairs of opposite sides are parallel.
Note: In some geometry courses, trapezoids are defined as quadrilaterals with at least one pair of opposite sides parallel. Assess the student’s response based on the definition used in the course. 
Questions Eliciting Thinking Is there more than one way to determine if a quadrilateral is a parallelogram? A rhombus?
If a quadrilateral is a square, what other special types of quadrilaterals would describe it? 
Instructional Implications Challenge the student to prove geometric theorems using coordinate geometry. Consider implementing MFAS task Triangle MidSegment Proof (GCO.3.10).
Consider implementing Diagonals of a Rectangle (GGPE.2.4) and Midpoints of Sides of a Quadrilateral (GGPE.2.4). 