Getting Started 
Misconception/Error The student is unable to describe the relationship between the graphs of 6 and 6 on a number line. 
Examples of Student Work at this Level The student:
 Relates an observation about the numbers but not their graphs. For example, the student says, “they are the same number with different signs” or “one is negative and one is positive.”
 Explains in terms of an application of integers without addressing the graphs.
 Draws a number line and graphs 6 and 6 but does not describe the relationship between the graphs.

Questions Eliciting Thinking How would you graph 6 on a number line? How would you graph 6 on a number line? What is the same or different about the graphs?
What do you know about the relationship between 6 and 6?
What do you know about the graphs of numbers that are opposites? 
Instructional Implications Guide the student to observe that 6 and 6 are opposites. Review the definition of opposites in terms of the number line. Be sure the student understands that the opposite of any number, n, is the number that is the same distance from zero but on the opposite side of zero on the number line. Ask the student to use the number line to identify and graph a variety of rational numbers (including some with fractional and negative values) and their opposites. Encourage the student to interpret the negative symbol (–) as meaning “the opposite of” when it precedes a number (e.g., interpret –5 as the opposite of five).
Consider implementing the MFAS tasks What Is the Opposite, Explaining Opposites, and Graphing Points on the Number Line (6.NS.3.6). 
Moving Forward 
Misconception/Error The student is unable to describe the relationship between the graphs of ordered pairs (whose coordinates differ by sign) in terms of reflections. 
Examples of Student Work at this Level The student:
 Describes the numerical value of the coordinates but not their graphs. For example, the student says, “one point has a positive four and the other has a negative four” or “the xcoordinates are opposites and the ycoordinates are the same.”
 Explains a procedure for graphing each point on a grid, such as, “go five to the right then down four.”
 Only describes the quadrants in which each point is graphed.

Questions Eliciting Thinking Can you graph these pairs of points in the coordinate plane? How do their graphs compare?
What is a reflection? Can you describe the graphs in terms of reflections? 
Instructional Implications Provide graphing opportunities that enable the student to observe that points with coordinates of the form:
 (x, y) and (x, y) are reflections of each other across the yaxis.
 (x, y) and (x, y) are reflections of each other across the xaxis.
 (x, y) and (x, y) are reflections of each other across both axes.
Describe the relationship between the graphs as reflections and use related terminology such as the word image. For example, model saying, “The point (2, 8) is the image of point (2, 8) after a reflection across the xaxis.” Give the student the coordinates of points and ask the student to determine the coordinates of their images after reflections across each axis and after a sequence of reflections across both axes.

Almost There 
Misconception/Error The student is unable to describe the relationship between the graphs of ordered pairs in terms of reflections when both coordinates differ in sign. 
Examples of Student Work at this Level The student explains that the graphs of:
 6 and 6 are the same distance from zero on the number line but on opposite sides of zero.
 (5, 4) and (5, 4) are reflections of each other across the xaxis.
 (2, 7) and (2, 7) are reflections of each other across the yaxis.
However, the student is unable to describe the relationship between (6, 3) and (6, 3) in terms of reflections. For example, the student says:
 One is above the xaxis and the other is below.
 One is in the first quadrant and the other is in the third quadrant.

Questions Eliciting Thinking What if you reflected (6, 3) across the yaxis? What would its coordinates be? What if you reflected this point again across the xaxis? Now what would its coordinates be? 
Instructional Implications Provide graphing opportunities that enable the student to observe that points with coordinates of the form (x, y) and (x, y) are reflections of each other across both axes. Describe the relationship between the graphs as reflections and use related terminology such as the word image. For example, model saying, “The point (2, 8) is the image of point (2, 8) after a reflection across the xaxis followed by a reflection across the yaxis.” Guide the student to observe that changing the order of the sequence does not alter the location of the image point. Give the student the coordinates of points and ask the student to determine the coordinates of their images after a sequence of reflections across both axes. 
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 explains that the graphs of:
 6 and 6 are the same distance from zero on the number line but on opposite sides of zero.
 (5, 4) and (5, 4) are reflections of each other across the xaxis.
 (2, 7) and (2, 7) are reflections of each other across the yaxis.
 (6, 3) and (6, 3) are reflections of each other across both axes.

Questions Eliciting Thinking Can you describe the relationship between two points whose coordinates are (a, b) and (a, b)?
If two points are reflections of each other across the yaxis, what must be true of their coordinates? 
Instructional Implications Ask the student to draw a circle on the coordinate plane whose center is at (0, 0) and with a radius of 4. Then ask the student to compare (4, 0) to (0, 4), (4, 0), and (0, 4) in terms of fractions of rotations around the circle. For example, guide the student to observe that (0, 4) is a onequarter (or 90°) counterclockwise turn from (4, 0). Challenge the student to make similar comparisons with points not on an axis and to describe each comparison in terms of both a clockwise and counterclockwise rotation. Guide the student to observe that a reflection across the xaxis followed by a reflection across the yaxis (or vice versa) is the same as a halfturn (or 180° rotation) about the origin. 