Getting Started 
Misconception/Error TThe student does not describe the relative positions of the numbers or describes them incorrectly. 
Examples of Student Work at this Level The student:
 Describes the relative positions of the pairs of numbers incorrectly.
 Addresses the relative size of the pairs of numbers rather than their relative positions on the number line.
 Describes the location of the graph of each number rather than the its position relative to the other number in the pair.
 Attempts to describe the distance between each pair of numbers.

Questions Eliciting Thinking Can you draw number lines and graph each pair numbers?
Where is relative to 10.5 on the number line? Is it to the left or to the right of 10.5? 
Instructional Implications Review the structure of the number line and guide the student to graph pairs of integers. Guide the student to use the graph to describe the relative positions of integers within each pair using language such as “to the left of” and “to the right of.” Assist the student in generalizing about the order of numbers on the number line, for example, observing that a number to the right of a given number is always larger. Eventually reintroduce rational numbers and ask the student to graph sets of rational numbers. Finally, ask the student to create a number line scaled with the integers and use it to describe the relative positions of pairs of rational numbers.
If needed, review the meaning of the inequality symbols and provide examples of their use. Ask the student to read inequality statements and provide feedback. Then give the student a list of statements involving inequality symbols; ask the student to determine if the statements are true or false and to correct the false ones. Provide additional opportunities for the student to use inequality symbols to both read information given in problems and write responses.
Consider implementing MFAS tasks Graphing Points on the Number Line (6.NS.3.6). 
Moving Forward 
Misconception/Error The student is unable to generalize the description of the inequality. 
Examples of Student Work at this Level The student:
 Correctly draws number lines and graphs the values in each of the numerical problems but is unable to describe how the numbers are positioned relative to each other on the number line.
 Correctly describes the relative positions of specific pairs of numbers but is unable to describe the relative position of x and y given that x > y.

Questions Eliciting Thinking You graphed the pairs of numbers correctly, but can you describe in words how the numbers are positioned relative to each other on the number line?
I see that you assigned values to x and y. Can you describe in general how x and y are positioned on the number line relative to each other? 
Instructional Implications Provide opportunities for the student to graph sets of rational numbers on the number line. Ask the student to use the graph to describe the relative positions of the numbers using language such as “to the left of” and “to the right of.” Assist the student in generalizing about the order of numbers on the number line, for example, observing that a number to the right of a given number is always larger. 
Almost There 
Misconception/Error The student’s explanation contains errors or lacks precision. 
Examples of Student Work at this Level The student correctly describes the relative positions of the numbers but:
 Includes statements about the distances between the pairs of numbers that are incorrect.
 Uses imprecise terms such as “behind,” “in front of,” or “last” to describe relative positions.

Questions Eliciting Thinking All of your descriptions about the relative positions of the numbers are correct, but you made some errors in calculating the distances between them. Can you show me how you determined these distances?
What did you mean by “behind” or “in front of”? Can you describe the relative positions of the pairs of numbers using phrases like “to the right of” or to “the left of”?
Which value is larger: x or y? On the number line, would x be to the left or to the right of y? 
Instructional Implications Provide direct feedback to the student on his or her response and assist the student in describing the relative positions of pairs of numbers in a concise and precise manner. Consider changing the numbers in this task and implementing it again with the student.
If necessary, address the misconception that zero is in the “center” or “middle” of the number line. Explain that the rational number line is infinitely long and contains no center or middle. When graphing numbers, eventually allow the student to draw only the portion of the number line that will reasonably accommodate the numbers to be graphed. For example, when graphing a set of numbers between 57 and 92, the student might draw an appropriately scaled number line that only shows the portion from 50 to 100. 
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 says that on the number line, 10.5 is to the left of , 7.2 is to the right of 4.5, 2 is to the left of zero, and x is to the right of y.

Questions Eliciting Thinking How many units to the left of zero is 2? How many units to the left of is 10.5?
Suppose 7 < n? How would these numbers be placed relative to each other on the number line? 
Instructional Implications Introduce the student to the concept of absolute value. Explain this concept in terms of the number line but also introduce the student to an algebraic definition (i.e., x = x if x 0 and x if x < 0). Guide the student to distinguish between the magnitudes of integers, as expressed by their absolute values, and the order of integers. Present the student with examples of rational numbers given in context (include integers as well as both positive and negative fractions and decimals) and ask the student to interpret the meanings of the numbers in terms of order and magnitude. For example, given temperatures of 20 °C and 5 °C, the student should be able to explain that 5° is greater or warmer than 20° (and write the inequality 5 > 20) but 20 deviates more from zero or freezing than 5. 