Getting Started 
Misconception/Error The student is unable to correctly scale the number line or graph the given values. 
Examples of Student Work at this Level The student:
 Scales the number line incorrectly.
 Scales the number line correctly but does not graph the given values.
 Scales the number line correctly and graphs the values using an unconventional technique.
Additionally, the student may have difficulty explaining the relationship between a number and its opposite in terms of the number line.

Questions Eliciting Thinking What does it mean to scale a number line?
How do you indicate placement of a value on the number line when graphing? 
Instructional Implications Provide instruction on constructing and scaling number lines. Remind the student that intervals between notches must be equal, and the scale must be appliedÂ so thatÂ equal differences between numbers are represented by corresponding equal distances on the number line. Guide the student to use a point or dot to clearly show the graph of a number. Also, indicate that if the pointÂ is named by a letter such as A, the letter is conventionally placed above itsÂ graph on the number line. Guide the student to use a scale that is appropriate to the values to be graphed and explain that it is not always necessary to show the location of zero. For example, to graph 100, 103, and 109, the portion of the number line shown might be from 100 to 110 and scaled in increments of one. However, when graphing 100, 150, and 175, the portion of the number line shown might be from 100 to 200 and scaled in increments of 25. Provide additional opportunities to scale number lines and graph given sets of values.
Provide instruction on opposites as described in Moving Forward. 
Moving Forward 
Misconception/Error The studentÂ does not understand opposites in termsÂ of the number line. 
Examples of Student Work at this Level The student is able to correctly graph 4, 0, and 4 but cannot explain the relationship between the graph of a number and its opposite in terms of the number line. For example, the student:
 Explains opposites in terms of signs. Answers may include:
 The opposite of a number is always negative.
 Opposites are the same number with different signs.
 They are the same number used differently.
 Its inverse is the opposite.
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 Attempts an explanation in terms of the number line which is vague or incorrect.
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Questions Eliciting Thinking What does the word opposite mean in mathematics?
Can you describe the location of 4 and 4 on the number line in terms of zero?
What is generally true about the graph of a number and its opposite? 
Instructional Implications Define the opposite of a number in terms of the number line. Be sure the student understands that the opposite of any number, n, is the number that is (1) the same distance from zero as n on the number line Â but (2) on the opposite side of zero from n on the number line. Ask the student to use the number line to identify and graph a variety of rational numbers (including fractional and negative values) and their opposites. Encourage the student to interpret the negative symbol (â€“) as meaning â€śthe opposite ofâ€ť when it precedes a number [e.g., interpret â€“5 as the opposite of five and â€“ (â€“ 5) as the opposite of 5]. Extend the studentâ€™s understanding of opposites in terms of the number line to zero. Explain that zero is its own opposite because it is the only number that is the same distance from zero as zero. Consequently, â€“ 0 = 0. Guide the student to read expressions such as â€“n as, â€śthe opposite of nâ€ť and to be flexible in considering possible values of n. Indicate that the value of n in an expression such as â€“n could be any rational number including zero or a negative rational. Consequently the value of â€“n could be zero or positive.
Explicitly address any misconceptions the student might have about the sign of a numberâ€™s opposite. If the student says that the opposite of a number is always negative, provide a counterexample for the student by asking, â€śWhat is the opposite of 8? Is the opposite of 8 a negative number?â€ť
Provide additional opportunities to consider numbers and their opposites in the context of real world and mathematical applications. 
Almost There 
Misconception/Error The student's explanation is incomplete. 
Examples of Student Work at this Level The student attempts to explain the relationship between the graph of a number and its opposite, but the explanation lacks one of the two essential components: (1) the same distance from zero on the number line and (2) on opposite sides of zero on the number line. For example:
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Questions Eliciting Thinking Given any number, x, can you describe where the opposite of x is located on the number line?
Can opposites ever be on the same side of zero on the number line? 
Instructional Implications Model aloud the mathematical thinking required to graph opposites (e.g., the numbers must be the same distance from zero but on opposite sides of zero). Emphasize that there are two components to the relationship between the graph of a number and its opposite:
 A number and its opposite are equidistant from zero on the number line.
 A number and its opposite are on opposite sides of zero on the number line.
Provide opportunities to identify the opposite of a given number and explain whyÂ the two numbers are opposites.

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 given numbers and explains that opposites are numbers that are the same distance from zero but on opposite sides of zero on the number line.

Questions Eliciting Thinking Is the opposite of a number always negative? What kinds of numbers have opposites that are positive?
Is there any number whose opposite is zero? 
Instructional Implications Introduce the concept of absolute value in terms of the number line (e.g., the absolute value of a number is its distance from zero on the number line). Assist the student in becoming comfortable with the absolute value notation by initially reading values such as 5 as â€śthe distance from 0 to 5 on the number line.â€ť Use absolute value toÂ describe the magnitude of a signed number in practical applications (e.g., 40 might describe the vertical distance a diver travelled when descending into the ocean).
Consider implementing the MFAS task What Is the Opposite? 