Getting Started 
Misconception/Error The student does not understand the concept of opposite. 
Examples of Student Work at this Level The student is unable to correctly identify the opposite of zero and says:
 The opposite of zero is negative zero.
 Zero has no opposite.
 Zero cannot have an opposite because it cannot be positive or negative.
Or the student says (5) is 5 and offers an explanation that does not appeal to the meaning of the term opposite.

Questions Eliciting Thinking What does the word opposite mean in mathematics? Can you describe opposites in terms of the number line?
What does the negative sign mean?
How do you read aloud â€“ (â€“ 5)? 
Instructional Implications Introduce the student to 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 to define the term opposite and to 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).
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 n units 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 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.
Provide additional opportunities to consider numbers and their opposites in the context of real world and mathematical applications. 
Making Progress 
Misconception/Error The studentâ€™s explanations are incomplete or imprecise. 
Examples of Student Work at this Level The student correctly identifies the opposite of zero as zero and says that â€“(â€“5) = 5. However, the studentâ€™s explanations are incomplete or imprecise. For example, the student explains that the opposite of zero is zero because:
 Zero is â€śits own number.â€ť
 Zero is â€śbetween positive and negative.â€ť
 Thereâ€™s only one zero on the number line.
Or the student says (5) = 5 because:
 Two negatives or â€śa negativeâ€ť make a positive.
 5 + 5 = 10.
 Of an incomplete understanding of the symbol â€śâ€“.â€ť

Questions Eliciting Thinking What is the definition of the term opposite?
How do you read aloud â€“ (â€“ 5)?
Can you explain the opposite of 5 in terms of the number line? 
Instructional Implications Be sure the student understands that the opposite of any number, n, is the number that is n units 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 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]. 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. Provide practice with graphing and interpreting opposites in a variety of contexts. 
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 states that the opposite of zero is zero and that â€“ (â€“ 5) is 5. The student explains â€“ (â€“ 5) in terms of:
 Opposites by interpreting the â€“ symbol outside the parentheses as meaning â€śthe opposite ofâ€ť (e.g., the student says, â€śThe opposite of 5 is 5.â€ť)Â
 The relationship between the distance from zero of 5 and 5.
 Multiplication by interpreting â€“ symbol outside the parentheses as meaning â€ś1 timesâ€ť [e.g., â€“ (â€“ 5) is 1(5)].

Questions Eliciting Thinking Why is zero the opposite of zero?
Can you describe the distance between a number, n, and zero on the number line in terms of absolute value? Can you describe the distance between n and â€“n?
Does â€“n always represent a negative number? When would â€“n represent a positive number? 
Instructional Implications If the student has a firm understanding of opposites in terms of a number line, introduce the student to an algebraic definition of opposites (e.g., define â€“ n as the product of negative one and n or 1 Ă— n). Encourage the student to also think about opposites in terms of multiplication by 1.
If the student has a firm understanding of absolute value in terms of the number line, introduce the student to an algebraic definition of absolute value (e.g., define n as equal to n when n = 0 but equal to â€“n when n < 0). Ask the student to compare positive and negative rational numbers as well as their absolute values. Guide the student to distinguish between comparisons of directions and comparisons of magnitude (e.g., absolute value) of pairs of numbers given in context. For example, if 20 meters and 10 meters represent elevations of location A and location B, respectively, then location A is below sea level while location B is above sea level. In addition, location B deviates from sea level more than location A since 20 > 10.
Introduce the student to graphing on the Cartesian plane. Consider implementing the MFAS task Point Locations (6.NS.3.6). 