Getting Started 
Misconception/Error The student is unable to use negative numbers to describe quantities. 
Examples of Student Work at this Level The student:
 Represents all quantities in the problem with positive numbers.
 Uses numbers unrelated to those given in the problem (e.g., adding or subtracting the given numbers or using numbers like 1 or 3 miles).

Questions Eliciting Thinking What is the difference between a gain and a loss?
Can you use a positive or negative sign to better represent these quantities? What might the positive symbol mean in the context of this problem? What might the negative symbol mean in the context of this problem?
Did you use the context given inÂ the problem? What does a â€śchange of positionâ€ť mean in football?
How would you answer the questions usingÂ the numbers given in the problems? 
Instructional Implications Expose the student to a variety of realworld situations in which integers are used to represent quantities such as gain/loss, increase/decrease, and above/below (e.g., sea level). Guide the student to represent integer quantities in the context of problems. Also, ask the student to describe a quantity that can be represented by given integers.
Consider implementing MFAS tasks Relative DecimalsÂ (6.NS.3.5)Â and Relative Fractions (6.NS.3.5)Â for further practice. 
Moving Forward 
Misconception/Error The student is unable to explain the meaning of zero within the context. 
Examples of Student Work at this Level When interpreting the meaning of zero, the student:
 Simply uses words such as â€śpositive,â€ť â€śnegative,â€ť â€śnone,â€ť or â€śnothing.â€ť
 Writes â€ś0â€ť or describes the location of zero on the number line.
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 Uses a context other than football (e.g., sea level or no money).
 Finds the sum of the answers to the previous two questions, 10.Â

Questions Eliciting Thinking Why did you write â€śpositiveâ€ť (or â€śnegativeâ€ť or â€śnoneâ€ť)? What does that mean in the context of football?
Why did you write â€ś0â€ť? What does that mean in the context of football? What might have happened to the ball for a description of â€ś0 yardsâ€ť?
How is zero related to sea level (or money)? How can zero be used to describe something happening in football? 
Instructional Implications Expose the student to a variety of realworld situations (e.g., gain/loss, increase/decrease, and above/below) in which zero can be used to describe quantities or change in quantities.
Have the student brainstorm with a group other reallife uses of integers including zero (or use a newspaper to hunt for ideas). Ask the student to write a brief sentence explaining how a positive, a negative, and zero can be used within that context. Next, have the student write his or her own word problem using integers within a chosen context.
Consider implementing MFAS tasks Relative DecimalsÂ (6.NS.3.5)Â and Relative FractionsÂ (6.NS.3.5)Â for further practice. 
Almost There 
Misconception/Error The student interprets zero as describing a location rather than a change in position. 
Examples of Student Work at this Level The student describes zero as:
 A place on the field as opposed to a change in position.
 The place where the ball is located.

Questions Eliciting Thinking What do you mean when you say zero is â€śin the end zoneâ€ť?
What does a â€śchange in positionâ€ť mean? If the change in position is zero, what might that mean? 
Instructional Implications Expose the student to a variety of realworld situations in which integers (or positive and negative rational numbers) can be used to describe both quantities and changes in quantities. Help the student understand the distinction between using integers to describe a quantity (such as a bank balance) and using integers to describe a change in a quantity (such as a credit or debit). Challenge the student to find additional examples of the use of integers in the real world and to describe the way in which the integers are used.
Consider implementing MFAS tasks Relative DecimalsÂ (6.NS.3.5)and Relative FractionsÂ (6.NS.3.5) for further practice. 
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 answers the first two questions correctly giving answers of 5 and 15.
When interpreting the meaning of zero, the student says:
 The ball ends up back at the same place it started after the same amount of gain and loss on the play.
 The player ran the ball forward but then got pushed back to the starting place.
 The ball was thrown but incomplete, so they gained zero yards on the play.
 The ball didnâ€™t move.
 There was no gain and no loss of yards.

Questions Eliciting Thinking What would the overall change be if the team gained 5 yards on one play and then lost 15 yards on the next play?
What is the difference between a ball being â€śon the zero yard lineâ€ť and â€śgaining zero yardsâ€ť? 
Instructional Implications Give the student more experience using rational numbers to represent quantities and interpreting the meaning of zero using a variety of contexts. Guide the student to use a number line to represent integers and changes to integer quantities.
Introduce the concept of opposites and have the student use a number line to graph pairs of opposite values.
Engage the student in a discussion of the different ways that the minus or negative symbol is used in mathematics. Encourage the student to interpret expressions such as â€“n as meaning â€śthe opposite of n.â€ť 