Getting Started 
Misconception/Error The student does not understand how to write and solve absolute value inequalities. 
Examples of Student Work at this Level The student:
 Is unable to correctly write either absolute value inequality.
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 Writes only the first inequality correctly but is unable to correctly solve it.
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Questions Eliciting Thinking How would you write â€śthe absolute value of 25â€ť? How can you represent the absolute value of an unknown number?
How did you solve the first absolute value inequality you wrote? Can you explain what the solution set contains? 
Instructional Implications Review the concept of absolute value and how it is written. If needed, guide the student to write the inequality described in the first problem as x > 8.7. Review, as needed, how to solve absolute value inequalities. Provide additional examples of absolute value inequalities and ask the student to solve them. Consider implementing MFAS task Solving Absolute Value Inequalities (ACED.1.1).
Model using simple absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem. For example, given the statement â€śall of the employees have salaries, s, that are within $10,000 of $40,000,â€ť guide the student to model the range of incomes with an absolute value inequality such as 40,000 â€“ s < 10,000. Likewise, given an absolute value inequality such as x â€“ 5 < 9, emphasize interpreting the solution set as all values within 5 units of nine. Be sure to include situations that give rise to absolute value equations of the form x â€“ a > b.
Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described. 
Moving Forward 
Misconception/Error The student is unable to represent a constraint on a difference using an absolute value inequality. 
Examples of Student Work at this Level The student correctly writes and solves the absolute value inequality described in the first problem. However, the student is unable to correctly write an absolute value inequality to represent the described constraint.
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Questions Eliciting Thinking What does it mean for one number to be â€świthin 1.5â€ť of another number?
Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values? What is the constraint on this difference?
Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? 
Instructional Implications Model using absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem. For example, given the statement â€śall of the employees have salaries, s, that are within $10,000 of the mean salary, $40,000,â€ť guide the student to model the range of incomes with an absolute value inequality such as 40,000 â€“ s < 10,000. Likewise, given an absolute value inequality such as x â€“ 5 < 9, emphasize interpreting the solution set as all values within 5 units of nine. Be sure to include situations that give rise to absolute value equations of the form x â€“ a > b.
Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described. 
Almost There 
Misconception/Error The student correctly writes both inequalities but errs in solving the first inequality or writing its solutions. 
Examples of Student Work at this Level The student:
 Only provides part of the solution set, for example, x > 8.7.
 Represents the solution set as a conjunction rather than a disjunction.
 Uses the wrong inequality symbol to represent part of the solution set.
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 Does not represent the solution set as a disjunction.
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Questions Eliciting Thinking Would the value 10 satisfy the first inequality? Why or why not?
What does 8.7 < m < 8.7 mean? What would the graph of this set of numbers look like?
Can you describe in words the solution set of the first inequality? 
Instructional Implications Provide feedback to the student concerning any errors made in solving the first inequality or representing its solution set. If needed, clarify the difference between a conjunction and a disjunction.
Consider implementing MFAS task Solving Absolute Value Inequalities (ACED.1.1). 
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 writes and solves the first inequality: x > 8.7 so that x < 8.7 or x > 8.7. The student correctly writes the second inequality as Â or . 
Questions Eliciting Thinking How would you describe the solution set of the first inequality in words?
How would you solve the second inequality? 
Instructional Implications Ask the student to solve the second inequality and interpret the solution set in the context of the problem.
Ask the student to identify and write as many equivalent forms of the second inequality as he or she can. Then have the student solve each form to show that they are equivalent.
Consider implementing MFAS task Solving Absolute Value Inequalities (ACED.1.1). 