Getting Started 
Misconception/Error The student does not understand how to write absolute value equations. 
Examples of Student Work at this Level The student does not write either equation correctly.
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Questions Eliciting Thinking Can you explain why you wrote your equation the way you did?
You wrote the equation in more than one way. Are the two ways equivalent?
How would you write â€śthe absolute value of 25â€ť? How can you write the absolute value of an unknown number? 
Instructional Implications Review the concept of absolute value and how it is written. Emphasize that the concept of absolute value can be used to describe the difference between two numbers. Model using absolute value to represent distances between values on the number line. For example, represent a numberâ€™s distance from zero as x â€“ 0 or x. Explain that distance is usually represented by a positive number, so if x is unknown, its distance from zero is best represented as x which represents a nonnegative value. Generalize this explanation to the distance between two numbers on the number line, for example, x and 12. Explain that x could be greater than 12 or x could be less than 12. Either way, x â€“ 12 (or 12 â€“ x) represents the distance between x and 12.
Provide examples of absolute value equations and ask the student to solve them. Ensure that the student uses absolute value notation correctly and represents solutions of absolute value equations appropriately (e.g., as x = 3 or x = 3 rather than x = Â±3).
Next, introduce the student to contexts in which absolute value is needed to represent described quantities, similar to the second problem on the worksheet. Model using absolute value to represent such quantities. Provide additional contexts and ask the student to write expressions or equations to model quantities or relationships described. 
Moving Forward 
Misconception/Error The student is unable to represent a difference using absolute value. 
Examples of Student Work at this Level The student correctly writes and solves the absolute value equation described in the first problem. However, the student is unable to correctly write an absolute value equation to represent the described difference.
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Questions Eliciting Thinking 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 difference?
Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees?
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 to represent differences between two numbers. For example, represent the difference between x and 12 as x â€“ 12 or 12 â€“ x. Emphasize that each expression simply means the difference between x and 12. Evaluate the expression x â€“ 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and 12.
Guide the student to write an equation to represent the relationship described in the second problem. Ask the student to solve the equation and provide feedback. Then explain why the equation the student originally wrote does not model the relationship described in the problem. For example, explain that an equation such as  = 74 â€“ 6 means that the difference between some value Â and zero is 74 â€“ 6 or 68 so that Â = 68 or Â = 68. Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem (i.e., the difference between Â and 74 is six).
Provide additional opportunities for the student to write and solve absolute value equations. 
Almost There 
Misconception/Error The student correctly writes both equations but errs in solving the first equation or writing its solutions. 
Examples of Student Work at this Level The student:
 Finds only one of the solutions of the first equation.
 Writes the solutions of the first equation using absolute value symbols.
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Questions Eliciting Thinking How many solutions can an absolute value equation have? Do you think you found all of the solutions of the first equation?
What are the solutions of the first equation? Should you use absolute value symbols to show the solutions? 
Instructional Implications Provide feedback to the student concerning any errors made. If needed, clarify the difference between an absolute value equation and the statement of its solutions.
Consider implementing MFAS task Solving Absolute Value Equations (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 equation: x = 17.4 so that x = 17.4 or x = 17.4. The student correctly writes the second equation as  Â â€“ 74 = 6 or 74 â€“  = 6.
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Questions Eliciting Thinking Why was it necessary to use absolute value to write this equation?
How many solutions do you think this equation has? Why are there two solutions? What would they mean in this context? 
Instructional Implications Ask the student to solve the second equation and interpret the solutions in the context of the problem.
Ask the student to identify and write as many equivalent forms of the equation as possible. Then have the student solve each equation to show that they are equivalent.
Consider implementing MFAS task Writing Absolute Value Inequalities (ACED.1.1). 