Getting Started 
Misconception/Error The student does not understand the meaning of absolute value. 
Examples of Student Work at this Level The student:
 Ignores the absolute value symbols and attempts to solve the equations as if the symbols were not there.
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 Continues to use the absolute value symbols when solving the equations.
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 Writes work that does not make mathematical sense.
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Questions Eliciting Thinking What does absolute value mean? How is it defined?
What is the absolute value of three? Of negative five? Of zero?
If the absolute value of some number is 9.2, what are all possible values of that number? 
Instructional Implications Review the concept of absolute value as distance from zero on a number line. Ask the student to identify all numbers with a given absolute value, for example,  ?  = 12. Have the student graph the two numbers (e.g., 12 and 12) on a number line and compare the results. Emphasize that since both 12 and 12 are 12 units from zero, they have the same absolute value. Model writing the absolute value of a number as two distinct values (rather than using the plus or minus notation). For example, write, â€śIf x = 12, then x = 12 or x = 12.â€ť Guide the student to consider both the absolute value of zero and the absolute value of negative numbers in light of the concept of absolute value as distance from zero on a number line. Provide additional opportunities to solve simple absolute value equations.
Introduce the student to an algebraic definition of absolute value (i.e., define n as equal to n when n = 0 but equal to â€“n when n < 0). Guide the student to apply the algebraic definition when determining the absolute value of a number. 
Moving Forward 
Misconception/Error The student is unable to apply an understanding of absolute value to solving multistep equations and equations with no solutions. 
Examples of Student Work at this Level The student correctly solves the first two equations: x = 9.2 and x = 0. However, the student is unable to correctly solve the second two equations: x = 8 and 5x2 = 10.
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Questions Eliciting Thinking How did you know that the absolute value of 9.2 could be either 9.2 or 9.2? How did you know the absolute value of zero is zero? What does absolute value mean?
What happens when you take the absolute value of 8 (or of 8)? Is the absolute value of 8 equal to 8?
If the absolute value of some number is 10, then what are the possible values of that number? 
Instructional Implications Review the meaning of absolute value in terms of a number line. Explain why the absolute value of a number cannot be negative (i.e., since distances are typically described using nonnegative numbers). Also introduce the student to an algebraic definition of absolute value (i.e., define n as equal to n when n = 0 but equal to â€“n when n < 0). Use the algebraic definition to further explain that the absolute value of a number is always greater than or equal to zero. Model how to indicate that an equation has no solutions.
Review the reasoning used to solve a simple absolute value equation such as x = 9.2. Emphasize that since there are two numbers whose absolute value is 9.2, there are two solutions to this equation, x = 9.2 or x = 9.2. Apply this same reasoning to solving multistep equations such as 5x2 = 10. Emphasize that the expression 5x â€“ 2 represents a number whose absolute value is 10. Since there are two numbers whose absolute value is 10 (i.e., 10 and 10), 5x â€“ 2 represents either 10 or 10. Explain that this leads to the set of equations 5x â€“ 2 = 10 and 5x â€“ 2 = 10. Ask the student to solve each equation and check its solution in the original absolute value equation.
Provide additional opportunities to solve absolute value equations. 
Making Progress 
Misconception/Error The student is unable to apply an understanding of absolute value to solving equations with no solutions. 
Examples of Student Work at this Level The student correctly solves all equations except the third one: x = 8.
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Questions Eliciting Thinking How did you know that the absolute value of 9.2 could be either 9.2 or 9.2? What does absolute value mean?
What happens when you take the absolute value of 8 (or of 8)? Is the absolute value of 8 equal to 8? 
Instructional Implications Review the meaning of absolute value in terms of a number line. Explain why the absolute value of a number cannot be negative (i.e., since distances are typically described using nonnegative numbers). Also introduce the student to an algebraic definition of absolute value (i.e., define n as equal to n when n = 0 but equal to â€“n when n < 0). Use the algebraic definition to further explain that the absolute value of a number is always greater than or equal to zero. Model how to indicate that an equation has no solutions.
Provide additional opportunities to solve absolute value equations. 
Almost There 
Misconception/Error The student makes an error when solving a multistep equation. 
Examples of Student Work at this Level The student correctly solves all equations except the fourth one: 5x2 = 10. The student understands that if 5x2 = 10, then 5x â€“ 2 = 10 or 5x â€“ 2 = 10. However, the student makes an algebraic error when solving one of these two resulting equations.
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Questions Eliciting Thinking There is mistake in your solution for the last equation. Can you find it?
Did you check to see if your solutions satisfy the original equations? 
Instructional Implications Provide feedback to the student concerning any errors made. If needed, review solving multistep equations. Provide additional opportunities to solve multistep absolute value equations. 
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 solves each equation finding the following solutions:
 x = 9.2 or x = 9.2
 x = 0
 No solution is possible.
 x = 2.4 or x = 1.6 (or their fractional equivalents).
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Questions Eliciting Thinking Why is no solution possible to the equation x = 8?
Why is there only one solution to the equation x = 0?
What do you think about this equation: 3x+4 + 6 = 2? Will this equation have any solutions? 
Instructional Implications Introduce the student to writing absolute value equations to solve problems. Provide opportunities to solve word problems by writing and solving absolute value equations.
Consider implementing MFAS task Writing Absolute Value Equations (ACED.1.1).
Introduce the student to solving absolute value inequalities. 