Getting Started 
Misconception/Error The student does not understand how to calculate percent change. 
Examples of Student Work at this Level The student:
 Subtracts 3.75 â€“3.44 = 0.31 or 3.44 â€“3.75=  0.31 and says the percent change is 31% or 31 cents.
 Calculates the percent that one price is of the other.
 Calculates 3.75 â€“ 3.44 = 0.31, divides 0.31 by 3.44, and then attempts to convert the result to a percent.

Questions Eliciting Thinking I see that you found the difference in the two prices. Do you know what to do next? Is the difference the same as the percent change?
What does percent change mean? Do you know how it is calculated?
It looks like you found what percent one price is of the other. Is that the same as percent change?
What should the difference be compared to when calculating percent change? The original amount or the new amount? 
Instructional Implications Guide the student through the process of calculating percent change: (1) find the difference between the two given quantities, (2) calculate the percent that the difference is of the original quantity, and (3) interpret the percent change as an increase or decrease in the context of the problem.
If needed, provide instruction on calculating the percent one quantity is of another. Describe finding the percent as a proportional scaling. Use a tape diagram or double number line to help the student visualize the relationship among the part, the whole, the unknown percent, and 100%. Guide the student to write and solve a proportion to find the unknown percent. 
Moving Forward 
Misconception/Error The student sets up the calculation correctly but is unable to correctly calculate the quotient. 
Examples of Student Work at this Level The student sets up the calculation as Â but is unable to correctly divide 0.31 by 3.75. For example, the student:
 Is unable to complete the calculation.
 Divides incorrectly.
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Questions Eliciting Thinking I see that you found a difference of $0.31 between the two prices. Can you explain to me how you found the percent?
Can you write a proportion that will help you calculate the percent? 
Instructional Implications Provide instruction on how to calculate percent. Describe finding the percent that one quantity is of another as a proportional scaling. Use a tape diagram or double number line to help the student visualize the relationship among the part, the whole, the unknown percent, and 100%. Guide the student to write and solve a proportion to find the unknown percent. 
Almost There 
Misconception/Error The student makes a minor computational error or has difficulty interpreting the percent change in context. 
Examples of Student Work at this Level The student:
 Rounds 0.082666â€¦ to 0.0826 and says the percent decrease is 8.26%.
 Locates the decimal point incorrectly when converting to a percent.
 Neglects to convert to a percent.
 Calculates the difference between the two prices yet does not explain that it is a percent increase or decrease.

Questions Eliciting Thinking Can you tell me what this percent means in the context of this problem?
Can you show your work on your paper so that someone reading your work could tell exactly what you did? 
Instructional Implications Help the student find and correct his or her mistake. Provide the student with additional opportunities to calculate percent change. Have the student work with a partner to compare strategies and calculations and to reconcile any differences.
Expose the student to interpretations of percent change by classmates at the Got It level. Provide additional opportunities for the student to interpret percent change in problem contexts. 
Got It 
Misconception/Error The student provides a complete and correct response to all components of the task. 
Examples of Student Work at this Level The student subtracts $3.44 from $3.75 and then determines the percent that this difference, $0.31, represents of the original price. The student explains that gasoline prices dropped 8.3%. 
Questions Eliciting Thinking How did you calculate the percent?
What is the meaning of this percent in the context of the problem?
What if the original price had been $3.44 and todayâ€™s price was $3.75? How would that change your response to this problem? 
Instructional Implications Provide problems in which the percent increase/decrease is given but in which the student must find either the original value or the later value. 