Getting Started 
Misconception/Error The student is unable to interpret the meaning of the variable in the context of the problem. 
Examples of Student Work at this Level The student can neither describe what x represents nor correctly list the possible values of x. The student may determine that if the total value of the coins is 50 cents, then x = 5. However, the student is unable to interpret the meaning of x = 5 when asked.

Questions Eliciting Thinking Can you restate the problem in your own words?
Where does the 10 in 10x come from? What does the 10 represent?
For the third question, you said that x = 5. What does this solution mean in the context of this problem? 
Instructional Implications Ask the student to consider the coefficient in the expression 10x and relate it to the context of the problem in order to understand its meaning. Then have the student consider the description of the meaning of 10x and ask the student to conjecture what x represents. Guide the student through responses to the first two problems.
Provide many mathematical and realworld contexts that describe unknown quantities that can be represented by variables and variable expressions. Ask the student to clearly define the variable as a quantity and to write expressions for other quantities described in terms of the variable. For example, “Andrew went to the store to buy some cheese crackers. He divided the cheese crackers equally into sandwich bags and gave a bag to each of four friends in math class.” Ask the student to describe the unknown quantities (e.g., the total number of crackers purchased and the number of crackers per bag), to represent one of the unknown quantities with a variable (e.g., x is the number of crackers per bag), and to represent the other unknown quantity in terms of x (e.g., 4x represents the total number of crackers).
If needed, guide the student to be precise in describing the quantity represented by the variable. For example, given the situation, “Sally has s spoons then buys two more,” guide the student to describe s as the number of spoons Sally originally had rather than simply as “spoons.” Emphasize that a precise description indicates that the variable represents a specific quantity.
Consider implementing the MFAS tasks for 6.EE.1.2 and/or CPALMS lesson plans Decoding Word PhrasesTranslating Verbal Phrases to Variable Expressions (ID 28322), Let's Translate!! (ID 55214), and Expressions, Phrases and Word Problems, Oh My! (ID 47911). 
Moving Forward 
Misconception/Error The student has an incomplete understanding of the quantity represented by the variable. 
Examples of Student Work at this Level The student clearly states that x represents the value of each coin. However, when identifying possible values of x, the student:
 Names additional values of x that do not correspond to the values of U.S. coins.
 States that x could equal any number or anything times 10.
 Correctly determines that x = 5 when the total value of coins is 50 cents in the third question and then states that five is the only possible value for x in the expression 10x.
The student correctly lists possible values of x but does not clearly state that x represents the value of each coin. The student says that x represents:
 An unknown number.
 The number of groups of 10.
 The total value of the coins.
The student may or may not be able to determine that when the total value of the coins is 50 cents, x = 5.

Questions Eliciting Thinking What does x represent? What are its possible values?
If you did not know the total value of the coins, what values of x might be possible?
You correctly listed possible values of x. How would you describe these values? Does your description fit your answer you gave to the first question? 
Instructional Implications If the student clearly describes the meaning of the variable but is unable to correctly list possible values of x, guide the student to refer to its meaning and to the context of the problem to conjecture possible values of the variable. Be sure the student understands that until the total value of the coins is known, there are several possible values of x. If the student correctly lists possible values of the x but does not clearly describe its meaning, guide the student to refer to these values when explaining what x represents. In either case, ask the student to explain why x cannot be 20.
Provide opportunities to use variables to represent numbers and to write expressions to represent quantities in realworld and mathematical problems. 
Almost There 
Misconception/Error The student is unable to determine the value of the variable when the total value of the coins is given. 
Examples of Student Work at this Level The student clearly states that x represents the value of each coin and correctly lists possible values of x. However, the student is unable to determine the value of x when the total value of the coins is 50 cents.

Questions Eliciting Thinking What does 10x represent?
Can you write an equation to solve for x given that the total value of the coins is 50 cents? 
Instructional Implications Assist the student in writing an equation that can be solved to find the value of x when the total value of the coins is 50 cents. Ask the student to solve the equation and to explain the meaning of the solution in the context of the problem.
Provide opportunities to use variables to represent numbers and to write expressions to represent quantities in realworld and mathematical problems. 
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 states that x represents the value of each coin. The student states that the possible values of x are 1, 5, 10, 25, 50, and 100. The student states if 10x = 50 then x = 5 and provides a sufficient explanation.

Questions Eliciting Thinking If x = 5, what kind of coin is in Gavin’s pocket?
Why did you choose these numbers as possible values of x?
What if the total value of the coins was $1.30? What would be the value of x? 
Instructional Implications Challenge the student to further explore the meaning of variables and expressions with a problem such as:
Francis has seven cows grazing in a field and more cows divided evenly into three pens. The total number of cows is represented by the expression 3c + 7. What does c represent in this context? What would it mean for c to equal four? Using the same variable, c, write an expression for the total number of cows if Francis were to move the cows into four pens instead of three.
Consider implementing the MFAS tasks for the 6.EE.2.7 standard. 