Getting Started 
Misconception/Error The student is unable to use variables to represent numbers and write expressions. 
Examples of Student Work at this Level The student is unable to represent the quantities described with variables and variable expressions. Instead, the student:
 Attempts to provide specific examples of numbers of points consistent with the descriptions.
 Indicates that he or she does not understand.

Questions Eliciting Thinking Is the number of points scored by either person given in the problem?
If you knew Justin’s score, what would you do to find Mark’s score?
If you knew Mark’s score, what would you do to find Nadine’s score?
Do you know what a variable is? Why would you need to use a variable in this problem? 
Instructional Implications Review the concept of a variable. Provide scenarios in which an unknown quantity can be represented by a variable such as “the number of miles that I run each day.” Emphasize that the variable stands for a number and is not a name or label. Then present another quantity that is described in terms of the variable (e.g., “Each day Mike runs twice as many miles as I do.”). Guide the student to represent the new quantity in terms of the variable (e.g., as 2x). Frequently remind the student that the variable represents a specific quantity, so 2x represents twice that quantity. Then ask the student to use the expression to calculate a specific quantity (e.g., ask, “If I ran 5 miles today, how far did Mike run?”). Model using the expression to calculate Mike’s distance.
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, “Jack is 5 years older than his brother Mark.” Ask the student to describe the unknown quantities (e.g., Jack’s age and Mark’s age), to represent one of the unknown quantities with a variable (e.g., x is Jack’s age), and to represent the other unknown quantity in terms of x (e.g., x – 5 represents Mark’s age).
Consider implementing the CPALMS Lesson Plan Let’s Translate! (ID 55214) and/or CPALMS Lesson Plan Decoding Word PhrasesTranslating verbal phrases to variable expressions (ID 28322). 
Moving Forward 
Misconception/Error The student attempts to use variables and write expressions to solve realworld problems but writes incorrect expressions. 
Examples of Student Work at this Level The student does not sufficiently describe the quantity represented by the variable and writes incorrect expressions to represent the second quantity in each problem.
The student records the wrong operation (e.g., 3 + j for “three times as many” or 5m for “five points more than”).

Questions Eliciting Thinking What does the variable represent in your expression? Can you be more specific?
What operation is suggested by the word times (or product, quotient, sum, difference)?
What operation is indicated by the phrase more than (or fewer than)? 
Instructional Implications Review the concept of a variable. Provide verbal descriptions of one unknown quantity described in terms of another. Ask the student to clearly define a variable to represent one unknown quantity and to write an expression in terms of the variable to represent the other unknown quantity. Emphasize that variables represent quantities and should be explicitly described as such (e.g., the variable m represents the number of points Mark scored rather than m represents Mark).
Review vocabulary associated with various mathematical operations. Have the student make a chart or table that includes vocabulary that suggests operations along with the related symbols. Provide the student with opportunities to practice writing variable expressions from verbal descriptions. Consider implementing the CPALMS Lesson Plan Expressions, Phrases and Word Problems, Oh My! (ID 47911). Also, consider using the MFAS task Writing Expressions (6.EE.1.2). 
Almost There 
Misconception/Error The student demonstrates an understanding of using variables to represent quantities but may not clearly define the variables. 
Examples of Student Work at this Level The student:
 Does not clearly define the variables but writes correct expressions.
 Uses an x to indicate multiplication creating an ambiguous expression (e.g., 3xj).
Note: The student may have more than one minor error.

Questions Eliciting Thinking What does the variable stand for in your expression? Can you be more specific?
Can you rewrite your expression without using “x” to indicate multiplication? Why do you think “x” should not be used to indicate multiplication in this expression? 
Instructional Implications Review the meaning of a variable and guide the student to describe variables as quantities (e.g., the variable m represents the number of points Mark scored rather than m represents Mark). If needed, make explicit the difference between the variable x and the multiplication symbol “x”, and discuss the purpose of each. Transition the student to using the conventions of algebra to show multiplication. Provide additional opportunities to represent quantities with variables and variable expressions. 
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 defines j as the number of points Justin scored and represents the number of points scored by Mark as 3j. The student may describe the number of points scored by Nadine as 3j + 5. The student may also redefine the number of points Mark scored by assigning a new variable to this quantity such as m and then describe the number of points scored by Nadine as m + 5.

Questions Eliciting Thinking Can you solve for j (or m)? Why or why not?
Is there only one possible value for j (or m)?
What are some possible values for j (or m)?
If Justin scored 8 points, how many points did Nadine score? 
Instructional Implications Challenge the student with more complex descriptions (e.g., represent the number of points scored by Nadine if she scored five points less than twice the number of points scored by Mark). Then ask, “Is it possible for Mark and Nadine to have scored the same amount of points (a tie)? If so, what would that score be?”
Consider using the MFAS task Gavin’s Pocket (6.EE.2.6) to assess whether the student understands that a variable can represent a number in a set as well as a single unknown number. 