Getting Started 
Misconception/Error The student does not understand what it means for expressions to be equivalent. 
Examples of Student Work at this Level The student identifies expressions that are not equivalent to 6(y + 1) and may fail to identify ones that are. The student may also incorrectly apply or cite properties of operations to justify choices.
Â Â Â
Â
Â Â Â
Â 
Questions Eliciting Thinking What does it mean for two expressions to be equivalent?
What do the parentheses in 6(y + 1) indicate? Can you rewrite 6(y + 1) in an equivalent form without the parentheses?
What do you know about the Distributive Property?
If you are multiplying (y + 1) by six, will the six be distributed (multiplied) to both terms? 
Instructional Implications Explain what it means for two expressions to be equivalent (i.e., two expressions are equivalent if they always result in the same number when evaluated for the same values of the variables). Demonstrate the equivalence of two expressions such as 2x + y and y + 2x by evaluating each for the same value of x and y. Explain to the student that it is not possible to evaluate each expression for every possible value of x and y to check for equivalence; however, properties of operations can be used to verify equivalence (e.g., 2x + y = y + 2x by the Commutative Property of Addition).
Review the properties of operations and the associated vocabulary as needed (e.g., equivalent, expression, factor, term, coefficient, variable, constant, distribute). Emphasize the Distributive Property and how it can be used to both expand and factor expressions to generate equivalent expressions. Model using the Distributive Property to generate equivalent expressions. Emphasize that the properties of operations ensure that expressions are equivalent for every value of the variable(s). Provide opportunities for the student to use properties of operations to generate equivalent expressions.
Emphasize that expressions can be shown to not be equivalent by evaluating each for particular values of the variable and showing that they result in different numbers. However, to show that expressions are equivalent requires using definitions and properties. Show the student a pair of expressions such as 2x and 3x or 2x and . Evaluate the pairs of expressions for a particular value for which they are equal (e.g., x = 0 and x = 2, respectively). Then evaluate the pairs of expressions for another value to show that they are not always equal and are not, therefore, equivalent. Guide the student to apply properties of operations to determine equivalence.
Consider implementing other MFAS tasks aligned to standard 6.EE.1.4. 
Making Progress 
Misconception/Error The student correctly identifies all expressions equivalent to the given one but does not correctly apply properties of operations. 
Examples of Student Work at this Level The student identifies both 6y + 6(1) and 6y + 1 as equivalent to the given expression. However, the student:
 Tests the expressions by evaluating them at a particular value of the variable rather than applying properties of operations.
 Cites the wrong property in justifying anÂ equivalence.
Â Â Â

Questions Eliciting Thinking Can you determine if the expressions are equivalent without replacing the variable with a number and evaluating each expression? Explain.
Can you think of any properties you could use to justify your choices? Explain. 
Instructional Implications If needed, make clear that expressions can be shown to not be equivalent by evaluating each for particular values of the variable and showing that they result in different numbers. However, to show that expressions are equivalent requires using definitions and properties. Show the student a pair of expressions such as 2x and 3x or 2x and . Evaluate the pairs of expressions for a particular value for which they are equal (e.g., x = 0 and x = 2, respectively). Then evaluate the pairs of expressions for another value to show that they are not always equal and are not, therefore, equivalent. Guide the student to apply properties of operations to determine equivalence.
Review the properties of operations and the associated vocabulary as needed (e.g., term, coefficient, variable, constant, distribute). Emphasize the Distributive Property and how it can be used to both expand and factor expressions to generate equivalent expressions. Model using the Distributive Property to generate equivalent expressions. Emphasize that the properties of operations ensure that expressions are equivalent for every value of the variable(s). Provide opportunities for the student to use properties of operations to generate equivalent expressions.
Consider implementingÂ other MFAS tasks aligned to standard 6.EE.1.4. 
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 identifies 6(y) + 6(1) and 6y + 6 as equivalent to 6(y + 1) and cites the Distributive Property as justification. The student may also cite the Identity Property of Multiplication to justify the equivalence of 6(y) + 6(1) and 6y + 6.

Questions Eliciting Thinking What property assures us that 6(1) = 6?
Can you generate another equivalent expression using the Commutative Property? 
Instructional Implications Challenge the student to write an expression equivalent to 4(x + y + 3z), c(a + b + c), and/or (8 + 2g)5 using the Distributive Property (and/or Commutative Property).
Consider implementingÂ MFAS task Property Combinations (6.EE.1.4). 