Getting Started 
Misconception/Error The student is unable to write the given expression in an equivalent form. 
Examples of Student Work at this Level The student writes an expression that is not equivalent to (x + 2) + (x + 2) + (x + 2).

Questions Eliciting Thinking What does it mean for an expression to be equivalent to (x + 2) + (x + 2) + (x + 2)? Is the expression you wrote equivalent?
Can you explain how you found the expression you wrote?
How can you tell if two expressions are equivalent? 
Instructional Implications Explain what it means for expressions to be equivalent (i.e., the value of each expression is the same when evaluated for the same values of the variables). Demonstrate that two expressions [e.g., 2(a + 3) and 2a + 6] are equivalent by asking the student to evaluate each expression for various values of a. Also, provide an example of two expressions such as 2(a + 3) and 2a + 3 and demonstrate that they are not equivalent by evaluating each expression for a particular value of a. Be sure the student understands that the demonstration that two expressions are equivalent for a variety of values does not constitute a proof that they are equivalent. To prove two expressions are equivalent, properties and theorems must be used.
Provide instruction on the Associative and Commutative Properties and be very clear in describing what each property states, both in words and in symbols. For example, explain that the Commutative Property of Addition states that it does not matter the order in which two numbers are added. Illustrate this property by writing “a + b = b + a for all values of a and b.” Show the student specific examples of the use of the properties (e.g., 2a + b = b + 2a by the Commutative Property). Demonstrate how the properties can be used to simplify computation [e.g., the expression (44 + 28) + 56 can be rewritten as (28 +44) + 56 by the Commutative Property which can then be rewritten as 28 + (44 + 56) by the Associative Property so that it can be evaluated as 28 + 100 = 128].
Provide instruction on the use of the Distributive Property to generate equivalent expressions. Begin by describing parentheses as an example of grouping symbols. Use algebra tiles to model an expression such as 3x + 2. Then have the student produce two groups of 3x + 2. Show the student the expression 2(3x +2) and help relate the algebraic expression to the physical model of the expression. Encourage the student to explain how two groups of 3x +2 are the same as 6x + 4. Describe combining like terms as an application of the Distributive Property. Define associated vocabulary as needed (e.g., equivalent, expression, factor, term, coefficient, variable, distribute). Provide the student with additional opportunities to apply the Distributive Property to rewrite expressions in equivalent forms. 
Making Progress 
Misconception/Error The student rewrites the expression in an equivalent form but is unable to adequately justify the equivalence. 
Examples of Student Work at this Level The student rewrites the given expression in an equivalent form. When justifying the equivalence, the student provides answers such as:
 They are the same.
 The variables and numbers are the same.
 They will be the same if you substitute a number for x.
 They both equal 3x + 6.
 You just combine the x’s and the twos.
 It’s a simpler form (or shorter form) of (x + 2) + (x + 2) + (x + 2).

Questions Eliciting Thinking What properties of operations do you know? Can you describe them? Which properties of operations did you use to write this expression?
What does it mean for this expression to be simpler? What properties did you use to make it simpler? 
Instructional Implications Review the Commutative, Associative, and Distributive Properties. Model using these properties to justify the equivalence of the expression that the student wrote. Provide the student with an algebraic expression and ask him or her to generate equivalent expressions using only the Commutative Property, only the Associative Property, and only the Distributive Property. Then ask the student to explain how each property was used. Next, provide two expressions whose equivalence can be justified using a combination of these properties. Challenge the student to describe which properties of operations justify the equivalence. 
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 rewrites the expression in an equivalent form and explains why the expressions are equivalent by citing or describing relevant properties of operations.
The student uses the:
 Commutative Property to write an expression such as (2 + x) + (2 + x) + (2 + x), and explains the equivalence either formally (e.g., by referencing the Commutative Property) or informally (e.g., by explaining, “The order is switched”).
 Associative and Commutative Properties to write an expression such as (x + x + x) + (2 + 2 + 2), and explains the equivalence either formally or informally.
 Distributive Property to write an expression such as 3(x + 2), and explains the equivalence either formally or informally.

Questions Eliciting Thinking Do you know the name of the property that you used here?
Can you use the same property to write a different equivalent expression?
Can you write another equivalent expression that uses different properties? 
Instructional Implications Allow the student the opportunity to generate more equivalent expressions using different combinations of the properties of operations. If the student used only the Commutative and Associative Properties, assist the student in developing an understanding of the Distributive Property. Consider implementing CPALMS Lesson Plan Distributing and Factoring Using Area (ID 366).
Discuss the properties of operations more formally. Ensure students can describe the properties using their names (e.g., Commutative Property of Addition). Guide the student to describe the properties of operations using algebraic statements [e.g., the Distributive Property states that a(b + c) = ab + ac].
Challenge the student to:
 Write an expression equivalent to 3x(2x + 3y – 7), using the Distributive Property.
 Use the Commutative Property to write as many expressions equivalent to 5c(8a + 7b) as possible.
 Use as many properties as possible to generate expressions equivalent to 3(4x + 8y) + 12x.
Consider administering other MFAS tasks for standard 6.EE.1.3.
