Getting Started 
Misconception/Error The student is unable to apply the Distributive Property to expand expressions. 
Examples of Student Work at this Level The student only multiplies the first term in parentheses when distributing. For example, the student:
 Multiplies 8 by x but not .
 Multiplies 12 by 6 (or 6) but not â€“x, producing answers such as 7x â€“ 74 or 9x â€“ 74.

Questions Eliciting Thinking What does the Distributive Property tell you? In general, how do you multiply something like a(b + c)?
What should the eight multiply? What should the â€“6 multiply? 
Instructional Implications Show the student, using a numerical example such as 5(2 + 9), that a(b + c) is not equal to ab + c. Review how the Distributive Property is used to expand expressions of the form a(b + c) where a, b, and c contain rational coefficients, both positive and negative. Model using the Distributive Property by initially rewriting an expression such as 5(2x + 9) as Â and then as 10x + 45. Describe this use of the Distributive Property as expanding the expression. Be sure the student understands that the Distributive Property applies to subtractions as well, since any subtraction can be rewritten as an addition {e.g., an expression such as 6(4y â€“ 5) = 6[4y + (5)] = (6 x 4y) + [6 x (5)] = 24y + (30) or 24y â€“ 30}. Encourage the student to show work carefully when distributing.
Provide additional opportunities to expand expressions using the Distributive Property. 
Moving Forward 
Misconception/Error The student neglects to combine like terms or makes errors in combining like terms. 
Examples of Student Work at this Level The student:
 Adds or subtracts unlike terms (e.g., 6x â€“ 2 = 4x).
 Does not combine like terms, leaving a final answer of:
 (6x â€“ 2) â€“ (72 â€“ 6x)
 6x â€“ 2 â€“ 72 + 6x (or â€“6x)

Questions Eliciting Thinking What are like terms? What approach did you take to combine the like terms in this problem?
Do you see a way to rewrite this expression so that there are fewer terms? 
Instructional Implications Review the Distributive Property and explain how it can be used to combine variable terms such as 5x and 2x [e.g., 5x + 2x = (5 + 2)x = 3x]. Eventually, introduce the concept of like terms and provide numerous examples and nonexamples of like terms. Demonstrate that an expression such as 2x + 4 cannot be rewritten as 6x by substituting a value for x in each expression and showing that the resulting values are not equal. Challenge the student to find a sum that is equivalent to 6x.
Provide additional opportunities to rewrite expressions using the Commutative, Associative, and Distributive Properties and to combine like terms.
Consider implementing the MFAS tasks associated with standards 6.EE.1.3 and 6.EE.1.4. 
Almost There 
Misconception/Error The student makes errors when calculating with rational coefficients and constants. 
Examples of Student Work at this Level The student makes errors when working with signed numbers. For example, the student rewrites:
 6(12 â€“ x) as â€“72 â€“ 6x.
 (â€“2) + 72 as 70 or â€“ 70.Â
The student makes errors when working with fractions (e.g., the student multiplies by 8, getting a product of ).

Questions Eliciting Thinking Can you show me how you distributed 6 to (12 â€“ x)?
Can you show me how you multiply a whole number by a fraction? 
Instructional Implications Review operations with integers and rational numbers, as needed. Provide practice with operations on rational numbers by routinely including rational numbers in a variety of contexts and mathematical settings. Provide practice problems involving distribution of negative values. Begin with distributing integers [e.g., â€“3(â€“2x+8)] then transition to expressions involving fractions. Ask the student to clearly illustrate application of the Distributive Property [e.g., by writing ] before simplifying. 
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 correctly distributes and combines like terms, producing the answer 12xÂ â€“ 74. The student shows all steps of his or her work.

Questions Eliciting Thinking How could you use this expression in the context of this problem? 
Instructional Implications Provide additional practice problems in which the student must combine given expressions [e.g., A regular pentagon has a side length of . A regular octagon has a side length of 14 +Â â€“0.75x. What is the sum of their perimeters?]
Consider implementing other MFAS tasks for the 7.EE.1.1 standard. 