Getting Started 
Misconception/Error The student is unable to describe an algebraic expression using mathematical terms. 
Examples of Student Work at this Level The student is unable to correctly use terms such as sum, difference, product, and quotient to describe expressions and their parts. When describing the expressions in #3, the student:
 Confuses operation words (e.g., says “product” instead of “quotient”).
 Avoids the use of mathematical terms such as sum, difference, product, and quotient by describing:
 (y  3)20 as “y minus three times twenty.”
 5 + as “five plus x divided by nine.”
 Uses imprecise language such as “5 sum x over 9.”
 Lists operations found in the expression.
 Lists the steps needed to evaluate the expression.
 Gives a definition of each of the listed operation words.
 Does not understand what it means to describe an expression and instead:
 Evaluates it for some value of the variable.
 Rewrites it as an equation, trying to solve for the variable, saying y = 60.
 Provides imprecise or ambiguous descriptions such as:
 The difference of y and 3 times 20.
 The quotient of x and 9 and the sum of the quotient and 5.

Questions Eliciting Thinking What were you asked to do in this exercise?
Can you use the terms sum, difference, product, and quotient to describe these expressions?
What is a math word for “over?” What operation is implied by this word? 
Instructional Implications Review mathematical terminology related to operations and expressions such as sum, difference, product, quotient, term, coefficient, constant, and factor. Model the correct use of mathematical terminology and use it frequently. Give the student a set of expressions and ask the student to identify parts of the expressions using these terms (e.g., given 3 + x ask the student to identify the terms, coefficients, and factors). Include expressions such as 3(x – 8) and guide the student to view the expression (x – 8) as a factor. When possible, provide context to reinforce the idea of an expression as a single entity. For example, the expression 3(x – 8) might describe the area of a rectangle whose length is given by (x – 8) and whose width is 3. Ask the student to describe expressions such as 2 + 5x using terms such as sum, difference, product, and quotient. Encourage the student to use mathematical terminology and to be precise in its use. 
Moving Forward 
Misconception/Error The student is unable to view a part of an expression as a single entity. 
Examples of Student Work at this Level The student understands that a and 8 are not factors but does not view (8 – a) as a single entity so is unable to recognize it as a factor. The student says:
 8 and a are being subtracted.
 5 is the only factor because it is the only thing being multiplied.
 a is a variable and factors are numbers.

Questions Eliciting Thinking What does a factor mean? What is being multiplied in this problem?
Can a variable be a factor? Can an entire expression be a factor? 
Instructional Implications Review the meaning of the term factor. Provide expressions such as 3(x – 8) or (5n + 2)(n – 4) and guide the student to view each expression as containing two factors. Make clear that factors can be expressions as well as numbers and variables. When possible, provide context to reinforce the idea of an expression as a single entity. For example, the expression 3(x – 8) might describe the area of a rectangle whose length is given by (x – 8) and whose width is 3. Give the student a list of expressions and ask the student to identify those that are written as a product of factors as opposed to those written as a sum. For example, identify 2x(x – 1) as a product of factors while 3x + 2 is a sum (although the first term contains two factors). Also, have the student clearly identify the factors [e.g., as 2, x, and (x – 1)].
Review terminology related to exponential expressions such as base and power. Show the student expressions such as or and ask the student to identify the base and the power in each case. Again, reinforce the idea that an expression, rather than just a single number or variable, can serve as the base. 
Almost There 
Misconception/Error The student does not have a complete understanding of the concept of a coefficient. 
Examples of Student Work at this Level The student:
 Agrees that the only coefficient in the expression 15 – x – 8 is 15.
 Confuses coefficients and factors and says the coefficients are 15 and or 15.
 Confuses coefficients and constants and says coefficients are numbers that don’t get changed, so it would be 8 (i.e., a constant).
 Confuses coefficients and variables and says coefficients are letters standing for numbers, so it would be “x” (i.e., a variable).
 Says if you don’t see a number in front of the variable, it has a coefficient of positive one.
 Says you can’t tell what factors or coefficients are because you don’t know what the value of the variable is.
 Is unclear in explaining 15 and 1 are coefficients because “1 is also a variable.”

Questions Eliciting Thinking What is the meaning of the word coefficient?
How is a coefficient different from a factor (or constant or variable)?
What is the coefficient of x? What is the coefficient of –x? 
Instructional Implications Review the meaning of variable, coefficient, constant, term and factor, as needed, depending on the student’s errors. Provide feedback to the student regarding specific misconceptions and allow the student to revise his or her work. The worksheet for this assessment is editable so can be rewritten using different numbers and variables to give the student additional practice describing expressions and identifying parts of 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:
 Explains that the factors of 5 · (8  a) are 5 and (8  a) but not the terms 8 and a.
 Identifies the coefficients of 15  x  8 as 15 and 1.
 Describes (y  3)20 in words as “the product of twenty and the difference between y and three” and describes 5 + as “the sum of five and the quotient of x and 9.”

Questions Eliciting Thinking Can you write an expression that uses three factors, one a sum, one a difference, and one a constant?
What is the difference between an expression with three terms and one with three factors? 
Instructional Implications Introduce the student to the concept of expanded versus factored form of an expression and ask the student to convert between the two. Explain that an expression that is written as a product of factors such as 4(x + 5) is in factored form. Using the Distributive Property, the expression can be rewritten as 4x + 20 which is called its expanded form. Provide expressions in each form and ask the student to identify the given form and then rewrite the expression in the alternate form.
Have the student practice finding equivalent expressions by using various MFAS tasks from 6.EE.1.3 and 6.EE.1.4. The student can also practice evaluating expressions using MFAS task Substitution Resolution (6.EE.1.2). 