Getting Started 
Misconception/Error The student is unable to evaluate expressions for given values of their variables. 
Examples of Student Work at this Level The student does not evaluate the expression for the given value of the variable but instead:
 Draws a grid and counts spaces to find the area, rather than using the formula.
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 Changes all operations to multiplication after substituting into the formula (e.g., writing 0.5 Â· 8 Â· 6 Â· ).
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 Rewrites the expression as a sequence of numbers without regard to the operations symbols (e.g., A = ).
 Rearranges the expression after substituting into the formula (e.g., writing â€śF =28 + 32 Â· â€ť).
 Does not evaluate the expression but attempts to perform operations with the numbers in the expression (e.g., changing Â to 1.8, then adding 1.8 to 32 to get 33.8 or adding 28 and 32 and writing an answer of 60).
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Questions Eliciting Thinking What do the variables in the expression mean? What should you do with the values assigned to each variable?
What operation is understood when no operation symbol is shown, as in bh? What should you do with the numbers that you substitute for each of those variables?
What does multiplying by mean? Is that the same as dividing by two or multiplying by two? 
Instructional Implications Explain the purpose of each formula and the meaning of the variables. Assist the student in understanding the structure of each formula and the operations that are represented.
Provide the student with instruction on evaluating expressions. Ask the student first to carefully rewrite the expression with the given values substituted for the variables. Be sure the student understands the operations used in the formulas and includes these operations when writing numerical expressions. Then guide the student to use the order of operations rules to evaluate the expression. Ask the student to initially show work in a stepbystep manner so the result of each computation can be determined.
Provide additional opportunities to evaluate formulas and expressions for given values of the variables. 
Moving Forward 
Misconception/Error The student makes errors in the use of the order of operations. 
Examples of Student Work at this Level The student performs order of operations incorrectly:

Questions Eliciting Thinking What are the rules for the order of operations? According to these rules, how do you determine whether you should multiply or add first?
When are you supposed to do division before multiplication? What operations should be done from left to right?
What does 3x mean? What do we call the three in an expression like this? 
Instructional Implications Review the order of operations rules with the student, especially with regard to the studentâ€™s specific error. Help the student understand what it means to complete multiplications and divisions from left to right. The student may interpret this to mean to complete all operations from left to right, so model for the student the proper application of this rule. Encourage the student to show work in a stepbystep manner so the result of each computation can be determined.
Provide additional opportunities to evaluate formulas and expressions for given values of the variables. 
Almost There 
Misconception/Error The student makes computational errors or provides insufficient work to justify answers. 
Examples of Student Work at this Level The student:
 Converts from a fraction to decimal incorrectly.
 Calculates incorrectly with fractions or decimals.
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 Does not include appropriate units with answers (uses no units or wrong units).
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 Evaluates exponents incorrectly, saying =32.
 Makes minor calculation errors.
 Carelessly writesÂ as 24.
 Does not show enough work to support an answer.Â

Questions Eliciting Thinking What units are used in the problem? What units are appropriate for the answer?
Can you check your work or rework the problem to see if you get the same answer?
How did you determine your answers? Can you explain in more detail? Can you explain which properties you used to justify your answers? 
Instructional Implications Provide feedback to the student regarding any errors made and allow the student to revise his or her work. Remind the student of the importance of including the correct unit of measure with numerical answers when appropriate. If needed, review the difference between linear, square, and cubic units. Review evaluating exponential expressions, as needed. Show the student the difference between similarly written expressions such as 3 Â· 4,Â , and .
Review fraction and decimal operations as needed. Emphasize the difference between multiplying by two and multiplying by (and that multiplying by is the same as dividing by two). Emphasize the importance of using order of operations, even with rational numbers. 
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:
 Converts 28Â° C to 82.4Â° F (or 82),Â
 Evaluates the expression at xÂ = 4 getting a value of 268, andÂ
 Uses the area formula to calculate an area of 124 .
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Questions Eliciting Thinking How could you determine what Celsius temperature is equivalent to freezing (32Â°F) in #1?
What symbol(s) could you add to the expression so you would have to do the final multiplication before the division in #2?
If each of the lengths in the figure doubled, how would the area change in #3? 
Instructional Implications Provide the student with additional practice evaluating expressions with rational number values. 