Getting Started 
Misconception/Error The student evaluates the expression without regard to the order of operations rules. 
Examples of Student Work at this Level The student:
 Completes operations from left to right.
 Completes operations from right to left and makes numerous computational errors.

Questions Eliciting Thinking How did you decide what to do first in this problem?
Are you familiar with the order of operations rules? Would they apply to this problem?
Can you show me how you completed the division?
Is 4 Ă· 1 the same as 1 Ă· 4? 
Instructional Implications Provide direct instruction on order of operations. Begin with simple expressions that involve only whole numbers and two operations. Gradually transition to more complex expressions involving multiple operations. Then introduce expressions containing a variety of rational numbers written as both decimals and fractions.
Review adding, subtracting, multiplying, and dividing signed numbers. Be sure the student understands the Inverse Property of Addition.
Provide additional instruction on adding, subtracting, multiplying, and dividing rational numbers. Begin with expressions that contain positive fractions and decimals and provide focused instruction on any operation with which the student struggles. Then ask the student to evaluate expressions that include both positive and negative decimals and fractions. 
Moving Forward 
Misconception/Error The student makes computational errors in working with rational numbers. 
Examples of Student Work at this Level The student:
 Makes sign errors when multiplying and dividing rational numbers.
 Is unable to correctly add signed numbers.
 Is unable to correctly divide decimal numbers.

Questions Eliciting Thinking How do you multiply signed numbers? How do you know if the result is positive or negative?
How do you add signed numbers? How do you know if the result is positive or negative?
How do you divide decimal numbers? 
Instructional Implications Review adding, subtracting, multiplying, and dividing signed numbers. Be sure the student understands the Inverse Property of Addition.
Provide additional instruction on adding, subtracting, multiplying, and dividing rational numbers. Begin with expressions that contain positive fractions and decimals and provide focused instruction on any operation with which the student struggles. Then ask the student to evaluate expressions that include both positive and negative decimals and fractions. 
Almost There 
Misconception/Error The student makes errors in completing operations of equal priority. 
Examples of Student Work at this Level The student multiplies before dividing even though the division occurs first in the expression.

Questions Eliciting Thinking What do the order of operations rules say?
How are multiplication and division related in the order of operations?
How are addition and subtraction related in the order of operations? 
Instructional Implications Review the order of operations rules and allow the student to find and correct his or her error. Provide additional opportunities for the student to evaluate expressions that contain multiple instances of operations of equal priority. Provide feedback, as needed. 
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 applies the order of operations rules and makes no computational errors. The student writes:
= â€“10 â€“ 6 + 4 Ă· (0.5)(2) = â€“10 â€“ 6 + (8)(2) = â€“10 â€“ 6 + 16 = â€“16 + 16 = 0

Questions Eliciting Thinking What do the order of operations rules say? Will you always get an incorrect answer if you do not follow these rules?
What if an expression involves only addition? Can you use properties of operations to justify adding in an order that is different from the given one? 
Instructional Implications Provide additional opportunities to evaluate more complex expressions containing rational numbers. (E.g., challenge the student with expressions that involve complex fractions). Encourage the student to use properties of operations to simplify calculations, when possible.
Ask the student to solve realworld problems involving operations with rational numbers. 