Getting Started 
Misconception/Error The student is unable to determine the correct operations to use to complete the problems. 
Examples of Student Work at this Level The student:
 Uses division rather than multiplication to solve the first problem.
 Uses multiplication rather than division to solve the second problem.
 Does not perform any operation other than converting the numbers given in scientific notation to standard notation.

Questions Eliciting Thinking What is each problem asking you to do?
How did you decide which operation to use?
What words in this problem suggested division to you?
What words in this problem suggested multiplication to you? 
Instructional Implications Review with the student language that suggests multiplication and language that suggests division. Provide the student with additional problems and ask him or her to determine the appropriate operation to solve each problem.
If necessary, provide additional instruction on converting between standard and scientific notation and on performing operations with numbers expressed in scientific notation. 
Moving Forward 
Misconception/Error The student can only complete the calculations with numbers in standard notation. 
Examples of Student Work at this Level The student converts all numbers to standard notation to complete calculations. The student may or may not make calculation errors. 
Questions Eliciting Thinking Why did you convert these numbers to standard notation?
Can you convert 100,000 to scientific notation? Could you have completed the multiplication with the numbers in scientific notation?
Can you convert 1000 to scientific notation? Could you have completed the division with the numbers in scientific notation? 
Instructional Implications Provide instruction on converting between standard and scientific notation. Include converting numbers of the form which are not in scientific notation (e.g., ) to scientific notation.
Review the Product Property of Exponents and the Quotient Property of Exponents. Using a few examples, demonstrate the ease and efficiency of calculating with numbers in scientific notation. Ask the student to convert 100,000 (in the first problem) and 1000 (in the second problem) to scientific notation and to redo his or her calculations leaving the final answersÂ in scientific notation.
Provide a set of practice problems in which the student must perform operations with numbers expressed in scientific notation. Include problems where both standard and scientific notation are used. 
Almost There 
Misconception/Error The student makes errors working with numbers expressed in scientific notation. 
Examples of Student Work at this Level The student converts numbers to scientific notation to perform the necessary operation. However, the student:
 Makes a conversion error. For example, the student writes 100,000 as .
 Models each problem using scientific notation and the correct operation but is unable to complete one or both.
 Makes an error in completing a calculation with numbers written in scientific notation. For example, the student writesÂ Â orÂ .

Questions Eliciting Thinking How did you convert this number to scientific notation?
What does the Product Property of Exponents say?
What does the Quotient Property of Exponents say? 
Instructional Implications Provide feedback to the student concerning his or her specific error. As needed, review the Product Property of Exponents and the Quotient Property of Exponents. Ask the student to correct his or her error. Then provide additional problems in which the student must perform operations with numbers expressed in scientific notation. Include problems in which the results are not in scientific notation [e.g., ] and must be converted to scientific notation. 
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 completes operations with all numbers in scientific notation:
 (3.8 x ) x () = 3.8 x cm
 Â = 3.98 x

Questions Eliciting Thinking What kinds of numbers are best suited to scientific notation?
How would you solve an addition or subtraction problem if the numbers were only given in scientific notation? How does that relate to adding and subtracting numbers in decimal format? 
Instructional Implications Have the student add and subtract numbers in scientific notation by using MFAS task Sums and Differences in Scientific Notation.
Provide the student with problems, such as (5.8 x ) x (6.2 x ). Ask the student to find the product (e.g., 35.96 x ) and estimate it using scientific notation (e.g., as 3.6 x ). 