Getting Started 
Misconception/Error The student does not have an effective strategy for multiplying multidigit numbers. 
Examples of Student Work at this Level The student:
 Lines up the numbers vertically with regard to place value and then only multiplies digits with the same place value.
 Computes only some of the partial products.

Questions Eliciting Thinking Can you show me how you multiplied the numbers?
What if there were no decimal points in these numbers? Would you multiply them differently?
Can you show me how you would multiply 36 by 42? 
Instructional Implications Show the student the correct answer to each problem and explore with the student why his or her strategy failed.
Provide the student with focused instruction on the use of the standard algorithm for multiplication of multidigit numbers. Discuss how each partial product is determined, and guide the student to develop a strategy for determining the number of partial products needed to complete the multiplication. Remind the student of the actual meaning of the digits that he or she is multiplying and to think about the actual value of the product (e.g., when a two in the tens place is multiplied by a three in the hundreds place, one is actually multiplying 20 by 300, so the product is 6000). Encourage the student to use graph paper to better organize his or her work.
Encourage the student to estimate the product before applying the multiplication algorithm. After multiplying, ask the student to evaluate the reasonableness of the product by comparing it to the estimate. 
Moving Forward 
Misconception/Error The student has an effective strategy for multiplying multidigit numbers but makes a systematic error with regard to one aspect of the process. 
Examples of Student Work at this Level The student rewrites the problem in a vertical format, rightjustifying the digits and attempts to use the standard algorithm for multiplying multidigitÂ decimal numbers but:Â
 Consistently makes multiplication or addition errors.
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 Computes a partial product incorrectly.
 Does not align digits correctly when computing partial products.

Questions Eliciting Thinking Did you estimate the product before you multiplied?
You made a number of computational errors. Can you check your work to find them?
How did you determine the partial products? What did you actually multiply to find each one?
How should the partial products be written? Does it matter how the digits are aligned? 
Instructional Implications Assist the student in locating and correcting computationalÂ errors. Â Have the student partner with another student to compare answers and reconcile any differences.
Discuss how the partial products are determined and calculated. Use the Commutative Property to demonstrate two different but equivalent approaches to multiplying the two numbers. Guide the student to observe that although the partial products are different in the two multiplications, their sums are the same.
Discuss with the student the actual values of the digits in the partial products and assist the student in lining up partial products according to the place value of the digits. Encourage the student to use graph paper to better organize his or her work. Provide the student with additional opportunities to multiply multidigit decimal numbers and provide feedback.
Encourage the student to estimate the product before usingÂ the multiplication algorithm. After multiplying, ask the student to evaluate the reasonableness of the product by comparing it to the estimate. 
Almost There 
Misconception/Error The student has an effective strategy for multiplying multidigit decimal numbers but makes a calculation or other minor error. 
Examples of Student Work at this Level The student uses the standard multiplication algorithm correctly but:
 Makes a computational error in one of the problems.
 Locates the decimal point incorrectly in one of the products. Upon questioning, the student is able to selfcorrect.

Questions Eliciting Thinking Can you check your work? I think you may have a small error.
Did you estimate the product before you multiplied? Is your answer consistent with your estimate? Where should the decimal point be located? 
Instructional Implications Assist the student in locating and correcting any errors. Â Provide the student with additional opportunities to multiply multidigit decimal numbers. Have the student partner with another Almost There student to compare answers and reconcile any differences.
Have the student complete problems in which the factors have been multiplied, but the student must locate the decimal point in the final answer (e. g., given 24.48 x 9.026 = 22095648, the student places the decimal point in the product). 
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 both problems within 5  7 minutes, getting answers of 54.05 and 53.32114.

Questions Eliciting Thinking Can you explain how you knew where to place the decimal point in your answer?
Does it matter which number is placed on top and which is placed on the bottom when setting up a multiplication problem like this? 
Instructional Implications Encourage the student to consider and explain why his or her strategy works. AskÂ the student to explain the relationship between previously used strategies for multiplying multidigit numbers and the standard algorithm.
Allow the student to serve as a peer helper, assisting Getting Started and Moving Forward students with strategy issues or place value challenges. 