Getting Started 
Misconception/Error The student is unable to explain how to use an area model to find the quotient. 
Examples of Student Work at this Level Despite prompting and support, the student cannot explain how to use an area model to find the quotient in a division problem. The student may notice that 16 times 100 is equal to 1600 but is unsure how this relates to using the area model to divide. The student may also notice the relationship between the divisor and the partial quotients but is still unable to explain how the area model is used to divide. 
Questions Eliciting Thinking Can you use an area (or array) model to find the product in a multiplication problem?
How is multiplication like division?
Can thinking about multiplication help you understand the area model for division? 
Instructional Implications Use an easier problem, such as 95Â 5, and provide directÂ instruction on how to use an area model to find the quotient in a division problem. Begin by drawing an open array to represent the dividend; the dimension of one side will be labeled with the divisor. Tell the student that when an area model is used to find the quotient in a division problem, one is trying to find the missing dimension. Show the student how to break up the dividend into numbers that are more easily divided by the divisor.
Consider using the MFAS task, "Multiplying Using an Array or Area Model"Â to assess the studentâ€™s understanding of using an area or array model to multiply multidigit numbers. 
Moving Forward 
Misconception/Error The student needs much prompting to explain the area model for division. 
Examples of Student Work at this Level The student needs prompting from the teacher to explain each step of the process of using an area model to find the quotient in a division problem. When asked to divide 4500 by 36 on his or her own, the student is unable to do so or makes many errors throughout the process. 
Questions Eliciting Thinking Why is 1,600 subtracted from 2016? What does that represent?
What about the 96? Where did that come from? 
Instructional Implications Guide the student through the process of finding the quotient in a division problem using an area model. Provide repeated practice. Begin with division problems that result in no remainders.
Encourage the student to think about how to break up the dividend into numbers that are more easily divided by the divisor. 
Almost There 
Misconception/Error The student makes an error when using the area model or needs prompting to correctly determine the quotient. 
Examples of Student Work at this Level The student explains how to use the area model to find the quotient in a division problem with little or no prompting. However, the student makes an error in calculation or needs minor prompting at some point during the process.
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Questions Eliciting Thinking Can you explain what you did?
Did you use the same strategy as in the example?
I think you may have made a mistake in this part of your work. Can you find your mistake? 
Instructional Implications Provide repeated practice using an area model to determine the quotient of two multidigit numbers. When necessary, review how to use an area or array model to find the product of multidigit numbers. Help the student observe the relationship between using an area model for division and using an area model for multiplication. 
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 explains how to use the area model to divide and then determines (using an area model) that 4500 Ă· 36 = 125.

Questions Eliciting Thinking How is this strategy like the standard algorithm?
What does the standard algorithm do differently? 
Instructional Implications Encourage the student to compare the area model toÂ the standard algorithm to examine the relationship between the two processes.
Guide the student to use a partial quotients strategy to find the quotient in division problems. An example is shown below.
