Getting Started 
Misconception/Error The student cannot correctly find the quotient using any strategy. 
Examples of Student Work at this Level The student attempts a strategy other than one of the suggested strategies and is unsuccessful. For example, the student:
 Divides 75 by three using the standard algorithm for division to determine an answer of 25 days.
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 Subtracts 0.75 from three and determines the answer to be 2.25 days.
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 Multiplies 75 by three and determines the answer to be 225 days.
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Questions Eliciting Thinking What does the three represent in this problem? What does the 0.75 represent? Suppose Mason runs one mile each day. How many days would it take him to run three miles?
What mathematical operation should you use to determine the answer to this problem?
How big is 0.75? Is your answer reasonable? 
Instructional Implications Provide additional instruction on decimal numbers and place value. Model decimal numbers using manipulatives, concrete models, 10 x 10 grids, and drawings. Then model how to divide a decimal by a whole number and a whole number by a decimal using these models.
Guide the student to understand that the problem can be solved by division, that is, the number of days that it takes Mason to run 3 miles can be found by dividing 3 miles by the distance he can run each day, 0.75 miles. Encourage the student to use a model or strategy based on place value, properties of operations, or the relationship between multiplication and division to solve the problem. For example, have the student use 10 x 10 grids to represent the number three. Then have the student divide the representation into parts that each represent 0.75. Emphasize that the number of parts representing 0.75 models the number of days in the problem.
Model how to reinterpret the problem in terms of multiplication (i.e., number of days x 0.75 = 3). Then encourage the student to use multiplication to solve the problem. This can be accomplished by first suggesting that the student multiply 0.75 by two. Then ask the student to compare the result to 3 miles and determine what to do next to solve the problem.
Expose the student to a variety of strategies through both direct instruction and by allowing other students who have successfully used these strategies to present their work.
Consider using the MFAS Task Decimals In Expanded Form (5.NBT.1.3). 
Making Progress 
Misconception/Error The student uses the standard algorithm or unsuccessfully uses one of the suggested strategies. 
Examples of Student Work at this Level The student:
 Successfully uses a strategy other than one based on place value, properties of operations, or the relationship between multiplication and division such as the standard algorithm for division.
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 Attempts a repeated addition strategy but makes addition errors.
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Questions Eliciting Thinking Can you think of another way to divide these numbers that is based on place value?
Can you draw a model to show how place value can be used to divide?
Can you use a 10 x 10 grid to help you divide these numbers? How about an array or area model? 
Instructional Implications Encourage the student to use a model or strategy based on place value, properties of operations, or the relationship between multiplication and division to solve the problem. For example, have the student use 10 x 10 grids to represent the number three. Then have the student divide the representation into parts that each represent 0.75. Emphasize that the number of parts representing 0.75 models the number of days in the problem.
Model how to reinterpret the problem in terms of multiplication (i.e. number of days x 0.75 = 3). Then encourage the student to use multiplication to solve the problem. This can be accomplished by first suggesting that the student multiply 0.75 by two. Then ask the student to compare the result to 3 miles and determine what to do next to solve the problem.
Work with the student on becoming proficient with a strategy he or she prefers. Then introduce other strategies and provide opportunities for the student to use them. 
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 solves the problem using a drawing or model, a strategy based on place value or properties of operations, or the relationship between multiplication and division getting an answer of 4 days. The student is able to explain the strategy used.
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Questions Eliciting Thinking Can you divide these numbers using another division strategy?
Can you draw an area model for division to show your understanding? 
Instructional Implications Encourage the student to use the standard algorithm for division of decimals.
Provide opportunities to add, subtract, multiply, and divide decimals written to the thousandths place. Provide opportunities to divide decimals by decimals. 