Getting Started 
Misconception/Error The student does not write ratios correctly or consistently. 
Examples of Student Work at this Level The student:
 Does not write the ratio in the order asked in one or both problems.
 Writes a ratio as a whole number.
 Adds (or subtracts) the given values to find the ratio.

Questions Eliciting Thinking What does a ratio mean? How is that different from a quotient?
How are ratios written?
Does the order matter when writing a ratio? Is there more than one ratio associated with the given values?
Can you draw a picture to demonstrate the ratio described? 
Instructional Implications Remind the student that a ratio is a comparison of two quantities and is typically written in one of three forms a to b, a:b, or . Provide examples of a variety of ratios described in context and guide the student to write the ratios in an accepted form.
Explain how the description of a ratio is related to the order in which the numbers are written in the ratio. Encourage the student to pay close attention to the way ratios are described in problems. Provide the student with a variety of contexts in which ratios are described and ask the student to write ratios in multiple ways, varying the order of the quantities in the ratios. 
Moving Forward 
Misconception/Error The student does not understand the concept of a unit rate. 
Examples of Student Work at this Level The student cannot write the unit rate. Instead, the student writes:
 3 (dividing 12 by 4) or 48 (multiplying 12 and 4) or 8 (subtracting 4 from 12) or 16 (adding 12 and 4).
 explaining, “just take the 12:4 and make it into a fraction.”

Questions Eliciting Thinking What does “unit rate” mean? What does it mean to have one unit of something?
Does the order of the wording or order of the numbers matter? How is asking for “the price of one gallon of milk” different from asking for “the number of gallons of milk I can get for $1”?
How are fractions and ratios related? How are fractions and unit rates related? 
Instructional Implications Have the student review writing fractions in equivalent forms. Then, review the meaning of a unit rate and provide direct instruction on converting ratios to unit rates. Initially, provide examples that result in unit rates that contain only whole numbers (e.g., 12:3 as a unit rate is written 4:1). Transition the student to writing unit rates that contain fractions (e.g., 2:3 as a unit rate is written :1). Be sure the student understands that the order of the words in the description dictates the order in which the numbers in the unit rate are written.
Compare and contrast unit rates (a:1) and rates of the form 1:a. Make explicit the significance of the “one” unit as the second part of the comparison. Give the student additional opportunities to write ratios as unit rates in two different forms, one of the form a:1 and the other of the form :1. 
Making Progress 
Misconception/Error The student is unable to explain what a unit rate means within the context of the problem. 
Examples of Student Work at this Level The student:
 Explains “more fiction books were sold” or “Julia reads more books” without making a specific numerical comparison between the two related quantities.
 Explains the ratio rather than the unit rate.
 Reverses the number comparison.
 Uses ratio and rate vocabulary improperly or not at all (e.g., “they start with 12 books and give 1 to each of 4 kids”).

Questions Eliciting Thinking You said “more fiction books were sold” – compared to what?
What does the ratio mean, using the words of the problem? When you change the ratio to a rate out of one, what does the “one” represent? What does the other number represent? 
Instructional Implications Model explaining the meaning of rates in the context of problems. Use unit rate language (e.g., “for each one,” “for every one,” and “per one unit of”) when interpreting unit rates or describing their meaning. Provide additional opportunities for the student to write and interpret unit rates. 
Almost There 
Misconception/Error The student is unable to write a unit rate when it is a fraction compared to one. 
Examples of Student Work at this Level The student writes , 2, 2:1 or 1:2, rather than :1.
The student may have given an answer based on performing an operation with the given numbers:
 Three, subtracting three from six.
 Two, dividing the six by three.
 One, subtracting one from two to get “1 unit.”

Questions Eliciting Thinking How do you find a unit rate? Did you use that process this time?
What would you need to divide each number by in order for the second number in the ratio to become a one? 
Instructional Implications Provide instruction and additional opportunities to write unit rates that contain fractions (e.g., 2:3 as a unit rate is written :1). Show the student that an efficient strategy is to divide each number in the ratio by the second number in the ratio. Be sure the student understands that ratios sometimes contain rational numbers and writing rational numbers as fractions is often more efficient than writing them as decimals.
Consider using the MFAS tasks Writing Unit Rates, Identifying Unit Rates and Explaining Rates (6.RP.1.2) for additional practice. 
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 writes ratios of:
(1a) 12:4, 12 to 4, , or (2a) 3:6, 3 to 6, , or
The student writes rates of:
(1b) 3:1, 3 to 1, , or (2b) :1, to 1, , or
(1c) The student is able to use appropriate ratio and rate language to explain how to change the ratio to a unit rate (e.g., “I found the unit rate by dividing both numbers by the number of nonfiction books”).
The student is able to explain what the unit rate means within the context of the problem.
(1d) For every three fiction books sold by the bookstore, one nonfiction book is sold or for every nonfiction book sold, three fiction books are sold. (2c) For every of a book that Emily reads, Julia reads one whole book or Julia can read one book during the time it takes Emily to read half a book. 
Questions Eliciting Thinking Can a ratio have more than one unit rate associated with it?
How would the wording of the question change so that it results in writing the ratio in a different order? 
Instructional Implications Give the student experiences with ratios and unit rates with rational number components.
Give the student practice using ratios to find other related quantities (e.g., if there were 12 nonfiction books sold, how many fiction books were sold?) and to record the results in a table of equivalent ratios. 