Getting Started 
Misconception/Error The student is unable to correctly write the described ratios. 
Examples of Student Work at this Level The student:
 Reverses the order of the numbers in the ratios.
 Uses the same ratio for red to blue and blue to red.
 Performs some operation with the given numbers.

Questions Eliciting Thinking What is a ratio? What two quantities are being compared in this problem? How are they being compared? Is the order important?
Do you know what a unit rate is? A unit rate compares a number to what? 
Instructional Implications Review the concept of ratio. Describe ratios as comparisons of two quantities and point out that the quantities may or may not contain the same units of measure. Emphasize the meaning of ratios in context and the use of ratio language (e.g., â€śfor each,â€ť â€śfor every,â€ť and â€śperâ€ť) when interpreting ratios or describing their meaning. Give the student additional opportunities to write and interpret ratios in the context of a variety of problems.
Then, provide instruction on finding unit rates with associated whole number quantities. Describe unit rates as a comparison of one quantity to one unit of another quantity. Compare and contrast ratios, rates, and unit rates. Model how to determine unit rates from given rates. Consider implementing CPALMS lesson plan Itâ€™s Carnival Time! (ID 47394), and then assessing the studentâ€™s progress with any of the following MFAS tasks: Writing Unit Rates (6.RP.1.2), Identifying Unit Rates (6.RP.1.2), Explaining Rates (6.RP.1.2), and/or Book Rates (6.RP.1.2).
Next, model finding unit rates with quantities that include fractions and mixed numbers. Review operations with fractions and mixed numbers as needed. Provide the student with additional opportunities to determine unit rates. Emphasize the meaning of the unit rate in context and model the use of ratio language when describing the meaning.
Consider implementing MFAS task Unit Rate Area (7.RP.1.1). 
Moving Forward 
Misconception/Error The student is unable to transform the ratios into unit rates. 
Examples of Student Work at this Level The student writes each ratio correctly but does not demonstrate an understanding of a unit rate or how to convert a ratio to a unit rate. The student:
 Writes a ratio of the given numbers in decimal form (correctly or incorrectly).
 Calculates the quotient and/or product of the given values (correctly or incorrectly), then:
 Uses that value as the unit rate.Â
 Writes a ratio comparing the quotient to the product of the given values (or the product to 1).
 Uses the numerator and denominator as parts of a ratio (e.g., 8:9 and 9:8).

Questions Eliciting Thinking What is the difference between a ratio and a unit rate? What two quantities are being compared in each? Does the order matter?
How did you get that value? What would that answer mean in the context of this problem? 
Instructional Implications Clarify the definition of unit rate as a comparison of one quantity to one unit of another quantity. Emphasize that the unit of one has to be the second part of the comparison. Reinforce the meaning of unit rates in context and encourage the student to use unit rate language (e.g., â€śfor every one,â€ť â€śfor each one,â€ť â€śper oneâ€ť) when describing the meaning of unit rates in context. Using a table, tape diagram, or double number line, model how to find the second unit rate. Be sure to point out that the two parts of the ratio cannot simply be reversed from a:1 to 1:a. Make it clear that rates and ratios can contain fractions.
Consider implementing MFAS task Explaining Rates (6.RP.1.2), Computing Unit Rates (7.RP.1.1), and Comparing Unit Rates (7.RP.1.1). 
Almost There 
Misconception/Error The student makes a minor error in calculating a unit rate. 
Examples of Student Work at this Level The student writes each ratio correctly and demonstrates an understanding of a unit rate. The student converts each ratio to a unit rate but:
 Reverses the order of each unit rate.
 Makes an error when multiplying or dividing in the process of converting a ratio to a unit rate.Â

Questions Eliciting Thinking Can you check your work to find the error? Does your answer make sense? 
Instructional Implications Help the student to identify and correct any mathematical errors. Review operations with fractions as needed. When the student is ready, consider implementing this task again but with different rational numbers. 
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 for the ratio of red to blue ribbon and calculates a unit rate of :1 or 1 to 1.
The student writes for the ratio of blue to red ribbon and calculates a unit rate of :1, showing work to support all answers.
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Questions Eliciting Thinking Why does the second part of the unit rate have to be one?
Can you interpret each unit rate? What do they tell you in the context of this problem? 
Instructional Implications Have the student use the unit rate to solve a problem. For example, ask the student to determine:
 How much red ribbon is needed if two feet of blue ribbon is used.
 How much of each ribbon is used if the total length of ribbon used is 12 feet.
Pair the student with a Moving Forward student. Have the student explain to the Moving Forward partner how to find the unit rates and what each means.
