Getting Started 
Misconception/Error The student can explain rates using rate language, but cannot reason about unit rates. 
Examples of Student Work at this Level The student explains the first rate by saying, â€śTwo pizzas for every one person,â€ť or â€śEach person gets two pizzas.â€ť The student explains the second rate by saying, â€śOne pizza for every two people,â€ť or â€śEvery two people get one pizza.â€ť However, the student cannot identify a unit rate. The student says:
 Both are unit rates because they both indicate a relationship between the number of pizzas and the number of people. The student makes no reference to a unit rate as a comparison of some quantity to one unit of another quantity.
 Both are unit rates because they have the same numbers â€śjust flipped.â€ť
 One pizza for two persons is a unit rate because â€śit is telling how many pizzas for two students.â€ť
 Both rates are unit rates because they both say â€śper.â€ť
 Neither are unit rates, â€śthey are just considered a rate.â€ť
 Neither are unit rates because the question above referenced them both as rates.

Questions Eliciting Thinking With which rate would you get more pizza?
How much pizza does each person get using the second rate?
What is a rate? Can you give me an example?
What is a unit rate? Can you give me an example? 
Instructional Implications Provide direct instruction on unit rates. Compare and contrast ratios and unit rates. Describe ratios as comparisons of two quantities and point out that the quantities may or may not contain the same units of measure. Describe unit rates as comparisons of two quantities and point out that the second part of the ratio must be â€śone unit.â€ť Make explicit the difference between a ratio (rate) and a unit rate. Emphasize the meaning of unit rates in context and the use of unit rate language (e.g., â€śfor each one,â€ť â€śper oneâ€ť) when interpreting or describing their meaning. Give the student additional opportunities to write and describe unit rates in context. Consider using MFAS task Writing Unit Rates (6.RP.1.2). 
Moving Forward 
Misconception/Error The student can explain rates using rate language, but identifies the unit rate as a fraction in simplest form. 
Examples of Student Work at this Level The student explains the first rate by saying, â€śTwo pizzas for every one person,â€ť or â€śEach person gets two pizzas.â€ť The student explains the second rate by saying, â€śOne pizza for every two people,â€ť or â€śEvery two people get one pizza.â€ť
The student identifies the second rate Â as a unit rate because â€śit is a fraction in simplest form.â€ť
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Questions Eliciting Thinking With which rate would you get more pizza?
How much pizza does each person get using the second rate?
According to the first rate (second rate), how many pizzas will the teacher order for 10 people?
What is a unit rate? What do you mean by simplest form?
Is Â considered a unit rate? Why or why not? 
Instructional Implications Provide direct instruction on unit rates. Make explicit the difference between â€ślowest termsâ€ť (or â€śsimplest formâ€ť) and a term with â€śone unit.â€ť Describe a unit rate as a comparison of two quantities and point out that the second part of the comparison must be â€śone unit.â€ť Compare and contrast two rates which can be simplified (e.g., ). Explain how both examples can be rewritten in lowest terms, but after rewriting in lowest terms, only one will be in the form of a unit rate. Then, model how to find unit rates for rates that do not easily reduce to Â (e.g., ). Provide additional opportunities for the student to practice identifying and writing unit rates. Consider using MFAS task Identifying Unit Rates (6.RP.1.2). 
Almost There 
Misconception/Error The student can explain rates using rate language, but identifies the unit rate as a rate involving a unit of one in either the numerator or denominator. 
Examples of Student Work at this Level The student explains the first rate by saying, â€śTwo pizzas for every one person,â€ť or â€śEach person gets two pizzas.â€ť The student explains the second rate by saying, â€śOne pizza for every two people,â€ť or â€śEvery two people get one pizza.â€ť
The student may elaborate by saying, â€śFor example, if you had 20 people, you would need 40 pizzas.â€ť When referring to the second rate, the student says, â€śFor example, if you had 20 people, you would need 10 pizzas.â€ť
The student identifies both rates as unit rates because â€śthey are both comparing something to one.â€ť
The student identifies both rates as unit rates because â€śthere is one unitâ€ť in each of them. For example, Â has a one in the denominator; has a one in the numerator.
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Questions Eliciting Thinking What is a unit rate?
Can the number one appear in either part of a ratio written as a unit rate?
Should the unit of one be in the numerator, denominator, or does it matter? 
Instructional Implications Clarify the definition of a unit rate. Describe unit rates as comparisons of two quantities and emphasize that the second part of the ratio must be the â€śoneâ€ť regardless of the unit type. Show the student some examples such as . Discuss the meaning of the examples and model the use of unit rate language when describing their meanings in context. Provide additional opportunities for the student to demonstrate his or her ability to identify unit rates in a variety of realworld contexts.
Compare and contrast unit rates (a:1) and rates of the form 1:a. Make explicit the significance of the â€śoneâ€ť unit as the second part of the comparison.
Using a double number line or tape diagram, illustrate how to find two unit rates for a given rate, one of the form a:1 and the other of the form :1 (e.g., if there is one pizza for every three people, there is Â pizza per person). Provide guided practice for the student. Pair the student with a Got It partner to compare answers and reconcile differences. 
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 explains the first rate by saying, â€śTwo pizzas for every one person,â€ť or â€śEach person gets two pizzas.â€ť The student explains the second rate by saying, â€śOne pizza for every two people,â€ť or â€śEvery two people get one pizza.â€ť
The student may elaborate by saying, â€śFor example, if you had 20 people, you would need 40 pizzas.â€ť When referring to the second rate, the student says, â€śFor example, if you had 20 people, you would need 10 pizzas.â€ť
The student identifies the first rate as the unit rate because it has a comparison of some quantity to â€śone unitâ€ť of another quantity. Furthermore, the student recognizes the second rate is not a unit rate because the comparison of â€śone unitâ€ť cannot be the first part (or numerator) of the comparison.
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Questions Eliciting Thinking With which rate would you get more pizza?
According to the second rate, how much pizza would each person get?
According to the first rate (second rate), how many pizzas are needed for 10 people?
Both rates have a â€śunit of oneâ€ť in them, does that make them both unit rates? Why or why not?
Can you determine the unit rate of the second rate ? 
Instructional Implications Have the student determine two unit rates for a given rate. Have the student then use the two unit rates to solve a problem, such as â€śGiven the rate of $25.00 in two hours, write two different equivalent unit rates. Determine how much money can be earned in six hours. Determine how many hours it would take to earn $112.50.â€ť Consider implementing MFAS task Book Rates (6.RP.1.2), if not done previously.
Pair the student with an Almost There partner. Have the pair work on additional practice problems, discuss their processes and compare their answers. 