Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55437
Comparing Unit Rates
Students are asked to compute unit rates from values that include fractions.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rate, unit rate
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ComparingUnitRates_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Comparing Unit Rates worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to reason about proportionally related quantities.
Examples of Student Work at this Level
The student multiplies 60 gallons by
hour and writes
or multiplies 75 gallons by
hour and writes
and can offer no rationale for doing so.
page 1 of 4 The student determines the fountain pumps 60 gallons in 12 minutes, and then multiplies 60 by 12 getting 720 gallons per hour.
The student determines the fountain pumps 75 gallons in 15 minutes, and then multiplies 75 by 15 getting 1,125 gallons per hour.
Questions Eliciting Thinking
What is a ratio or rate?
How is a unit rate different from a rate?
Why did you multiply by
hour? What would the number that you got mean?
How did you determine 60 gallons of water per 12 minutes? What does this ratio mean? How might it help you find the unit rate?
Instructional Implications
Review the concept of ratio and encourage the student to use a ratio table to write and explore patterns in equivalent ratios. Guide the student to use multiplication
(rather than repeated addition) to generate equivalent ratios. Encourage the student to use ratio language (e.g., “for every,” “for each,” “for each one,” “per”) when
describing and interpreting ratios and rates.
Provide direct instruction on unit rates. Describe unit rates as a comparison of some quantity to one unit of another quantity. Emphasize that the unit of one has to be the
second part of the comparison. Encourage the student to use tables, tape diagrams, and double number lines to model and explore equivalent ratios and rates.
Consider implementing CPALMS Lesson Plan Let’s Rate It! (ID#: 46379).
Consider implementing MFAS task Explaining Rates (6.RP.1.2) and MFAS task Unit Rate Length (7.RP.1.1) to further assess student.
Moving Forward
Misconception/Error
The student attempts to write a proportion to find the unit rate but does so incorrectly.
Examples of Student Work at this Level
The student determines that
of an hour equals 12 minutes, and then sets up a proportion using minutes and hours (e.g.,
=
).
Questions Eliciting Thinking
What is a unit rate? What kind of quantities are compared in unit rates?
Why did you change
hour to 12 minutes?
Why did you use a proportion? Is your answer per minute or per hour? Does your answer seem reasonable?
Can you think of another way to calculate the unit rate?
Instructional Implications
Encourage the student to use tables to generate equivalent rates (by multiplying or dividing) and to calculate unit rates. Guide the student to be mindful of the units of
measure of associated quantities.
Describe unit rates as a comparison of some quantity to one unit of another quantity, and model the use of proportions to determine unit rates. Emphasize the placement
of the unit of one when setting up a proportion. Next, compare and contrast the use of multiplication and division when determining unit rates to the use of proportions.
Provide opportunities for the student to explore the similarities and differences between the two methods.
Consider implementing the NCTM Illuminations Lesson titled Measuring Up (Lesson 3: What’s Your Rate?).
Almost There
Misconception/Error
The student makes a computational error in some aspect of his or her work.
Examples of Student Work at this Level
The student uses a ratio table to incrementally convert 75 gallons per 15 minutes to n gallons per hour, but makes an error in calculating at one step of the process.
page 2 of 4 The student converts
to 0.5.
Note: The student recognizes his or her own mistake when questioned.
Questions Eliciting Thinking
I think you made a small error. Can you find it in your work?
Why did you change fractions to decimals? What is one-fifth as a decimal?
How did you determine
of an hour is 12 minutes?
Instructional Implications
Provide the student with additional problems involving associated quantities described with fractions. Have the student work with a partner to compare answers and
reconcile any differences. Encourage the partners to compare their strategies for calculating unit rates.
Consider using MFAS task Unit Rate Area (7.RP.1.1).
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 300 gallons per hour for both, and says the fountains pump “at the same rate which is 300 gallons every hour.”
The student explains, “Sixty gallons is for just part of the hour, so you need all five parts to make one hour.”
The student explains, “Seventy­five gallons is just for The student divides 60 gallons by
of the hour, so you need all four parts to make the whole hour.”
of an hour to determine the correct unit rate of 300 gallons per hour.
Questions Eliciting Thinking
Can you write the unit rate in hours per gallon?
How much water would flow in
hours?
How long would it take for 450 gallons of water to recirculate?
Instructional Implications
Have the student graph the data and help the student discover the unit rate using the graph. Introduce the concept of constant of proportionality and relate it to the
slope of the graphed line.
Transition the student to modeling proportional relationships with equations of the form y = cx where c is the constant of proportionality. Guide the student to see the
relationship between a unit rate and the constant of proportionality.
Challenge the student to determine a unit rate in a given problem in context, and then apply the unit rate in order to solve another problem in the same context (e.g., ask
the student to convert
miles in
hours to a unit rate, and then determine how many hours it would take to travel 11 miles).
page 3 of 4 ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Comparing Unit Rates worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.7.RP.1.1:
Description
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured
in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the
complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
page 4 of 4