Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 68422
Unit Rate Length
Students are asked to write ratios and unit rates from fractional values.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, ratio, rate, unit rate, fraction
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_UnitRateLength_Worksheet.pdf
MFAS_UnitRateLength_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 Unit Rate Length worksheet.
1. The teacher asks follow-up questions, as needed.
TASK RUBRIC
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.
page 1 of 4 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., “for each,” “for every,” and “per”) 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 It’s Carnival Time! (ID
47394), and then assessing the student’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.
Writes a ratio comparing the quotient to the product of the given values (or the product to 1).
page 2 of 4 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., “for every one,” “for each one,” “per one”) 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.
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.
page 3 of 4 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.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Unit Rate Length 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