Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55436
Computing Unit Rates
Students are asked to compute and interpret unit rates in two different ways from values that include fractions and mixed numbers.
Subject(s): Mathematics
Grade Level(s): 7
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, ratio, rate, unit rate
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ComputingUnitRates_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 Computing Unit Rates worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student writes ratios that are not unit rates.
Examples of Student Work at this Level
The student:
Writes the ratio using the given values, and then reverses the order to get a second ratio (e.g.,
to
and
to
).
page 1 of 4 Changes the ratio
to
to decimal form, then puts the number one under each part of the gear ratio, forming the ratios
and
.
Questions Eliciting Thinking
What is a ratio? What two quantities are being compared in this problem? How are they being compared?
Do you know what a unit rate is?
What do you think the ratio
to
How would you interpret the ratio
means in the context of this problem?
? (Ask only if the student wrote such a ratio.)
Instructional Implications
Review the concept of ratio and point out that the associated quantities in ratios may or may not contain the same units of measure. 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 rates and
unit rates. Model how to determine unit rates from given rates. Be sure the student understands the concept of unit rate and is not hindered by his or her ability to
perform operations with fractions and mixed numbers.
Consider implementing CPALMS lesson plan It’s Carnival Time! (Resource 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 tasks Unit Rate Area (7.RP.1.1) and Unit Rate Length (7.RP.1.1).
Moving Forward
Misconception/Error
The student is unable to determine the second unit rate.
Examples of Student Work at this Level
The student correctly writes 3 to 1 for the first unit rate, but:
Reverses it and writes 1 to 3 for the second unit rate.
Cannot determine the second unit rate.
Questions Eliciting Thinking
Can you tell me what the rate 3:1 means? Can you rewrite this rate so that it tells us how many times the larger gear will turn for each one turn of the smaller gear?
Do ratios and rates have to contain only whole numbers?
Instructional Implications
Clarify the definition of unit rate 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. 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 tasks Explaining Rates (6.RP.1.2) and Unit Rate Length (7.RP.1.1).
Almost There
Misconception/Error
The student is unable to correctly interpret the unit rates in the context of the problem.
page 2 of 4 Examples of Student Work at this Level
The student:
Explains the procedure used for calculating the unit rates rather than interpreting them in the context of the problem.
Does not use ratio language when interpreting the rates and says, “The smaller gear turns three times and the larger gear turns one time.”
Questions Eliciting Thinking
What does 3:1 mean in the context of this problem?
How are the gears related? What does 3:1 mean about the relationship between how the gears turn?
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”) when interpreting unit rates
or describing their meaning. Have the student practice writing descriptions of rates using rate and unit rate language.
When the student is ready, consider editing the worksheet to include different rational values and then implement the task again.
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 both unit rates correctly: 3 to 1 and
to 1 or 0.3333… to 1 and
Explains that the smaller gear turns three times for each one turn of the larger gear and the larger gear turns
time for each one turn of the smaller gear.
Questions Eliciting Thinking
How did you determine the unit rates?
If a student said the unit rates are 3:1 and 1:3, what did that student do wrong? Why?
Why does the second part of the ratio have to be one?
Instructional Implications
Have the student use the unit rate to solve problems (e.g., “How many times will the smaller gear rotate when the larger gear rotates four and a half times?” or “How many
times will the larger gear rotate when the smaller gear rotates four and a half times?”).
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.
Challenge the student with the following problem: If Gear A turns n times for every one turn of Gear B, then how many times (in terms of n) will Gear B turn for every one
turn of Gear A?
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Computing 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
page 3 of 4 complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
page 4 of 4